Water and Its Properties

Q: Why is the density of water maximum at 277 K?

Warming ice past 273 K breaks some hydrogen bonds, the open cage collapses and the molecules pack closer, so the density rises. Above 277 K the increasing kinetic energy pushes the molecules apart faster than the cage collapses, so the density falls again.

Q: What is heavy water and how is it prepared?

Heavy water is deuterium oxide, D₂O. It is prepared by the prolonged electrolysis of alkaline water in five stages, because ordinary water is electrolysed faster and the residue grows richer in D₂O, or by fractional distillation using a very long column.

ChemistryHydrogenFor JEE aspirants

Water is the hydride of oxygen, $H_{2} O$ , and almost every one of the properties of water comes from two facts: the molecule is bent, and it forms hydrogen bonds. That is why water boils far above the other hydrides of its group, why ice floats and why water dissolves so much. This page covers the structure and properties of water, ice, heavy water, and hard water with the methods used to soften it. The topic is in the JEE Advanced syllabus; JEE Main and NEET have dropped it.

On this page1Structure2Hydrogen bonds, ice3Properties4Chemistry5Heavy water6Hardness7Softening8Examples

Key Formulas - Quick Reference

★ Must learn Water is bent, with oxygen $s p^{3}$ hybridised: two bond pairs and two lone pairs, bond angle $104. 5^{\circ}$ and dipole moment $1.84 D$ .
★ Must learn In ice each oxygen is joined tetrahedrally to four others: two by covalent bonds of $100 pm$ and two by hydrogen bonds of $176 pm$ .
★ Must learn Density is greatest at $277 K$ ( $1.000 g cm^{- 3}$ ), not at the freezing point. Ice is only $0.917 g cm^{- 3}$ , so it floats.
Melting point $273.2 K$ , boiling point $373.2 K$ , specific heat $4.177 J g^{- 1} K^{- 1}$ , dielectric constant $78.39$ .
Self-ionisation: $2 H_{2} O$ gives $H_{3} O^{+} + O H^{-}$ , with $K_{w} = 1 \times 1 0^{- 14}$ at $298 K$ , so pure water has $pH = 7$ .
Water is amphoteric: it is a base towards $HCl$ and an acid towards $N H_{3}$ .
Heavy water is $D_{2} O$ : molar mass $20.028$ , melting point $276.8 K$ , boiling point $374.4 K$ , density $1.104 g cm^{- 3}$ .
★ Must learn Temporary hardness comes from $Ca (HC O_{3})_{2}$ and $Mg (HC O_{3})_{2}$ and is removed by boiling or by Clark's method.
★ Must learn Permanent hardness comes from chlorides and sulphates of $Ca$ and $Mg$ and needs washing soda, calgon or ion exchange.
Degree of hardness is the mass of $CaC O_{3}$ equivalent to the calcium and magnesium salts in one million parts of water, expressed in ppm.

1. Water: Where It Is and Why It Matters

Water is the most abundant and most easily obtained of all chemical compounds. It is the principal constituent of the earth's surface, a significant component of every animal and vegetable body, and it plays a vital role in our existence. It makes up about $65%$ of the human body and about $95%$ of some plants.

The supply, however, is very unevenly spread. Deserts have no permanent surface water, while the oceans cover roughly $71%$ of the earth's surface and hold about $97%$ of all the water there is. Of the total, only about $2.7%$ is fresh water, and most of that is locked in polar ice caps and glaciers or lies deep underground, out of reach.

Water is the hydride of oxygen, $H_{2} O$ . Its unusual behaviour comes from two things and two things only: the molecule is bent, so it has a permanent dipole, and it forms hydrogen bonds. Every property on this page follows from those two facts.

2. Structure of the Water Molecule

In the water molecule the two hydrogen atoms are bonded to oxygen by two covalent bonds. The oxygen atom is $s p^{3}$ hybridised, and each bond is formed by the axial overlap of the $1 s$ orbital of a hydrogen atom with an $s p^{3}$ orbital of oxygen.

Oxygen is left with two bond pairs and two lone pairs, four electron pairs in all, so the electrons around it take up a tetrahedral arrangement. Only the two bonded atoms are visible, so the molecule has a bent shape. Lone pairs repel more strongly than bond pairs, and they squeeze the angle down from the regular tetrahedral value of $109. 5^{\circ}$ ( $10 9^{\circ} 2 8^{'}$ ) to $104. 5^{\circ}$ .

Figure 1: Four electron pairs around oxygen point tetrahedrally, but the two lone pairs squeeze the bond angle from

109. 5^{\circ}

down to

104. 5^{\circ}

Because the molecule is bent, the two bond moments do not cancel. Water therefore behaves as a permanent electrical dipole, and its measured dipole moment is $1.84 D$ , which confirms the polar nature directly. A linear molecule would have had zero dipole moment.

Exam Trick

If the bond angle question ever confuses you, count lone pairs. Methane has none and keeps $109. 5^{\circ}$ ; ammonia has one and drops to $10 7^{\circ}$ ; water has two and drops further to $104. 5^{\circ}$ . More lone pairs, smaller angle.

3. Hydrogen Bonding, Ice and the Density Anomaly

3.1 Association in the liquid

In the gaseous state water exists as individual $H_{2} O$ molecules. In the liquid state large aggregates form, because each molecule links to its neighbours through intermolecular hydrogen bonds. How far this association goes depends on temperature and pressure: heating breaks the bonds, cooling builds them.

This association, and nothing else, is responsible for the abnormally high freezing point, boiling point, heat of fusion and heat of vaporisation of water compared with the hydrides of the other elements of the oxygen family.

3.2 The structure of ice

In ice every $H_{2} O$ molecule is surrounded tetrahedrally by four others, with their oxygen atoms at the corners of a tetrahedron. Four hydrogen atoms surround each oxygen: two of them are held by covalent bonds at $100 pm$ , and the other two by longer hydrogen bonds at $176 pm$ .

Figure 2: Every oxygen atom in ice is surrounded tetrahedrally by four others. The long hydrogen bonds hold the molecules apart, leaving empty space.

The result is a highly ordered three-dimensional structure with large vacant spaces, best described as an open cage. Because of the cage, a given mass of ice occupies a larger volume than the same mass of liquid water, so ice is less dense and floats on water.

3.3 Why water is densest at 277 K

As ice is warmed past $273 K$ , some hydrogen bonds break. The cage-like structure begins to collapse, molecules move closer together, the volume falls and the density therefore rises. This continues up to $277 K$ , where the density reaches its maximum.

Beyond $277 K$ two effects compete. More hydrogen bonds keep breaking, which would raise the density, but the kinetic energy of the molecules is now increasing fast enough to push them apart. The second effect wins, so above $277 K$ the density falls steadily, although it stays higher than that of ice.

Figure 3: Water is densest at

277 K

, not at its freezing point. Below that temperature it expands again, which is why lakes freeze from the top.

Why this matters: when a lake cools in winter, the coldest water is no longer the heaviest, so it stays on top and freezes there. The ice sheet then insulates the water below, which remains liquid at about $277 K$ . Fish and other aquatic animals survive the winter because of this one anomaly.

Many crystalline forms of ice, more than a dozen, are known at different pressures, each with its own melting point. At one bar pressure ice has the normal hexagonal form; at low temperature it adopts a cubic form.

Ice at

273 K

every molecule has four hydrogen bonds
rigid tetrahedral open cage
density

0.917 g cm^{- 3}

floats on water

Water at

277 K

some hydrogen bonds broken
cage partly collapsed
density

1.000 g cm^{- 3}

, the maximum
sinks to the bottom of a lake

Key idea

Hydrogen bonds hold ice in an open cage, so ice is lighter than water; melting collapses the cage and water is densest at

277 K

Quick Recall: tap to check

What is the bond angle of water, and why is it not

109. 5^{\circ}

104. 5^{\circ}

: two lone pairs on the

s p^{3}

oxygen repel the bond pairs more strongly.

How long are the covalent and hydrogen bonds around each oxygen in ice?

100 pm

covalent,

176 pm

hydrogen bonds.

At what temperature is water densest?

277 K

(

4^{\circ} C

4. Physical Properties of Water

Property	Value
Molecular mass	$18.015$
Melting point	$273.2 K$
Boiling point	$373.2 K$
Temperature of maximum density	$277.1 K$
Maximum density	$1.000 g cm^{- 3}$
Density at $298 K$	$0.997 g cm^{- 3}$
Heat of vaporisation at $373 K$	$40.66 kJ mol^{- 1}$
Heat of fusion	$6.01 kJ mol^{- 1}$
Specific heat	$4.177 J g^{- 1} K^{- 1}$
Ionic product $K_{w}$ at $298 K$	$1.008 \times 1 0^{- 14} mol^{2} L^{- 2}$
Enthalpy of formation	$- 285.9 kJ mol^{- 1}$
Dielectric constant	$78.39$

4.1 Three consequences worth knowing

Abnormally high melting point, boiling point and heats of fusion and vaporisation compared with $H_{2} S$ , $H_{2} Se$ and $H_{2} Te$ , the other hydrides of group 16. Those molecules have no intermolecular hydrogen bonding; water does.

Figure 4: Follow the trend from

H_{2} Te

down to

H_{2} S

and water should boil near

190 K

. It boils at

373 K

, and hydrogen bonding is the reason.

High specific heat, thermal conductivity and surface tension. Water therefore moderates the climate and keeps the body temperature of living organisms steady: it takes a great deal of heat to warm it, and it gives that heat back slowly.
A very high dielectric constant, $78.39$ . This lets water dissolve most ionic compounds, which is why it is called the universal solvent. Ionic solids dissolve by ion-dipole interaction, that is by solvation of the ions, while covalent compounds such as alcohols, amines, urea, glucose and sugar dissolve because they can form hydrogen bonds with water.

5. Chemical Properties of Water

5.1 Action towards litmus

Pure water is neutral to litmus.

5.2 Thermal stability

Water is remarkably stable. Even at $1500 K$ only about $0.02%$ of it has broken up into its elements.

2 H_{2} O 1500 K 2 H_{2} + O_{2}

5.3 Self-ionisation

The small but measurable conductivity of pure water shows that a few molecules transfer a proton to one another, giving the hydronium ion and the hydroxide ion.

2 H_{2} O ⇌ H_{3} O^{+} + O H^{-}

The ionic product is $K_{w} = 1 \times 1 0^{- 14}$ at $298 K$ , so pure water at $298 K$ has $pH = 7$ and is neutral.

JEE Advanced

Neutral does not always mean pH 7. Self-ionisation breaks bonds, so it is endothermic and $K_{w}$ rises with temperature: $p K_{w}$ is $14.94$ at $273 K$ , $14.00$ at $298 K$ and $12.26$ at $373 K$ . Pure water always has $[H^{+}] = [O H^{-}] = K_{w}$ , so its pH is $\frac{1}{2} p K_{w}$ : $7.47$ in ice-cold water and $6.13$ in boiling water. Boiling water with pH 6.13 is still neutral, not acidic.

Figure 5: Pure water has

pH = 7

only at

298 K

. At

373 K

p K_{w} = 12.26

and neutral water has

pH = 6.13

; it is still neutral because

[H^{+}] = [O H^{-}]

5.4 Amphoteric behaviour

Water can act as an acid or as a base, depending on what it meets.

H_{2} O + N H_{3} ⇌ N H_{4}^{+} + O H^{-}

HCl + H_{2} O ⇌ H_{3} O^{+} + C l^{-}

In the first reaction water gives a proton away, so it is the acid. In the second it accepts one, so it is the base. A substance that can do both is called amphoteric.

5.5 Hydrolytic reactions

Water breaks up many non-metallic oxides, halides, phosphides, carbides and nitrides.

C a_{3} P_{2} + 6 H_{2} O 3Ca (OH)_{2} + 2P H_{3}

CaNCN + 3 H_{2} O CaC O_{3} + 2N H_{3}

Ca + 2 H_{2} O Ca (OH)_{2} + H_{2}

S O_{2} + H_{2} O H_{2} S O_{3}

The products are phosphine from calcium phosphide, ammonia from calcium cyanamide, and sulphurous acid from sulphur dioxide.

6. Heavy Water

Heavy water is the oxide of heavy hydrogen, written $D_{2} O$ or $_{1}^{2} H_{2} O$ , and also called deuterium oxide. The credit for its discovery goes to Urey, who first showed that ordinary water contains about one part of heavy water in $6000$ . Lewis and Donald isolated a few millilitres of it in $1933$ by the prolonged electrolysis of alkaline water.

6.1 Preparation by prolonged electrolysis

The source of heavy water is ordinary water. Because the $O - D$ bond is harder to break than the $O - H$ bond, ordinary water is electrolysed faster, and the residue left behind becomes richer in $D_{2} O$ at every stage. The industrial cell was designed by Brown, Daggett and Urey: a cylindrical steel vessel that acts as the cathode, with a perforated cylindrical sheet as the anode.

Figure 6: Ordinary water is electrolysed faster than heavy water, so each stage leaves a residue richer in

D_{2} O

than the one before.

In the first stage thirty cells are used, each filled with about $3%$ sodium hydroxide solution and run for about $72$ hours at $110$ volts. The volume falls to about one sixth, and the residue contains about $2.5%$ heavy water. The gases given off are burnt, and the water formed is returned to the previous stage, so nothing is wasted. The fifth stage is not electrolysis at all: the $99%$ heavy water is distilled to remove the alkali and other impurities.

6.2 Preparation by fractional distillation

Ordinary water boils at $373.2 K$ and heavy water at $374.4 K$ . The difference is small, so a very long fractionating column, about $13 m$ , is needed and the process is repeated many times. The lighter fraction, $H_{2} O$ , distils over first, and the residue becomes richer in $D_{2} O$ .

6.3 Physical properties

Heavy water is a colourless, tasteless and odourless liquid. Every physical constant is higher than the corresponding value for ordinary water, because the molecule is about $11%$ heavier.

Property	$H_{2} O$	$D_{2} O$
Molecular mass	$18.015$	$20.028$
Melting point	$273.2 K$	$276.8 K$
Boiling point	$373.2 K$	$374.4 K$
Temperature of maximum density	$277.1 K$	$284.2 K$
Maximum density	$1.000$	$1.106$
Density ( $g cm^{- 3}$ )	$0.997$	$1.104$
Heat of vaporisation ( $kJ mol^{- 1}$ )	$40.66$	$41.61$
Heat of fusion ( $kJ mol^{- 1}$ )	$6.01$	$6.28$
Ionic product	$1.008 \times 1 0^{- 14}$	$1.95 \times 1 0^{- 15}$
Enthalpy of formation ( $kJ mol^{- 1}$ )	$- 285.9$	$- 294.6$

Figure 7: Heavy water beats ordinary water on every constant. The biggest shift is the temperature of maximum density,

7.1 K

higher; the boiling points differ by only

1.2 K

, which is why distillation needs a very long column.

6.4 Chemical properties

Heavy water is chemically similar to ordinary water, but every reaction is slower, because the heavier deuterium atom makes its bonds harder to break.

With metals. Alkali and alkaline earth metals give heavy hydrogen, $D_{2}$ .
$2Na + 2 D_{2} O 2NaOD + D_{2}$
$Ca + 2 D_{2} O Ca (OD)_{2} + D_{2}$
$3Fe + 4 D_{2} O heat F e_{3} O_{4} + 4 D_{2}$

The products are sodium deuteroxide and calcium deuteroxide.
With metal oxides. The corresponding deutoxides are formed.
$N a_{2} O + D_{2} O 2NaOD$
$CaO + D_{2} O Ca (OD)_{2}$
With non-metallic oxides. The corresponding deutero acids are formed.
$N_{2} O_{5} + D_{2} O 2DN O_{3}$
$S O_{3} + D_{2} O D_{2} S O_{4}$
$P_{2} O_{5} + 3 D_{2} O 2 D_{3} P O_{4}$
With carbides, nitrides, phosphides and arsenides.
$Ca C_{2} + 2 D_{2} O Ca (OD)_{2} + C_{2} D_{2}$
$A l_{4} C_{3} + 12 D_{2} O 4Al (OD)_{3} + 3C D_{4}$
$M g_{3} N_{2} + 6 D_{2} O 3Mg (OD)_{2} + 2N D_{3}$
$C a_{3} P_{2} + 6 D_{2} O 3Ca (OD)_{2} + 2P D_{3}$
$N a_{3} As + 3 D_{2} O 3NaOD + As D_{3}$

The products are deuteroacetylene, deuteromethane, trideuterated ammonia, deuterophosphine and deuteroarsine.
Electrolysis. Heavy water containing a little $N a_{2} C O_{3}$ gives heavy hydrogen at the cathode.
$2 D_{2} O electrolysis 2 D_{2} + O_{2}$
Exchange reactions. Compounds carrying a mobile hydrogen atom exchange it for deuterium, partly or completely.
$NaOH + D_{2} O ⇌ NaOD + HDO$
$HCl + D_{2} O ⇌ DCl + HDO$
$N H_{4} Cl + 4 D_{2} O ⇌ N D_{4} Cl + 4HDO$
Deutero hydrates. Heavy water, like ordinary water, can be held as water of crystallisation, giving salts such as $N a_{2} S O_{4} \cdot 10 D_{2} O$ and $CuS O_{4} \cdot 5 D_{2} O$ .
Deuterolysis. The hydrolysis of a salt by heavy water is called deuterolysis.
$AlC l_{3} + 3 D_{2} O Al (OD)_{3} + 3DCl$
$BaS + 2 D_{2} O Ba (OD)_{2} + D_{2} S$

6.5 Biological effects and uses

Heavy water retards the growth of plants and animals. Tobacco will not grow in it, and pure heavy water kills small fishes, tadpoles and mice. In small quantity, however, it acts as a tonic and stimulates the growth of some plants, and certain moulds grow better in heavy water than in ordinary water.

As a neutron moderator. Fission of uranium-235 is brought about by slow neutrons. Substances that slow neutrons down are called moderators, and heavy water is the standard moderator in nuclear reactors.
For preparing deuterium. Electrolysis of heavy water gives $D_{2}$ directly.
As a tracer compound. Heavy water labels a particular hydrogen atom, so chemists can follow reaction mechanisms with it. It has been used to find the number of ionisable hydrogen atoms in oxyacids of phosphorus such as $H_{3} P O_{2}$ and $H_{3} P O_{3}$ .

In India heavy water is made by the Heavy Water Board. The first plant was set up at Nangal in Punjab in 1962. The present plants, at Kota, Manuguru, Baroda, Hazira, Thal and Tuticorin among others, use chemical exchange (hydrogen sulphide with water, or ammonia with hydrogen) instead of electrolysis, because it needs far less energy.

Key idea

Heavy water is

D_{2} O

: the same chemistry as water, but every constant is a little higher and every reaction a little slower, which is how prolonged electrolysis concentrates it.

Quick Recall: tap to check

Which is electrolysed faster,

H_{2} O

D_{2} O

H_{2} O

; the

O - D

bond is harder to break, so the residue becomes richer in

D_{2} O

What does

Ca C_{2}

give with heavy water?

Dideuteroacetylene,

C_{2} D_{2}

, and

Ca (OD)_{2}

Why is heavy water used in nuclear reactors?

It is a moderator: it slows fast neutrons so that they can cause fission of uranium-235.

7. Hard and Soft Water

Water is classified by how it behaves towards soap.

Soft water lathers readily with soap. Distilled water and rain water are the common examples.
Hard water does not lather easily. Sea water and most tap water are hard.

7.1 What causes hardness

Hardness is caused by dissolved bicarbonates, chlorides and sulphates of calcium and magnesium, picked up as the water passes through the ground and the rocks. Soap is a mixture of the sodium salts of higher fatty acids such as stearic, palmitic and oleic acid. The $C a^{2 +}$ and $M g^{2 +}$ ions present react with it and throw down an insoluble precipitate.

M^{2 +} + 2 C_{17} H_{35} COONa (C_{17} H_{35} COO)_{2} M + 2N a^{+}

Here M is calcium or magnesium, and the precipitate is the metal stearate. No lather appears until every calcium and magnesium ion has been precipitated, so hard water wastes a great deal of soap and is not fit for washing.

7.2 The two types of hardness

Figure 8: Which method works depends on which salt caused the hardness. Boiling only breaks up bicarbonates.

	Temporary hardness	Permanent hardness
Also called	carbonate hardness	non-carbonate hardness
Caused by	soluble bicarbonates of $Ca$ and $Mg$	chlorides and sulphates of $Ca$ and $Mg$
How it got there	carbonates dissolving in water that holds dissolved $C O_{2}$	the salts themselves dissolving
Removed by boiling	yes	no

7.3 Removing temporary hardness

(a) Boiling. The water is boiled for about fifteen minutes. Calcium bicarbonate gives insoluble calcium carbonate. Magnesium bicarbonate gives magnesium hydroxide instead, because $Mg (OH)_{2}$ is far less soluble than $MgC O_{3}$ . The precipitates settle out and are removed by filtration or decantation.

Ca (HC O_{3})_{2} heat CaC O_{3} + H_{2} O + C O_{2}

Mg (HC O_{3})_{2} heat Mg (OH)_{2} + 2C O_{2}

(b) Clark's method. A calculated quantity of lime water, that is calcium hydroxide, is added. The soluble bicarbonates are converted into insoluble carbonates, which settle and are filtered off. The quantity has to be calculated: excess lime would itself make the water hard again.

Ca (HC O_{3})_{2} + Ca (OH)_{2} 2CaC O_{3} + 2 H_{2} O

Mg (HC O_{3})_{2} + 2Ca (OH)_{2} 2CaC O_{3} + Mg (OH)_{2} + 2 H_{2} O

Each magnesium bicarbonate uses two moles of lime, because magnesium also comes down as the hydroxide.

Exam Trick

B for Bicarbonate, B for Boiling: only bicarbonate hardness goes when water is boiled. And magnesium always ends as the hydroxide: boiling gives $Mg (OH)_{2}$ , and Clark's method needs two moles of lime for each $Mg (HC O_{3})_{2}$ but only one for each $Ca (HC O_{3})_{2}$ .

7.4 Removing permanent hardness

(a) Washing soda. A calculated amount of sodium carbonate, $N a_{2} C O_{3} \cdot 10 H_{2} O$ , precipitates the offending ions as their carbonates.

M^{2 +} + C O_{3}^{2 -} MC O_{3}

(b) The calgon process. Sodium hexametaphosphate, $N a_{2} [N a_{4} (P O_{3})_{6}]$ , sold as calgon (the name means "calcium gone"), does not precipitate the ions at all. It locks them into a soluble complex instead.

2C a^{2 +} + N a_{2} [N a_{4} (P O_{3})_{6}] N a_{2} [C a_{2} (P O_{3})_{6}] + 4N a^{+}

The calcium and magnesium stay dissolved but are now tied up in a stable complex, so they cannot reach the soap. This is called sequestration.

Washing soda

N a_{2} C O_{3} \cdot 10 H_{2} O

precipitates

CaC O_{3}

MgC O_{3}

sludge must be removed
water gains

N a^{+}

Calgon

N a_{6} P_{6} O_{18}

no precipitate at all

C a^{2 +}

held in a soluble complex
ions stay, but cannot reach soap

(c) The permutit or zeolite process. Permutit is an artificial hydrated sodium aluminium silicate, $N a_{2} A l_{2} S i_{2} O_{8} \cdot x H_{2} O$ , made by fusing soda ash, sand and alumina. Hard water fed in at the top of a tank exchanges its calcium and magnesium ions for sodium ions as it passes down through the permutit bed.

N a_{2} Z + M^{2 +} MZ + 2N a^{+}

Here Z stands for the aluminosilicate framework. When the bed is exhausted it is regenerated by percolating about $10%$ sodium chloride solution through it, which drives the exchange the other way.

MZ + 2NaCl N a_{2} Z + MC l_{2}

(d) Organic ion exchangers: demineralised water. These are giant organic molecules carrying acidic groups such as $- S O_{3} H$ or $- COOH$ , which exchange $H^{+}$ , or basic groups such as $- OH$ or $- N H_{2}$ , which exchange $O H^{-}$ . Hard water is passed first through a bed of cation exchange resin:

C a^{2 +} + 2H - resin Ca (resin)_{2} + 2 H^{+}

and then through a bed of anion exchange resin, which removes the anions:

C l^{-} + OH - resin Cl - resin + O H^{-}

The $H^{+}$ ions produced in the first tank and the $O H^{-}$ ions produced in the second simply combine to give water.

H^{+} + O H^{-} H_{2} O

The water that comes out is free of all cations and anions, not merely of calcium and magnesium. It is called deionised or demineralised water, and this is how laboratory-grade water is made. The resins are regenerated with dilute hydrochloric or sulphuric acid and with sodium hydroxide.

Ca (resin)_{2} + 2HCl CaC l_{2} + 2H - resin

Figure 9: The cation bed swaps every metal ion for

H^{+}

and the anion bed swaps every anion for

O H^{-}

, so what leaves is pure water: deionised, not just softened.

7.5 Degree of hardness

Degree of hardness is the number of parts by mass of $CaC O_{3}$ , or of any calcium and magnesium salt equivalent to it, present in one million parts of water. It is expressed in parts per million, ppm.

Calcium carbonate is chosen as the reference because its molar mass, $100$ , is convenient and because it is the most insoluble salt that can be precipitated in water treatment. Water up to about $100$ to $150$ ppm is quite usable for cooking, bathing and washing clothes; beyond that it is unsuitable for domestic use.

Key idea

Hardness is

C a^{2 +}

and

M g^{2 +}

. Boiling or lime removes the bicarbonate part; washing soda, calgon and ion exchange deal with chlorides and sulphates; resins remove every ion.

8. Choosing a Softening Method: Flowchart and Mind Map

Which softening method to use depends on the kind of hardness and on how pure the water must be. The flowchart asks those questions in order; the mind map after it puts the whole page on one screen.

Figure 10: Flowchart: the boiling test decides temporary against permanent hardness, and the purity needed decides among the methods for permanent hardness.

Figure 11: Mind map: the whole page on one screen. A bent molecule that hydrogen bonds explains the first four branches; ions dissolved from rock explain the last two.

9. Solved Examples

Solved Example 1

The melting point of most solid substances increases with an increase of pressure acting on them. However, ice melts at a temperature lower than its usual melting point when the pressure is increased. This is because
(A) pressure generates heat
(B) the chemical bonds break under pressure
(C) ice is less dense than water
(D) ice is not a true solid

Solution:

Answer: (C). Ice has an open cage structure, so it occupies more volume than the water it came from. Pressure always pushes a system towards the state of smaller volume, so it favours melting.

For an ordinary solid the liquid is the bulkier phase, so pressure favours the solid and raises the melting point. Water is the exception, so its melting point falls as the pressure rises.

Solved Example 2

Which of the following is formed by the action of water on sodium peroxide?
(A)

H_{2}

(B)

N_{2}

(C)

O_{2}

(D)

C O_{2}

Solution:

Answer: (C). Sodium peroxide reacts with water to give sodium hydroxide and oxygen.

2N a_{2} O_{2} + 2 H_{2} O 4NaOH + O_{2}

The peroxide ion is disproportionating: some of its oxygen is oxidised to $O_{2}$ while the rest is reduced to $O H^{-}$ . No hydrogen is produced, which is the usual wrong guess here.

Solved Example 3

Heavy water is a compound of
(A) hydrogen and the heavier isotope of oxygen
(B) the heavier isotope of hydrogen and the heavier isotope of oxygen
(C) oxygen and the heavier isotope of hydrogen
(D) none of the above

Solution:

Answer: (C). Heavy water is $D_{2} O$ : ordinary oxygen combined with deuterium, the heavier isotope of hydrogen. The oxygen in it is ordinary $^{16} O$ .

Option (B) describes a substance that exists but is not what "heavy water" means, and (A) would be water made with heavy oxygen, which is a different compound again.

Solved Example 4

Calculate the degree of hardness of a sample of hard water which is found to contain

36 mg

MgS O_{4}

per kg of water.

Solution:

The aim is to find the mass of $CaC O_{3}$ equivalent to the $MgS O_{4}$ present in one million parts of water.

One kg of water is $1 0^{6} mg$ , so $1 0^{6}$ parts of water contain $36 mg$ , that is $36$ parts of $MgS O_{4}$ .

One mole of $MgS O_{4}$ ( $120 g$ ) is equivalent to one mole of $CaC O_{3}$ ( $100 g$ ), so:

mass of CaCO_{3} = \frac{100 \times 36}{120} = 30

Answer: the degree of hardness is $30$ ppm, which is well within the usable range for domestic water.

Solved Example 5

A sample of water contains

8.1 mg

Ca (HC O_{3})_{2}

per litre. Find its degree of hardness in ppm, and state which type of hardness it is. (Ca

= 40

, C

= 12

, O

= 16

, H

= 1

)

Solution:

Molar mass of $Ca (HC O_{3})_{2}$ $= 40 + 2 (1 + 12 + 48) = 162 g mol^{- 1}$ . One litre of water is $1 0^{6} mg$ , so the sample contains $8.1$ parts per million of $Ca (HC O_{3})_{2}$ .

ppm of CaCO_{3} = \frac{100 \times 8.1}{162} = 5

Answer: $5$ ppm, and it is temporary hardness, because a bicarbonate causes it. Simply boiling the water would remove it.

Solved Example 6

Why is the bond angle in water

104. 5^{\circ}

and not the regular tetrahedral

109. 5^{\circ}

Solution:

Oxygen in water is $s p^{3}$ hybridised and carries four electron pairs, so the basic arrangement is tetrahedral. But only two of those pairs are bond pairs; the other two are lone pairs.

A lone pair is held by one nucleus only, so it spreads out more than a bond pair, which is pulled in by two nuclei. Lone pair to lone pair repulsion is therefore stronger than bond pair to bond pair repulsion.

Answer: the two lone pairs press down on the two $O - H$ bonds and squeeze them together, reducing the angle from $109. 5^{\circ}$ to $104. 5^{\circ}$ . Ammonia, with one lone pair, lies in between at about $10 7^{\circ}$ .

Solved Example 7

Explain why a lake freezes from the surface downwards, and why fish survive under the ice.

Solution:

As the surface water cools it becomes denser and sinks, and warmer water rises to take its place. This circulation continues only until the whole lake reaches $277 K$ , the temperature of maximum density.

Cooled below $277 K$ the water becomes lighter again, so it stays at the top instead of sinking. That top layer reaches $273 K$ first and freezes, and the ice, being less dense still, floats.

Answer: the ice sheet then acts as an insulating blanket, and the water below stays liquid near $277 K$ . If ice were denser than water it would sink, the lake would freeze solid from the bottom up, and nothing living in it would survive.

Solved Example 8

Distinguish between temporary and permanent hardness, and give one method of removing each.

Solution:

Temporary hardness is caused by the soluble bicarbonates of calcium and magnesium. It is removed by boiling, which converts them to insoluble carbonates, or by Clark's method with a calculated quantity of lime.

Ca (HC O_{3})_{2} heat CaC O_{3} + H_{2} O + C O_{2}

Permanent hardness is caused by the chlorides and sulphates of the same two metals. Boiling has no effect on these, so washing soda, the calgon process or ion exchange must be used.

Answer: the test is the bicarbonate. If boiling removes the hardness it was temporary; if it does not, the hardness was permanent.

Solved Example 9

A water supply contains

16.2 mg L^{- 1}

Ca (HC O_{3})_{2}

and

14.6 mg L^{- 1}

Mg (HC O_{3})_{2}

. What mass of slaked lime,

Ca (OH)_{2}

, is needed to soften

1000 L

by Clark's method? (Ca

= 40

, Mg

= 24

, C

= 12

, O

= 16

, H

= 1

)

Solution:

Molar masses: $Ca (HC O_{3})_{2} = 162$ , $Mg (HC O_{3})_{2} = 146$ , $Ca (OH)_{2} = 74 g mol^{- 1}$ .

n_{Ca (HC O_{3})_{2}} = \frac{16.2 \times 1000}{162} = 100 mmol, n_{Mg (HC O_{3})_{2}} = \frac{14.6 \times 1000}{146} = 100 mmol

Lime needed: $1$ mol for each $Ca (HC O_{3})_{2}$ and $2$ mol for each $Mg (HC O_{3})_{2}$ , so $100 + 2 \times 100 = 300 mmol$ .

m = 0.300 \times 74 = 22.2 g

Answer: $22.2 g$ of $Ca (OH)_{2}$ . Using one mole for the magnesium salt would give $14.8 g$ and leave the water hard.

Solved Example 10

373 K

p K_{w} = 12.26

. Pure water at this temperature has
(A)

pH = 7.00

and is neutral
(B)

pH = 6.13

and is neutral
(C)

pH = 6.13

and is acidic
(D)

pH = 12.26

and is basic

Solution:

Answer: (B). In pure water $[H^{+}] = [O H^{-}]$ , so $pH = \frac{1}{2} p K_{w} = 6.13$ . The water is neutral because the two concentrations are equal; 7 is the neutral point only at $298 K$ .

Practice Questions

Water boils at $100^{\circ} C$ and freezes at $0^{\circ} C$ . Find the reason for it from the following.
(A) Water dissolves anything, however sparingly
(B) Water is a polar molecule
(C) The boiling and freezing temperatures of water were used to define the temperature scale
(D) Liquid water is denser than iceAnswer: (C). Those two numbers are not a property of water at all; the Celsius scale was defined by fixing them at $0$ and $100$ .
Water is oxidised to oxygen by
(A) $Cl O_{2}$ (B) $KMn O_{4}$ (C) $H_{2} O_{2}$ (D) $F_{2}$ Answer: (D). Fluorine is the only substance electronegative enough to take electrons from oxygen in water: $2 F_{2} + 2 H_{2} O$ gives $4HF + O_{2}$ .
The dielectric constant of $D_{2} O$ is
(A) equal to that of water (B) slightly less than that of water (C) slightly more than that of water (D) half that of waterAnswer: (B). It is $78.06$ against $78.39$ for ordinary water, so heavy water is a slightly poorer solvent for ionic compounds.
One of the following statements is incorrect. Point it out.
(A) Permanent hardness can be removed by boiling water
(B) Hardness of water affects soap consumption
(C) Temporary hardness is due to the bicarbonates of $Ca$ and $Mg$
(D) Permanent hardness is due to the soluble sulphates, chlorides and nitrates of $Ca$ and $Mg$ Answer: (A) is incorrect. Boiling removes only temporary hardness; permanent hardness needs washing soda, calgon or ion exchange.
Why must the quantity of lime be calculated carefully in Clark's method?Answer: Excess calcium hydroxide stays dissolved in the water and makes it hard again, so only the calculated amount is added.
A sample of water contains $16.2 mg$ of $Ca (HC O_{3})_{2}$ per litre. Calculate its degree of hardness in ppm.Answer: $10$ ppm, from $\frac{100 \times 16.2}{162}$ .

Common Mistakes to Avoid

Watch out

Saying water is bent because oxygen is $s p^{2}$ hybridised. It is $s p^{3}$ : four electron pairs, two of them lone pairs.
Claiming water is densest at its freezing point. The maximum is at $277 K$ , about four degrees above it.
Confusing the two densities. Ice is $0.917 g cm^{- 3}$ while water at $277 K$ is $1.000 g cm^{- 3}$ , which is why ice floats.
Writing $MgC O_{3}$ as the product of boiling magnesium bicarbonate. Magnesium comes down as $Mg (OH)_{2}$ , and Clark's method needs two moles of lime for it.
Mixing up calgon with washing soda. Washing soda precipitates the ions as carbonates; calgon leaves them in solution, locked inside a complex.
Calling demineralised water the same as softened water. Ion exchange resins remove every cation and anion, not merely $C a^{2 +}$ and $M g^{2 +}$ .
Assuming heavy water is water with heavier oxygen. It is $D_{2} O$ : ordinary oxygen with deuterium.
Expecting heavy water to react at the same rate as ordinary water. Every reaction is slower, because the $O - D$ bond is harder to break.

Frequently Asked Questions

Why does ice float on water?

In ice each oxygen is hydrogen bonded tetrahedrally to four others, giving an open cage with large empty spaces. The same mass therefore takes up more room as ice than as water, so ice has a lower density, about $0.917 g cm^{- 3}$ , and floats.

Why is the density of water maximum at 277 K?

Warming ice past $273 K$ breaks some hydrogen bonds, the open cage collapses and the molecules pack closer, so the density rises. Above $277 K$ the increasing kinetic energy pushes the molecules apart faster than the cage collapses, so the density falls again.

Why does water have an abnormally high boiling point?

Because of intermolecular hydrogen bonding. Following the trend of $H_{2} Te$ , $H_{2} Se$ and $H_{2} S$ , water should boil near $190 K$ . It boils at $373 K$ instead, because breaking the hydrogen bonds between molecules needs a great deal of extra energy.

What is heavy water and how is it prepared?

Heavy water is deuterium oxide, $D_{2} O$ . It is prepared by the prolonged electrolysis of alkaline water in five stages, because ordinary water is electrolysed faster and the residue grows richer in $D_{2} O$ , or by fractional distillation using a very long column.

What is the difference between temporary and permanent hardness?

Temporary hardness is caused by the soluble bicarbonates of calcium and magnesium and disappears on boiling. Permanent hardness is caused by their chlorides and sulphates, which boiling does not touch, so washing soda, the calgon process or ion exchange has to be used.

How does the calgon process soften water?

Calgon is sodium hexametaphosphate. Instead of precipitating the calcium and magnesium ions it ties them up inside a soluble complex, so they stay dissolved but can no longer reach the soap. This locking away of ions is called sequestration.

Is hard water asked in NEET?

Not directly. NMC removed the Hydrogen chapter, which holds water, heavy water and hardness, from the NEET syllabus. Hydrogen bonding in water and the anomalous density of ice still matter for chemical bonding and for biology, where water's high specific heat and solvent power come up often.

Is water and heavy water in the JEE syllabus?

In JEE Advanced, yes: the syllabus lists the physical and chemical properties of water and heavy water under the Hydrogen unit. JEE Main dropped the Hydrogen chapter, although hydrogen bonding and the ionic product of water are still tested there through bonding and equilibrium.

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