JEE Advanced 2024 Paper 1, Chemistry Section 3 Q1: Enthalpies for Different Types of Reaction

JEE Advanced2024Paper 1Chemistry Section 3

Consider the following volume $-$ temperature ( $V - T$ ) diagram for the expansion of $5$ moles of an ideal monoatomic gas.

Considering only $P$ - $V$ work is involved, the total change in enthalpy (in Joule) for the transformation of state in the sequence $X \to Y \to Z$ is ______.

[Use the given data: Molar heat capacity of the gas for the given temperature range, $C_{V, m} = 12$ J K $^{- 1}$ mol $^{- 1}$ and gas constant, $R = 8.3$ J K $^{- 1}$ mol $^{- 1}$ ]

Your answer

Solution

The path has two legs: X $\to$ Y is isothermal (constant $T$ ) and Y $\to$ Z is isochoric (constant $V$ ).

Leg X $\to$ Y (isothermal, $T$ constant): For an ideal gas $Δ H$ depends only on temperature, so $Δ H_{X Y} = 0$ .

Leg Y $\to$ Z (isochoric, $T$ : 335 K $\to$ 415 K, $Δ T = 80$ K):

$Δ U_{Y Z} = n C_{V, m} Δ T = 5 \times 12 \times 80 = 4800$ J.

$Δ H_{Y Z} = Δ U_{Y Z} + Δ (P V) = Δ U_{Y Z} + n R Δ T = 4800 + 5 \times 8.3 \times 80 = 4800 + 3320 = 8120$ J.

Total $Δ H_{X Y Z} = 0 + 8120 = 8120$ J.

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JEE Advanced 2024 Paper 1, Chemistry Section 3 Q1: Enthalpies for Different Types of Reaction

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