Consider the reaction: $\mathrm{N}_{2}+3 \mathrm{H}_{2} \longrightarrow 2 \mathrm{NH}_{3}$ carried out at constant temperature and pressure. If $\Delta \mathrm{H}$ and $\Delta \mathrm{U}$ are the enthalpy and internal energy changes for the reaction, which of the following expressions is true?

(C) $\Delta \mathrm{H}<\Delta \mathrm{U}$

(B) $\Delta \mathrm{H}=\Delta \mathrm{U}$

(D) $\Delta \mathrm{H}>\Delta \mathrm{U}$

JEE Main · 2005 · 08 May 2005 · Offline · Chemical Thermodynamics

Consider the reaction:

N_{2} + 3 H_{2} ⟶ 2 NH_{3}

carried out at constant temperature and pressure. If

Δ H

and

Δ U

are the enthalpy and internal energy changes for the reaction, which of the following expressions is true?

Answer: (C)

The link between the two energy changes for a gas reaction is

Δ H = Δ U + Δ n_{g} R T

, where

Δ n_{g}

is the change in the number of gas moles. For

N X_{2} + 3 H X_{2} 2 NH X_{3}

the gas count drops from four moles to two, so

Δ n_{g} = 2 - 4 = - 2

and

Δ H = Δ U - 2 R T

. Since

2 R T

is positive,

Δ H

comes out smaller than

Δ U

, that is

Δ H < Δ U

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option