JEE Main · 2019 · Shift-IImediumTHERMO-124

The difference between H and U is ( H - U), when the combustion of one mole of heptane (l) is carried out at a…

Thermodynamics · Class 11 · JEE Main Previous Year Question

Question

The difference between $\Delta H$ and $\Delta U$ is ( $\Delta H - \Delta U$ ), when the combustion of one mole of heptane (l) is carried out at a temperature $T$ , is equal to:

Options

a
$-4RT$
✓
b
$3RT$
c
$4RT$
d
$-3RT$

Correct Answera

$-4RT$

Detailed Solution

🧠 $\Delta H - \Delta U = \Delta n_g RT$ — only gaseous species count For heptane combustion, write the balanced equation and count only gas-phase moles.

🗺️ Calculation Balanced: $\ce{C7H16(l) + 11 O2(g) -> 7 CO2(g) + 8 H2O(l)}$

Gas-phase species: 7 mol $\ce{CO2}$ formed, 11 mol $\ce{O2}$ consumed. $\ce{C7H16}$ and $\ce{H2O}$ are liquid — excluded.

$\Delta n_g = 7 - 11 = -4$

$\Delta H - \Delta U = \Delta n_g RT = -4RT$

⚠️ Trap: $\ce{H2O}$ is liquid in this reaction. Including it as gas would change $\Delta n_g$ from $-4$ to $+4$ — the most common wrong answer.

$\boxed{\text{Answer: (a) } -4RT}$

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