36 g of liquid water at its boiling point (373 K, 1 atm) is converted completely to steam at the same temperature and pressure. Given Delta_vapH=40.7 kJ mol^-1 and R=8.314 J mol^-1K^-1, treat steam as ideal and neglect the liquid volume. Find Delta U in kJ (one decimal).

JEE Main levelNumerical answerDifficulty 2 of 3td127

$36 g$ of liquid water at its boiling point ( $373 K$ , $1 atm$ ) is converted completely to steam at the same temperature and pressure. Given $Δ_{v a p} H = 40.7 kJ mo l^{- 1}$ and $R = 8.314 J mo l^{- 1} K^{- 1}$ , treat steam as ideal and neglect the liquid volume. Find $Δ U$ in $kJ$ (one decimal).

Numerical answer type, answer in kJ, tolerance 0.1.

n = 36/18 = 2 mol

and

Δ H = 2 \times 40.7 = 81.4 kJ

Δ U = Δ H - Δ n_{g} RT

with

Δ n_{g} = 2

2 \times 8.314 \times 373 = 6.20 kJ

Δ U = 81.4 - 6.20 = 75.2 kJ