Five moles of an ideal gas at 293K is expanded isothermally from an...

$n = 5, T = 293K = const, \Delta U = 0$

${P}_{1} = 2 . 1MPa, {P}_{2} = 1 . 3MPa$

${P}_{ext} = 4 . 3MPa = const .$

$W = - {P}_{ext}\left({V}_{2} - {V}_{1}\right) = - {P}_{ext}\left(\dfrac{nRT}{{P}_{2}} - \dfrac{nRT}{{P}_{1}}\right)$

or, $W = - {P}_{ext}nRT\left(\dfrac{1}{{P}_{2}} - \dfrac{1}{{P}_{1}}\right)$

$= - 4 . 3 \times 5 \times 8 . 314 \times 293\left(\dfrac{1}{1 . 3} - \dfrac{1}{2 . 1}\right)$

$= - 4 . 3 \times 5 \times 8 . 314 \times 293\left(\dfrac{2 . 1 - 1 . 3}{1 . 3 \times 2 . 1}\right)$

$= - 15347 . 7J$

or, $W = - 15 . 35kJ$

$\Delta{U}^{0} = q + W$

$∴ q = - W$

or, $q = 15 . 35kJ$ (for $5$ moles)

$∴ q / mole = \dfrac{15 . 35}{5} = 3kJ{mol}^{- 1}$