Question

Which of the following statements (s) is/are false?

• A. All adiabatic processes are isoentropic (or isentropic) processes
• B. When $(\Delta G_{system}{)}_{T.P}<0;$ the reaction must be exothermic
• C. One mole of an ideal gas at $300K$ is expanded isothermally from an initial volume of one litre to $10$ litres. The $\Delta E$ for the process is $0$, where $E$ is internal energy
• D. The heat of vaporisation of water at ${100}^{\circ }C$ is $40.6kJ/mol$. When $9g$ of water vapour condenses to liquid at ${100}^{\circ }C$ of $1atm$, then $\Delta S_{system}=54.427J/K$

Answer 1

Answer: (A), (B)

When $(\Delta G_{system}{)}_{T.P}<0;$ the reaction must be exothermic

(a) An isentropic process is a thermodynamic process that is both adiabatic and reversible. Hence, all adiabatic processes are not isoentropic (or isentropic) processes.
(b) For $\Delta G<0$, the reaction can be endothermic or exothermic.
As we know,
$\Delta G=\Delta H-T\Delta S$
For $\Delta G<0$ at constant temperature and pressure
$\Delta H<T\Delta S$
Hence, reaction can be both exothermic and endothermic.
(c) If the gas is ideal, its expansion at constant temperature is called isothermal expansion and it will be accompained by no change in internal energy. Hence, $\Delta E=0$.
(d) Given,
$\text{Mass of}{H}_{2}O=9gm$
$\text{Number of moles of}{H}_{2}O=\frac{9}{18}=0.5mol$
$\text{Heat of vaporisation of system}=40.6\times {10}^{3}J/mol$
$\Delta S_{system}=\frac{40.6\times {10}^3\times 0.5}{373}J/K$
$=20.3\times 2.68$
$=54.42J/K$