Question

Which of the following statement (s) is / are correct?

• A. For adiabatic expansion of an ideal gas, $T{V}^{\gamma -1}$ = constant
• B. Work done in reversible isothermal expansion is greater than that done in reversible adiabatic expansion for the same increase of volume
• C. Buffer capacity is maximum when concentration of weak acid and salt of its conjugate base is equal
• D. Equilibrium constant of an exothermic reaction decreases with increase of temperature generally

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A For adiabatic expansion of an ideal gas, $T{V}^{\gamma -1}$ = constant
B Work done in reversible isothermal expansion is greater than that done in reversible adiabatic expansion for the same increase of volume
C Buffer capacity is maximum when concentration of weak acid and salt of its conjugate base is equal
D Equilibrium constant of an exothermic reaction decreases with increase of temperature generally

A) We know that for an adiabatic expansion $T{V}^{\gamma -1}=$ constant
B) The isothermal expansion process uses the heat transferred from the surroundings to do its work, whereas for the adiabatic expansion $q=0$ and the process uses the system's internal energy to perform its work. So, the work done in reversible isothermal expansion is greater than that done in reversible adiabatic expansion for the same increase of volume. We can also figure this out from the following graph.

C) Buffer capacity $\left(\beta \right)$ is defined as the moles of an acid or base necessary to change the $pH$ of a solution by $1$.
From the Henderson - hasselbalch equation, we know that
$pH=p{K}_a+{\log }_{10}\left(\frac{\left[base\right]}{\left[Acid\right]}\right)$.
Extrapolating further from this, a buffer is most effective when $pH$ equals the $p{K}_a$. So, $log\frac{\left[base\right]}{\left[Acid\right]}$ equals $0$, then the concentrations of acid and conjugate base are approximately equal.
D) According to Le-Chatelier's principle, In exothermic reaction the equilibrium shifts towards the left when the temperature increases, i.e. less product is formed. So, the equilibrium constant decreases.