Question

For a given reaction, $\Delta$H = 35.5kJmol$^{-1}$ and $\Delta$S = 83.6JK$^{-1}$mol$^{-1}$. The reaction is spontaneous at (Assume that $\Delta$H and $\Delta$S do not vary with temperature.)

• A. T > 425 K
• B. All temperature
• C. T < 298 K
• D. T < 425 K

Answer 1

Answer: (A)

T > 425 K

Answer 2

The spontaneity of a reaction is determined by the Gibbs Free Energy change ($\Delta$G), given by the equation $\Delta$G = $\Delta$H - T$\Delta$S. A reaction is spontaneous when $\Delta$G < 0. Given $\Delta$H = 35.5 kJmol$^{-1}$ = 35500 Jmol$^{-1}$ and $\Delta$S = 83.6 JK$^{-1}$mol$^{-1}$. For spontaneity, $\Delta$H - T$\Delta$S < 0, which implies $\Delta$H < T$\Delta$S. Rearranging for temperature, T > $\frac{\Delta H}{\Delta S}$. Substituting the given values: T > $\frac{35500 \text{ Jmol}^{-1}}{83.6 \text{ JK}^{-1}\text{mol}^{-1}}$ = 424.64 K. Therefore, the reaction is spontaneous at temperatures greater than 424.64 K. Among the given options, "T > 425 K" is the condition that guarantees spontaneity.