Question

For a certain reaction, $\Delta H = -210$ kJ and $\Delta S = -150$ J K$^{-1}$. Find the temperature so that $\Delta G = 0$.

• A. 1100 K
• B. 1200 K
• C. 1400 K
• D. 1300 K

Hint:

Always double-check unit consistency! Enthalpy is almost always given in kilojoules (kJ) while entropy is usually given in joules (J). Failing to convert kJ to J is the most common mistake made in these thermodynamic calculations.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The Gibbs free energy equation is $\Delta G = \Delta H - T\Delta S$. At equilibrium, or when $\Delta G = 0$, we have $T = \Delta H / \Delta S$.

Step 2: Formula Application:
Note the units: $\Delta H = -210$ kJ $= -210,000$ J. $\Delta S = -150$ J K$^{-1}$.

Step 3: Explanation:
$0 = -210,000 - T(-150)$ $150T = 210,000$ $T = \frac{210,000}{150} = \frac{21,000}{15} = 1400$ K.

Step 4: Final Answer:
The temperature is 1400 K.