Question

The specific heat capacity of one mole of water is (R is the universal gas constant):

• A. $3R$
• B. $5R$
• C. $7R$
• D. $9R$

Hint:

Molar heat capacity of liquid water ≈ $75\ \mathrm{J\,mol^{-1}K^{-1}} \approx 9R$.
Do not confuse with ideal gas heat capacities (e.g., $C_V$ or $C_P$ for monatomic/diatomic gases).
Use $R=8.314\ \mathrm{J\,mol^{-1}K^{-1}}$ for numerical checks.

Answer 1

The Correct Option is D

• Specific heat capacity of liquid water (per mole) is approximately $75\ \mathrm{J\,mol^{-1}K^{-1}}$.
• Using $R \approx 8.314\ \mathrm{J\,mol^{-1}K^{-1}}$, $9R \approx 9\times8.314 = 74.826\ \mathrm{J\,mol^{-1}K^{-1}}$, which matches the known molar heat capacity of water.
• Therefore one mole of water has heat capacity approximately $9R$.