Which of the following is closest to the molar heat capacity (at constant pressure) of liquid water?

• A. 18.0 J mol^{-1} K^{-1}
• B. 75.3 J mol^{-1} K^{-1}
• C. 25.0 J mol^{-1} K^{-1}
• D. 4.18 J mol^{-1} K^{-1}

Answer: (B)

Verified step by step guidance

1. Understand that the molar heat capacity at constant pressure, \(C_p\), is the amount of heat required to raise the temperature of one mole of a substance by one kelvin (or degree Celsius).
2. Recall that the specific heat capacity of liquid water is commonly given as approximately 4.18 J g\(^{-1}\) K\(^{-1}\), which is the heat capacity per gram of water.
3. To find the molar heat capacity, convert the specific heat capacity from per gram to per mole by multiplying by the molar mass of water. The molar mass of water (H\(_2\)O) is about 18.0 g mol\(^{-1}\).
4. Set up the calculation: \(C_p = (\text{specific heat capacity}) \times (\text{molar mass}) = 4.18\ \text{J g}^{-1} \text{K}^{-1} \times 18.0\ \text{g mol}^{-1}\).
5. Perform the multiplication to find the molar heat capacity in J mol\(^{-1}\) K\(^{-1}\), which will give a value close to the correct answer.