Question

The C$_p$ of H$_2$O(l) is 75.3 J mol$^{-1}$ K$^{-1}$. What is the energy (in J) required to raise 180 g of liquid water from 10$^{\circ}$C to 15$^{\circ}$C? (H$_2$O = 18 u)

• A. 3.765
• B. 3765
• C. 753
• D. 376.5

Hint:

Heat = $nC_p\Delta T$. Moles = mass/molar mass.

Answer 1

The Correct Option is B

The heat ($q$) required to raise the temperature of a substance is given by $q = mc\Delta T$, where $m$ is the mass, $c$ is the specific heat capacity, and $\Delta T$ is the change in temperature. However, we are given the molar heat capacity (C$_p$), so we need to use the number of moles ($n$). The relationship is $q = nC_p\Delta T$. First, calculate the number of moles of water: $$ n = \frac{\text{mass}}{\text{molar mass}} = \frac{180 \, \text{g}}{18 \, \text{g/mol}} = 10 \, \text{mol} $$ Now, calculate the heat required: $$ q = (10 \, \text{mol})(75.3 \, \text{J mol}^{-1} \text{K}^{-1})(15 - 10) \, \text{K} = 3765 \, \text{J} $$