Question

It takes \(585 \mathrm{~J}\) of energy to raise the temperature of \(125.6 \mathrm{~g}\) mercury from \(20.0^{\circ} \mathrm{C}\) to \(53.5^{\circ} \mathrm{C}\). Calculate the specific heat capacity and the molar heat capacity of mercury.

Short answer

The specific heat capacity of mercury is \(0.139 \frac{\mathrm{J}}{\mathrm{g} \cdot \mathrm{°C}}\), and the molar heat capacity is approximately \(27.88 \frac{\mathrm{J}}{\mathrm{mol} \cdot \mathrm{°C}}\).

Step-by-step solution

Identify the given information and the formula to use

We are given the following information: - Energy (Q) = 585 J - Mass (m) = 125.6 g - Initial temperature (Ti) = 20.0°C - Final temperature (Tf) = 53.5°C Our goal is to find the specific heat capacity (c) and the molar heat capacity. We will use the formula for heat transfer: Q = mcΔT, where Q is the energy/heat, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

Calculate the change in temperature (ΔT)

ΔT = Tf - Ti ΔT = 53.5°C - 20.0°C ΔT = 33.5°C

Use the heat transfer formula to find the specific heat capacity (c)

Rearrange the formula to solve for c: c = Q / (m * ΔT) Plug in the given values: c = 585 J / (125.6 g * 33.5°C) c = 585 J / 4206.2 g°C c = 0.139 \(\frac{\mathrm{J}}{\mathrm{g} \cdot \mathrm{°C}}\) So, the specific heat capacity of mercury is 0.139 J/g°C.

Calculate the molar heat capacity

To find the molar heat capacity, we need the molar mass of mercury (Hg). The molar mass of Hg is 200.59 g/mol. Molar Heat Capacity = Specific Heat Capacity * Molar Mass Molar Heat Capacity = 0.139 \(\frac{\mathrm{J}}{\mathrm{g} \cdot \mathrm{°C}}\) * 200.59 \(\frac{\mathrm{g}}{\mathrm{mol}}\) Molar Heat Capacity ≈ 27.88 \(\frac{\mathrm{J}}{\mathrm{mol} \cdot \mathrm{°C}}\) The molar heat capacity of mercury is approximately 27.88 J/mol°C.