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Chapter 6: Problem 52

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

Expert verified
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

01

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.
02

Calculate the change in temperature (ΔT)

ΔT = Tf - Ti ΔT = 53.5°C - 20.0°C ΔT = 33.5°C
03

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.
04

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.

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Most popular questions from this chapter

For the following reactions at constant pressure, predict if \(\Delta H>\) \(\Delta E, \Delta H<\Delta E\), or \(\Delta H=\Delta E\) a. \(2 \mathrm{HF}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{F}_{2}(g)\) b. \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\) c. \(4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\)

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The enthalpy of combustion of solid carbon to form carbon dioxide is \(-393.7 \mathrm{~kJ} / \mathrm{mol}\) carbon, and the enthalpy of combustion of carbon monoxide to form carbon dioxide is \(-283.3 \mathrm{~kJ} / \mathrm{mol}\) CO. Use these data to calculate \(\Delta H\) for the reaction $$ 2 \mathrm{C}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}(g) $$

A biology experiment requires the preparation of a water bath at \(37.0^{\circ} \mathrm{C}\) (body temperature). The temperature of the cold tap water is \(22.0^{\circ} \mathrm{C}\), and the temperature of the hot tap water is \(55.0^{\circ} \mathrm{C}\). If a student starts with \(90.0 \mathrm{~g}\) cold water, what mass of hot water must be added to reach \(37.0^{\circ} \mathrm{C} ?\)

Consider the substances in Table 6.1. Which substance requires the largest amount of energy to raise the temperature of \(25.0 \mathrm{~g}\) of the substance from \(15.0^{\circ} \mathrm{C}\) to \(37.0^{\circ} \mathrm{C}\) ? Calculate the energy. Which substance in Table \(6.1\) has the largest temperature change when \(550 . \mathrm{g}\) of the substance absorbs \(10.7 \mathrm{~kJ}\) of energy? Calculate the temperature change.
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