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Chapter 6: Problem 106

In a bomb calorimeter, the reaction vessel is surrounded by water that must be added for each experiment. Since the amount of water is not constant from experiment to experiment, the mass of water must be measured in each case. The heat capacity of the calorimeter is broken down into two parts: the water and the calorimeter components. If a calorimeter contains \(1.00 \mathrm{~kg}\) water and has a total heat capacity of \(10.84 \mathrm{~kJ} /{ }^{\circ} \mathrm{C}\), what is the heat capacity of the calorimeter components?

Short Answer

Expert verified
The heat capacity of the calorimeter components is approximately 6.654 kJ/°C.

Step by step solution

01

Identify given values

We know the following: - Total heat capacity of the calorimeter (C_total) = 10.84 kJ/°C - Mass of water (m_water) = 1.00 kg
02

Find the specific heat capacity of water

The specific heat capacity of water (c_water) is a known value. For water at room temperature, c_water = 4.186 kJ/(kg °C)
03

Calculate the heat capacity of water

To find the heat capacity of water (C_water) in the calorimeter, we use the formula: C_water = m_water × c_water C_water = 1.00 kg × 4.186 kJ/(kg °C) C_water = 4.186 kJ/°C
04

Calculate the heat capacity of the calorimeter components

Now that we have the heat capacity of water, we can find the heat capacity of the calorimeter components (C_components) by subtracting the heat capacity of water from the total heat capacity of the calorimeter: C_components = C_total - C_water C_components = 10.84 kJ/°C - 4.186 kJ/°C C_components ≈ 6.654 kJ/°C The heat capacity of the calorimeter components is approximately 6.654 kJ/°C.

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Most popular questions from this chapter

At \(298 \mathrm{~K}\), the standard enthalpies of formation for \(\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{~g})\) and \(\mathrm{C}_{6} \mathrm{H}_{6}(l)\) are \(227 \mathrm{~kJ} / \mathrm{mol}\) and \(49 \mathrm{~kJ} / \mathrm{mol}\), respectively. a. Calculate \(\Delta H^{\circ}\) for $$ \mathrm{C}_{6} \mathrm{H}_{6}(l) \longrightarrow 3 \mathrm{C}_{2} \mathrm{H}_{2}(g) $$ b. Both acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) and benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) can be used as fuels. Which compound would liberate more energy per gram when combusted in air?

Consider \(2.00\) moles of an ideal gas that are taken from state \(A\) \(\left(P_{A}=2.00 \mathrm{~atm}, V_{A}=10.0 \mathrm{~L}\right)\) to state \(B\left(P_{B}=1.00 \mathrm{~atm}, V_{B}=\right.\) \(30.0 \mathrm{~L}\) ) by two different pathways: These pathways are summarized on the following graph of \(P\) versus \(V\) : Calculate the work (in units of J) associated with the two pathways. Is work a state function? Explain.

Nitromethane, \(\mathrm{CH}_{3} \mathrm{NO}_{2}\), can be used as a fuel. When the liquid is burned, the (unbalanced) reaction is mainly $$ \mathrm{CH}_{3} \mathrm{NO}_{2}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{N}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g) $$ a. The standard enthalpy change of reaction \(\left(\Delta H_{\mathrm{rxn}}^{\circ}\right)\) for the balanced reaction (with lowest whole- number coefficients) is \(-1288.5 \mathrm{~kJ}\). Calculate \(\Delta H_{\mathrm{f}}^{\circ}\) for nitromethane. b. A \(15.0\) - \(\mathrm{L}\) flask containing a sample of nitromethane is filled with \(\mathrm{O}_{2}\) and the flask is heated to \(100 .{ }^{\circ} \mathrm{C}\). At this temperature, and after the reaction is complete, the total pressure of all the gases inside the flask is 950 . torr. If the mole fraction of nitrogen \(\left(\chi_{\text {nitrogen }}\right)\) is \(0.134\) after the reaction is complete, what mass of nitrogen was produced?

The specific heat capacity of silver is \(0.24 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}\). a. Calculate the energy required to raise the temperature of \(150.0 \mathrm{~g}\) Ag from \(273 \mathrm{~K}\) to \(298 \mathrm{~K}\). b. Calculate the energy required to raise the temperature of \(1.0\) mole of Ag by \(1.0^{\circ} \mathrm{C}\) (called the molar heat capacity of silver). c. It takes \(1.25 \mathrm{~kJ}\) of energy to heat a sample of pure silver from \(12.0^{\circ} \mathrm{C}\) to \(15.2^{\circ} \mathrm{C}\). Calculate the mass of the sample of silver.

One mole of \(\mathrm{H}_{2} \mathrm{O}(g)\) at \(1.00 \mathrm{~atm}\) and \(100 .{ }^{\circ} \mathrm{C}\) occupies a volume of \(30.6 \mathrm{~L}\). When 1 mole of \(\mathrm{H}_{2} \mathrm{O}(g)\) is condensed to 1 mole of \(\mathrm{H}_{2} \mathrm{O}(l)\) at \(1.00\) atm and \(100 .{ }^{\circ} \mathrm{C}, 40.66 \mathrm{~kJ}\) of heat is released. If the density of \(\mathrm{H}_{2} \mathrm{O}(l)\) at this temperature and pressure is \(0.996 \mathrm{~g} / \mathrm{cm}^{3}\), calculate \(\Delta E\) for the condensation of 1 mole of water at \(1.00 \mathrm{~atm}\) and \(100 .{ }^{\circ} \mathrm{C}\).
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