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Chapter 6: Problem 67

The heat capacity of a bomb calorimeter was determined by burning \(6.79 \mathrm{~g}\) methane (energy of combustion \(=-802 \mathrm{~kJ} /\) \(\mathrm{mol} \mathrm{CH}_{4}\) ) in the bomb. The temperature changed by \(10.8^{\circ} \mathrm{C} .\) a. What is the heat capacity of the bomb? b. A \(12.6-\mathrm{g}\) sample of acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}\), produced a temperature increase of \(16.9^{\circ} \mathrm{C}\) in the same calorimeter. What is the energy of combustion of acetylene (in \(\mathrm{kJ} / \mathrm{mol}\) )?

Short Answer

Expert verified
The heat capacity of the bomb calorimeter is \(C_{bomb} = \frac{-802\text{ kJ/mol} \times \frac{6.79\text{ g}}{16.05 \text{ g/mol}}}{10.8^{\circ}\text{C}}\). The energy of combustion of acetylene is \(\frac{C_{bomb} \times 16.9 ^{\circ}\text{C}}{\frac{12.6\text{ g}}{26.04 \text{ g/mol}}}\).

Step by step solution

01

Calculate heat released by methane

We begin by finding the number of moles of methane (CH4) and then calculating the heat released by it. The molar mass of CH4 is 12.01 + 4(1.01) = 16.05 g/mol. Moles of methane = \(\frac{6.79\text{ g}}{16.05 \text{ g/mol}}\)
02

Calculate the heat generated from the burning methane

Using the energy of combustion given, we can calculate the total heat \(q_{CH4}\) generated by burning methane: \(q_{CH4} = -802\text{ kJ/mol} \times \frac{6.79\text{ g}}{16.05 \text{ g/mol}}\)
03

Calculate the heat capacity of the bomb

Knowing the heat generated and the temperature change, we can now calculate the heat capacity of the bomb calorimeter, C_bomb. The formula for heat capacity is: C_bomb = \(\frac{q_{CH4}}{\Delta T}\)
04

Calculate moles of acetylene

Now we can move on to part b of the problem. To find the energy of combustion for acetylene (C2H2), we first need to calculate the number of moles. The molar mass of C2H2 is 2(12.01) + 2(1.01) = 26.04 g/mol. Moles of acetylene = \(\frac{12.6\text{ g}}{26.04 \text{ g/mol}}\)
05

Calculate the heat generated by burning acetylene

Using the heat capacity of the bomb and the change in temperature for acetylene, we can calculate the total heat generated by burning acetylene, \(q_{C2H2}\), as: \(q_{C2H2} = C_bomb \times 16.9 ^{\circ}\text{C}\)
06

Calculate the energy of combustion of acetylene

Lastly, we can calculate the energy of combustion of acetylene by dividing \(q_{C2H2}\) by the moles of acetylene: \( \text{Energy of combustion} = \frac{q_{C2H2}} {\text{Moles of acetylene}}\)

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Most popular questions from this chapter

Which of the following processes are exothermic? a. \(\mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{~N}(g)\) b. \(\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{O}(s)\) c. \(\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{Cl}(g)\) d. \(2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)\) e. \(\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{O}(g)\)

A balloon filled with \(39.1\) moles of helium has a volume of \(876 \mathrm{~L}\) at \(0.0^{\circ} \mathrm{C}\) and \(1.00\) atm pressure. The temperature of the balloon is increased to \(38.0^{\circ} \mathrm{C}\) as it expands to a volume of \(998 \mathrm{~L}\), the pressure remaining constant. Calculate \(q, w\), and \(\Delta E\) for the helium in the balloon. (The molar heat capacity for helium gas is \(20.8 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{mol}\).)

Combustion of table sugar produces \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l)\). When \(1.46 \mathrm{~g}\) table sugar is combusted in a constant-volume (bomb) calorimeter, \(24.00 \mathrm{~kJ}\) of heat is liberated. a. Assuming that table sugar is pure sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s)\), write the balanced equation for the combustion reaction. b. Calculate \(\Delta E\) in \(\mathrm{kJ} / \mathrm{mol} \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) for the combustion reaction of sucrose. c. Calculate \(\Delta H\) in \(\mathrm{kJ} / \mathrm{mol} \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) for the combustion reaction of sucrose at \(25^{\circ} \mathrm{C}\).

If the internal energy of a thermodynamic system is increased by \(300 . \mathrm{J}\) while \(75 \mathrm{~J}\) of expansion work is done, how much heat was transferred and in which direction, to or from the system?

In which of the following systems is(are) work done by the surroundings on the system? Assume pressure and temperature are constant. a. \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) b. \(\mathrm{CO}_{2}(s) \longrightarrow \mathrm{CO}_{2}(g)\) c. \(4 \mathrm{NH}_{3}(g)+7 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\) d. \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)\) e. \(\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaCO}(s)+\mathrm{CO}_{2}(g)\)
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