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Chapter 8: Problem 15

Isooctane is a primary component of gasoline and gives gasoline its octane rating. Burning \(1.00 \mathrm{~mL}\) of isooctane \((d=0.688 \mathrm{~g} / \mathrm{mL})\) releases \(33.0 \mathrm{~kJ}\) of heat. When \(10.00 \mathrm{~mL}\) of is ooctane is burned in a bomb calorime- ter, the temperature in the bomb rises from \(23.2^{\circ} \mathrm{C}\) to \(66.5^{\circ} \mathrm{C}\). What is the heat capacity of the bomb calorimeter?

Short Answer

Expert verified
Answer: The heat capacity of the bomb calorimeter is 7.62 kJ/°C.

Step by step solution

01

Calculate the heat released when burning 10.00 mL of isooctane

We are given that burning 1.00 mL of isooctane releases 33.0 kJ of heat. Therefore, we can find the heat released when burning 10.00 mL of isooctane by multiplying the heat released for 1.00 mL by 10.00 mL: \(q = 33.0 \mathrm{~kJ/mL} \times 10.00 \mathrm{~mL} = 330.0 \mathrm{~kJ}\)
02

Calculate the change in temperature

The initial temperature of the bomb calorimeter is \(23.2^{\circ} \mathrm{C}\), and the final temperature is \(66.5^{\circ} \mathrm{C}\). To find the change in temperature, we can subtract the initial temperature from the final temperature: \(\Delta T = T_f - T_i = 66.5^{\circ} \mathrm{C} - 23.2^{\circ} \mathrm{C} = 43.3^{\circ} \mathrm{C}\)
03

Calculate the heat capacity of the bomb calorimeter

Now that we have the heat released (\(q = 330.0 \mathrm{~kJ}\)) and the change in temperature (\(\Delta T = 43.3^{\circ} \mathrm{C}\)), we can use the formula \(q = C \cdot \Delta T\) to find the heat capacity (C) of the bomb calorimeter: \(C = \frac{q}{\Delta T} = \frac{330.0 \mathrm{~kJ}}{43.3^{\circ} \mathrm{C}} = 7.62 \frac{\mathrm{kJ}}{^\circ \mathrm{C}}\) The heat capacity of the bomb calorimeter is 7.62 kJ/\(^{\circ} \mathrm{C}\).

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Most popular questions from this chapter

Calculate (a) \(g\) when a system does \(54 \mathrm{~J}\) of work and its energy decreases by \(72 \mathrm{~J}\). (b) \(\Delta E\) for a gas that releases \(38 \mathrm{~J}\) of heat and has \(102 \mathrm{~J}\) of work done on it.

Given $$ 2 \mathrm{Al}_{2} \mathrm{O}_{3}(s) \longrightarrow 4 \mathrm{Al}(s)+3 \mathrm{O}_{2}(g) \quad \Delta H^{\circ}=3351.4 \mathrm{~kJ} $$ (a) What is the heat of formation of aluminum oxide? (b) What is \(\Delta H^{\circ}\) for the formation of \(12.50 \mathrm{~g}\) of aluminum oxide?

Chlorine trifluoride is a toxic, intensely reactive gas. It was used in World War II to make incendiary bombs. It reacts with ammonia and forms nitrogen, chlorine, and hydrogen fluoride gases. When two moles of chlorine trifluoride reacts, \(1196 \mathrm{~kJ}\) of heat is evolved. (a) Write a thermochemical equation for the reaction. (b) What is \(\Delta H_{\mathrm{f}}^{\circ}\) for \(\mathrm{ClF}_{3} ?\)

Nitrogen oxide (NO) has been found to be a key component in many biological processes. It also can react with oxygen to give the brown gas \(\mathrm{NO}_{2}\). When one mole of NO reacts with oxygen, \(57.0 \mathrm{~kJ}\) of heat is evolved. (a) Write the thermochemical equation for the reaction between one mole of nitrogen oxide and oxygen. (b) Is the reaction exothermic or endothermic? (c) Draw an energy diagram showing the path of this reaction. (Figure \(8.4\) is an example of such an energy diagram.)

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