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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

Naphthalene, \(\mathrm{C}_{10} \mathrm{H}_{8}\), is the compound present in moth balls. When one mole of naphthalene is burned, \(5.15 \times 10^{3} \mathrm{~kJ}\) of heat is evolved. A sample of naphthalene burned in a bomb calorimeter (heat capacity \(=9832 \mathrm{~J} /{ }^{\circ} \mathrm{C}\) ) increases the temperature in the calorimeter from \(25.1^{\circ} \mathrm{C}\) to \(28.4^{\circ} \mathrm{C}\). How many milligrams of naphthalene were burned?

Given the following reactions, $$ \begin{aligned} \mathrm{N}_{2} \mathrm{H}_{4}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) & \Delta H^{\circ} &=-534.2 \mathrm{~kJ} \\ \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g) & \Delta H^{\circ} &=-241.8 \mathrm{~kJ} \end{aligned} $$ calculate the heat of formation of hydrazine.

Given $$ 2 \mathrm{CuO}(s) \longrightarrow 2 \mathrm{Cu}(s)+\mathrm{O}_{2}(g) \quad \Delta H^{\circ}=314.6 \mathrm{~kJ} $$ (a) Determine the heat of formation of \(\mathrm{CuO}\). (b) Calculate \(\Delta H^{\circ}\) for the formation of \(13.58 \mathrm{~g}\) of \(\mathrm{CuO}\).

Determine whether the statements given below are true or false. Consider specific heat. (a) Specific heat represents the amount of heat required to raise the temperature of one gram of a substance by \(1^{\circ} \mathrm{C}\). (b) Specific heat is the amount of heat flowing into the system. (c) When 20 J of heat is added to equal masses of different materials at \(25^{\circ} \mathrm{C}\), the final temperature for all these materials will be the same. (d) Heat is measured in \({ }^{\circ} \mathrm{C}\).

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.
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