Question

Acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}\), is used in welding torches. It releases a lot of energy when burned in oxygen. One gram of acetylene releases \(48.2 \mathrm{~kJ}\). When \(0.750 \mathrm{~g}\) of acetylene is burned in a bomb calorimeter (heat capacity = $\left.1.117 \mathrm{~kJ} /{ }^{\circ} \mathrm{C}\right)\(, the final temperature of the bomb is \)54.5^{\circ} \mathrm{C}$. What is the initial temperature of the calorimeter?

Short answer

Answer: The initial temperature of the calorimeter is 22.14 °C.

Step-by-step solution

Calculate the heat released by acetylene.

To find the heat released by acetylene, we multiply the mass of acetylene burned with the energy released per gram of acetylene: \(\text{Heat released} = (0.750 g) \times (48.2 kJ/g) = 36.15 kJ\)

Find the heat gained by the calorimeter.

Since the heat released by acetylene is equal to the heat gained by the calorimeter, we have: \(\text{Heat gained by the calorimeter} = 36.15 kJ\)

Calculate the temperature change of the calorimeter.

We can now use the formula for heat capacity to find the temperature change of the calorimeter: \(\text{Heat gained by the calorimeter} = \text{Heat Capacity} \times \Delta T \Rightarrow \Delta T = \frac{\text{Heat gained by the calorimeter}}{\text{Heat Capacity}}\) \(\Delta T = \frac{36.15 \, kJ}{1.117 \, kJ/^\circ C} = 32.36 ^\circ C\)

Find the initial temperature of the calorimeter.

Since we know the final temperature (\(T_{final}\)) and the temperature change (\(\Delta T\)), we can find the initial temperature (\(T_{initial}\)) by using the formula: \(T_{initial} = T_{final} - \Delta T\) \(T_{initial} = 54.5 ^\circ C - 32.36 ^\circ C = 22.14 ^\circ C\) The initial temperature of the calorimeter is \(22.14 ^\circ C\).