We said previously that the change in internal energy for a reaction is equal to heat plus work. We've also considered how to calculate heat and pressure-volume work. If we carry out a reaction at constant volume, then the reaction will not perform pressure-volume work, so the change in internal energy for the reaction is just equal to the heat at a constant volume. We can carry out a reaction at constant volume in a bomb calorimeter. A bomb calorimeter has a tightly sealed bomb at its center, which maintains a constant volume. The bomb contains a sample (which can undergo combustion) and oxygen. An ignition wire is used to initiate the reaction. The bomb is surrounded by water, which absorbs the excess thermal energy given off by the reaction. The amount of heat absorbed by the calorimeter equals the heat capacity of the calorimeter times the measured change in temperature. The heat absorbed by the calorimeter was released by the reaction, so the heat of the reaction is equal to negative heat of the calorimeter. Let's practice calculating the change in internal energy for the reaction. Our problem reads, "When 1.55 grams of liquid hexane undergoes combustion in a bomb calorimeter, the temperature rises from 25.87 °C to 38.13 °C. Find the change in internal energy for the reaction in kilojoules per mole of hexane. The heat capacity of the bomb calorimeter, determined in a separate experiment, is 5.73 kilojoules per degree Celsius. We'll start with our equation: change in internal energy for a reaction equals heat of the reaction when the reaction is performed at a constant volume. We can use this equation because the reaction is performed in the bomb calorimeter. We also know that the heat the reaction gives off is absorbed by the bomb calorimeter, so this is equal to the negative heat of the calorimeter. To calculate the heat of the calorimeter, we multiply the heat capacity of the calorimeter times the measured change in temperature. We can substitute in final temperature minus initial temperature for delta T. So to calculate the change in internal energy for the reaction, it's negative heat capacity of the calorimeter times the final temperature minus the initial temperature. Plugging in the values from the problem and completing the calculation, we get -70.25 kilojoules. This, however, is not our final answer. We are asked for the change in internal energy for the reaction in kilojoules per mole of hexane, but we didn't use one mole of hexane in this problem; we used 1.550 grams of hexane. So we'll need to use dimensional analysis to get the correct units. We'll start our dimensional analysis with -70.25 kilojoules per 1.550 grams of hexane. We can convert from grams of hexane to moles of hexane using the molar mass of hexane: one mole of hexane is 86.172 grams of hexane. Since we want to cancel out units of grams of hexane, which are initially in the denominator, we need to put grams of hexane in the numerator in our conversion factor. Completing this calculation, we should get -3906 kilojoules per mole of hexane.