We previously learned about a bomb calorimeter, which maintains a constant volume. When a combustion reaction is performed at a constant volume in a bomb calorimeter, the change in internal energy for the reaction is equal to the heat. A coffee cup calorimeter, on the other hand, maintains a constant pressure since it is open to the atmosphere. This allows us to calculate the change in enthalpy for a reaction, which equals heat when the reaction is carried out at a constant pressure. Coffee cup calorimeters can be particularly useful for reactions that occur in a solution. Let's practice finding the enthalpy of reaction from a coffee cup calorimeter experiment. Our problem reads, "The addition of HCl to silver nitrate solution precipitates silver chloride. When you combine 50 milliliters of 0.2 molar silver nitrate with 50 milliliters of 0.1 molar HCl in a coffee cup calorimeter, the temperature changes from 23.4 °C to 24.21 °C. Calculate the change in enthalpy in kJ for the reaction as written. Use 1 g per milliliter as the density, and 4.18 joules per gram-degree Celsius for the specific heat capacity of the solution." Let's start by considering our system. We have a coffee cup tower editor and we're adding 50 ml of silver nitrate solution to 50 milliliters of HCl solution, and a precipitation reaction is occurring. Since we're given amounts of two different reactants, we'll want to determine which is the limiting reactant. Our total amount of solution in the coffee cup calorimeter is then 100 milliliters. The precipitation reaction increases the temperature of the solution, and we want to know the change in enthalpy for the reaction. We can use the equation heat equals mass times specific heat capacity times change in temperature to determine how much thermal energy was absorbed by the solution. And we know that the energy absorbed by the solution was given off by the reaction, so the heat for the reaction is equal to negative heat of the solution. Then we can use dimensional analysis to take into account the amount of reactions we performed based on our limiting reagent. Let's calculate the heat absorbed by the solution. Our total mass of solution is 100 grams because we have 100 milliliters of solution and the density is 1 gram per milliliter. Our specific heat capacity is given in the problem: 4.18 joules per gram-degree Celsius. And the change in temperature is T final minus T initial, so it is 24.21 subtract 23.4 °C. Completing the calculation, we get 339 joules. This thermal energy absorbed by the solution was released by the reaction; that's why the temperature of the solution rises. So the heat of the reaction is -339 joules. We want to calculate the change in enthalpy for the reaction as it's written. This means the enthalpy change when 1 mole of silver nitrate combines with 1 mole of hydrochloric acid to produce 1 mole of silver chloride and 1 mole of nitric acid. However, we didn't use 1 mole of each of our reactants; we used 50 milliliters of 0.2 molar silver nitrate solution and 50 milliliters of 0.1 molar hydrochloric acid solution. So our next step is to determine the limiting reagent. If we convert to moles of each reactant by multiplying our liters of solution times our molarity, we combined 0.01 moles of silver nitrate with 0.005 moles of hydrochloric acid. The HCl will run out first since they react in a one-to-one molar ratio in the balanced chemical equation. Now that we know the limiting reagent, we can use dimensional analysis to compensate for the amount of reactant we used. We'll start the dimensional analysis with the energy we produced divided by the amount of limiting reagent we used to produce it. We can convert from moles of HCl to reactions using the coefficient in the balanced chemical equation for HCl: we need 1 mole of HCl for 1 reaction. Then we can convert from joules to kilojoules. Completing the calculation, we get -67.7 kilojoules per reaction. We can represent this as just -67.7 kilojoules since we know the enthalpy of the reaction is associated with the coefficients of the reaction as written. The negative sign indicates this is an exothermic reaction.