Question

In a bomb calorimeter, the reaction vessel is surrounded by water that must be added for each experiment. Since the amount of water is not constant from experiment to experiment, the mass of water must be measured in each case. The heat capacity of the calorimeter is broken down into two parts: the water and the calorimeter components. If a calorimeter contains \(1.00 \mathrm{~kg}\) water and has a total heat capacity of \(10.84 \mathrm{~kJ} /{ }^{\circ} \mathrm{C}\), what is the heat capacity of the calorimeter components?

Short answer

The heat capacity of the calorimeter components can be found by subtracting the heat capacity of water from the total heat capacity of the calorimeter. Given that the total heat capacity is 10.84 kJ/°C and the mass of water is 1.00 kg, we can calculate the heat capacity of water as 4.18 kJ/°C (using the specific heat capacity of water 4.18 kJ/(kg°C)). Then, the heat capacity of the calorimeter components is 10.84 kJ/°C - 4.18 kJ/°C = 6.66 kJ/°C.

Step-by-step solution

Identify the given values and the unknown variable

In this problem, we are given the mass of the water (m) as 1.00 kg, the total heat capacity of the calorimeter (C_total) as 10.84 kJ/°C, and we need to find the heat capacity of the calorimeter components (C_calorimeter).

Using the formula for heat capacity of water

The heat capacity of water (C_water) can be calculated using the formula: C_water = m * C_p where m is the mass of water and C_p is the specific heat capacity of water, which is approximately 4.18 kJ/(kg°C). So, we need to multiply the mass of the water by the specific heat capacity of water to find the heat capacity of water.

Calculate the heat capacity of water

Using the formula in step 2, we can find the heat capacity of water as: C_water = (1.00 kg) * (4.18 kJ/(kg°C)) C_water = 4.18 kJ/°C

Calculate the heat capacity of the calorimeter components

Now that we have the heat capacity of water, we can find the heat capacity of the calorimeter components by subtracting the heat capacity of water from the total heat capacity of the calorimeter: C_calorimeter = C_total - C_water C_calorimeter = (10.84 kJ/°C) - (4.18 kJ/°C) C_calorimeter = 6.66 kJ/°C The heat capacity of the calorimeter components is 6.66 kJ/°C.