Under constant-volume conditions, the heat of combustion of naphthalene (C10H8) is 40.18 kJ/g. A 2.50-g sample of naphthalene is burned in a bomb calorimeter. The temperature of the calorimeter increases from 21.50 to 28.83 °C. (b) A 1.50-g sample of a new organic substance is combusted in the same calorimeter. The temperature of the calorimeter increases from 21.14 to 25.08 °C. What is the heat of combustion per gram of the new substance?

Verified step by step guidance

1. Step 1: Understand the concept of heat of combustion. It is the amount of heat released when a substance is burned completely in oxygen under constant volume conditions. In this problem, we are dealing with a bomb calorimeter, which measures the heat of combustion.
2. Step 2: Calculate the total heat released by the naphthalene sample using its heat of combustion. Use the formula: \( q = m \times \Delta H_{combustion} \), where \( q \) is the heat released, \( m \) is the mass of the sample, and \( \Delta H_{combustion} \) is the heat of combustion per gram.
3. Step 3: Determine the heat capacity of the calorimeter. The heat released by the naphthalene sample causes a temperature change in the calorimeter. Use the formula: \( q = C_{cal} \times \Delta T \), where \( C_{cal} \) is the heat capacity of the calorimeter and \( \Delta T \) is the change in temperature.
4. Step 4: Calculate the heat released by the new organic substance using the same calorimeter. Use the formula: \( q = C_{cal} \times \Delta T \), where \( \Delta T \) is the temperature change caused by the combustion of the new substance.
5. Step 5: Determine the heat of combustion per gram of the new substance. Use the formula: \( \Delta H_{combustion} = \frac{q}{m} \), where \( q \) is the heat released and \( m \) is the mass of the new substance.

Key Concepts

Heat of Combustion

The heat of combustion is the amount of energy released when a substance undergoes complete combustion with oxygen. It is typically expressed in kilojoules per gram (kJ/g) and is a crucial parameter in thermochemistry, as it helps quantify the energy content of fuels. Understanding this concept is essential for calculating the energy released during the combustion of different substances.

Calorimetry

Calorimetry is the science of measuring the heat of chemical reactions or physical changes. In a bomb calorimeter, the heat released from a combustion reaction is absorbed by the surrounding water, leading to a temperature change that can be measured. This temperature change is used to calculate the heat of combustion, making calorimetry a vital tool in thermodynamic studies.

Temperature Change and Specific Heat Capacity

The temperature change in a calorimeter is directly related to the amount of heat absorbed by the water, which can be calculated using the formula q = mcΔT, where q is the heat absorbed, m is the mass of the water, c is the specific heat capacity, and ΔT is the change in temperature. This relationship is fundamental for determining the heat of combustion of a substance based on the observed temperature change in the calorimeter.