Question

The heat capacity of a bomb calorimeter was determined by burning 6.79 g methane (energy of combustion \(=-802 \mathrm{kJ} /\) \(\mathrm{mol} \mathrm{CH}_{4}\) in the bomb. The temperature changed by \(10.8^{\circ} \mathrm{C} .\) a. What is the heat capacity of the bomb? b. A 12.6 -g sample of acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2},\) produced a temperature increase of \(16.9^{\circ} \mathrm{C}\) in the same calorimeter. What is the energy of combustion of acetylene (in \(\mathrm{kJ} / \mathrm{mol} )\) ?

Short answer

a. The heat capacity of the bomb calorimeter is -31.53 kJ/°C. b. The energy of combustion of acetylene is approximately -1100.16 kJ/mol.

Step-by-step solution

Determine the moles of methane burned

To determine the number of moles of methane burned, we use the formula: Moles = Mass / Molar mass The molar mass of methane (CH4) is approximately 16 g/mol (12 for C, and 4 for H). Given mass of methane = 6.79 g Moles of methane = 6.79 g / 16 g/mol = 0.4244 mol

Calculate the heat released by methane

Now that we know the moles of methane, we can find the heat released by methane during combustion using the given energy of combustion: Heat released by methane (Q) = moles * energy of combustion Given energy of combustion for methane = -802 kJ/mol Q = 0.4244 mol * -802 kJ/mol = -340.49 kJ

Calculate the heat capacity of the bomb calorimeter

Now we can calculate the heat capacity of the bomb calorimeter using the formula: Heat capacity (C) = Heat released by methane (Q) / Temperature change Given temperature change = 10.8 °C C = -340.49 kJ / 10.8 °C = -31.53 kJ/°C So, the heat capacity of the bomb calorimeter is -31.53 kJ/°C.

Calculate the heat released by acetylene

To find the energy of combustion of acetylene, we first need to calculate the heat released by acetylene using the formula: Heat released by acetylene (Q) = Heat capacity of the bomb calorimeter * Temperature change Given temperature change = 16.9 °C Q = -31.53 kJ/°C * 16.9 °C = -533.14 kJ

Determine the moles of acetylene burned

We need to find the moles of acetylene in the 12.6 g sample. The molar mass of acetylene (C2H2) is approximately 26 g/mol (24 for C, and 2 for H). Given mass of acetylene = 12.6 g Moles of acetylene = 12.6 g / 26 g/mol = 0.4846 mol

Calculate the energy of combustion of acetylene

Finally, we can calculate the energy of combustion of acetylene using the formula: Energy of combustion of acetylene = Heat released by acetylene / Moles of acetylene Energy of combustion = -533.14 kJ / 0.4846 mol = -1100.16 kJ/mol So, the energy of combustion of acetylene is approximately -1100.16 kJ/mol.

Key concepts

Heat Capacity

When we talk about heat capacity, we are discussing the ability of an object or system to store heat. Heat capacity is defined as the amount of heat required to raise the temperature of an object by one degree Celsius. In the context of a bomb calorimeter, which is used to measure the energy of combustion, understanding heat capacity becomes crucial.

In our exercise, the heat capacity of the bomb calorimeter was determined by the heat released from burning methane. The formula to find heat capacity ( C ) is:

• Heat Capacity ( C ) = Heat released ( Q ) / Temperature Change

In this case, the heat released from burning methane was -340.49 kJ, and the temperature change was 10.8 °C, leading to a calculated heat capacity of -31.53 kJ/°C for the calorimeter. This value helps us understand how the calorimeter responds to heat, directly affecting how we calculate the energy of combustion for other substances.

Energy of Combustion

Energy of combustion refers to the amount of energy released when a substance burns completely in oxygen. This is an important concept in chemistry, especially when dealing with thermochemical processes such as those in bomb calorimetry.

In our scenario, the energy of combustion was measured both for methane and acetylene. For methane, each mole releases -802 kJ. After determining the moles of methane burned, the energy released during the combustion process was calculated as -340.49 kJ. This was achieved using:

• Q = Moles * Energy of combustion

Knowing the energy of combustion of one substance, we can predict the total energy released and use that to determine the calorimeter's heat capacity, which in turn helps us find the energy of combustion of other substances, like acetylene. This process involves measuring the produced heat and compensating for any losses using the calorimeter's known properties.

Moles of Substance

Moles are a basic unit in chemistry that allows us to measure and quantify the amount of a substance. Using the concept of moles, we can connect measurements in grams to a standard quantity based on Avogadro's number (approximately 6.022 × 10²³ entities per mole). The molar mass of a substance plays a vital role here, as it allows conversion between the physical quantity (mass) and moles.

In the given exercise, the molar mass helped convert the mass of both methane (CH extsubscript{4}) and acetylene (C extsubscript{2}H extsubscript{2}) into moles:

• Methane ( ext{Molar mass} = 16 ext{ g/mol} ), 6.79 g → 0.4244 mol
• Acetylene ( ext{Molar mass} = 26 ext{ g/mol} ), 12.6 g → 0.4846 mol

Understanding how to accurately determine moles is essential, as it forms the basis for further thermochemical calculations, such as calculating the energy associated with combustion.

Temperature Change

Temperature change is a direct result of the heat exchange in any thermodynamic process, and it is crucial in calculating the enthalpy changes associated with reactions. In bomb calorimetry, measuring the temperature change of the calorimeter helps determine how much heat was absorbed or released by the chemical reaction.

For this exercise, the change in temperature allowed us to calculate both the heat capacity of the bomb calorimeter and the energy of combustion for acetylene. By monitoring the temperature shifts ( ΔT ), which were 10.8°C for methane and 16.9°C for acetylene, we could evaluate the corresponding heat changes:

• Q = C × ΔT

This formula shows how temperature change is fundamental in deriving the heat changes within a controlled environment like a calorimeter. This detailed tracking ensures that the calculations of energetic contributions from reactions are precise and reliable.