Problem 57 - Chemistry: The Central Science

Question

A \(2.200-g\) sample of quinone \(\left(\mathrm{C}_{6} \mathrm{H}_{4} \mathrm{O}_{2}\right)\) is burned in a bomb calorimeter whose total heat capacity is \(7.854 \mathrm{~kJ} /{ }^{\circ} \mathrm{C}\). The temperature of the calorimeter increases from \(23.44\) to \(30.57^{\circ} \mathrm{C}\). What is the heat of combustion per gram of quinone? Per mole of quinone?

Step-by-Step Solution

Answer

The heat of combustion per gram of quinone is \(25.46 \, kJ/g\) and the heat of combustion per mole of quinone is \(2750.21 \, kJ/mol\).

Step 1: Calculate the total heat released#__tag_content# To find the total heat released when the 2.200g quinone sample is burned, we can use the provided heat capacity of the calorimeter and the temperature change as follows: Total heat released (Q) = Heat capacity of the calorimeter × Change in temperature The change in temperature can be found by subtracting the initial temperature from the final temperature: ΔT = T_final - T_initial = 30.57 °C - 23.44 °C = 7.13 °C Now we can find the total heat released: Q = 7.854 kJ/°C × 7.13 °C = 56.00462 kJ

Step 2: Calculate the heat of combustion per gram#__tag_content# To find the heat of combustion per gram of quinone, we can divide the total heat released from Step 1 by the weight of the quinone sample: Heat of combustion per gram (q) = Total heat released (Q) ÷ Weight of quinone sample q = 56.00462 kJ ÷ 2.200 g = 25.45755 kJ/g

Step 3: Calculate the molar mass of quinone#__tag_content# To find the heat of combustion per mole of quinone, we need to first calculate the molar mass of quinone. The formula of quinone is C6H4O2. We can find the molar mass by adding the molar mass of each element in quinone as follows: Molar mass of quinone (M) = (6 × molar mass of C) + (4 × molar mass of H) + (2 × molar mass of O) M = (6 × 12.01 g/mol) + (4 × 1.01 g/mol) + (2 × 16.00 g/mol) = 108.06 g/mol

Step 4: Calculate the heat of combustion per mole#__tag_content# Now that we have the molar mass of quinone, we can find the heat of combustion per mole by multiplying the heat of combustion per gram (from Step 2) by the molar mass of quinone (from Step 3): Heat of combustion per mole (Q_mol) = Heat of combustion per gram (q) × Molar mass of quinone (M) Q_mol = 25.45755 kJ/g × 108.06 g/mol = 2750.20763 kJ/mol The heat of combustion per gram of quinone is \(25.46 \, kJ/g\) and the heat of combustion per mole of quinone is \(2750.21 \, kJ/mol\).

Key Concepts

Bomb Calorimetry

Bomb calorimetry is a technique used to measure the heat of combustion of a substance. This is done by burning a sample in a sealed container, called a bomb calorimeter. The heat from the combustion is absorbed by the surrounding water and calorimeter, causing a rise in temperature. By knowing the heat capacity of the calorimeter, which is the amount of heat required to raise its temperature by 1 degree Celsius, we can calculate the total energy released during combustion.
To find the heat released, we use the formula:

• Total Heat Released ( Q ) = Heat Capacity of Calorimeter × Change in Temperature ( ΔT )

The change in temperature is determined by the difference between the final and initial temperatures. This method allows for an accurate measurement of the energy content, as all energy is confined within the calorimeter. Remember, this setup accounts for all heat produced, even factors like incomplete combustion are minimized by the well-sealed system.

Molar Mass Calculation

Calculating the molar mass of a compound is essential when working with chemical equations and reactions. The molar mass is the mass of one mole of a substance and is measured in grams per mole ( g/mol ).
For molecular compounds like quinone ( C_6H_4O_2 ), molar mass is calculated by adding up the atomic masses of all the atoms present in the molecular formula:

• Carbon ( C ): 12.01 g/mol
• Hydrogen ( H ): 1.01 g/mol
• Oxygen ( O ): 16.00 g/mol

To find the molar mass of quinone:

• Molar Mass = (6 × Molar Mass of C) + (4 × Molar Mass of H) + (2 × Molar Mass of O)
• Molar Mass = (6 × 12.01) + (4 × 1.01) + (2 × 16.00) = 108.06 g/mol

Having the molar mass allows you to convert from grams to moles, an essential skill for stoichiometry and understanding reaction proportions.

Combustion Reaction

A combustion reaction involves the burning of a substance in the presence of oxygen. This type of reaction is exothermic, meaning it releases heat. Combustion reactions are especially important in energy production, where fuels like hydrocarbons release energy when burned.
For quinone, the combustion reaction can be understood as converting the chemical energy stored in the molecule into heat and light. This is the basis for measuring the heat of combustion. To understand a combustion reaction:

• Identify the fuel (e.g., quinone).
• Ensure oxygen is available for the reaction.
• The products typically include CO_2 and H_2O as common outcomes for organic compounds.

Understanding the combustion reaction is crucial in calculating the energy changes that occur. Knowing the exact reactants and products helps in fine-tuning reactions for applications like industrial processing and energy generation. Proper calorimetry helps in quantifying these reactions accurately.