Question

A 1.50 -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 \(8.500 \mathrm{~kJ} /{ }^{\circ} \mathrm{C}\). The temperature of the calorimeter increases from 25.00 to \(29.49^{\circ} \mathrm{C}\). (a) Write a balanced chemical equation for the bomb calorimeter reaction. (b) What is the heat of combustion per gram of quinone and per mole of quinone?

Short answer

The balanced chemical equation for the combustion of quinone is: C₆H₄O₂ + 6O₂ → 6CO₂ + 2H₂O. The heat of combustion per gram of quinone is 25.443 kJ/g, and per mole of quinone is 2748.499 kJ/mol.

Step-by-step solution

(a) Balanced chemical equation

To write a balanced chemical equation for the combustion of quinone in a bomb calorimeter, we need to know that quinone reacts with oxygen (O₂) during combustion and produces carbon dioxide (CO₂) and water (H₂O). The unbalanced equation for this reaction is as follows: C₆H₄O₂ + O₂ → CO₂ + H₂O Now we will balance the equation: C₆H₄O₂ + 6O₂ → 6CO₂ + 2H₂O So, the balanced chemical equation for the combustion of quinone is: C₆H₄O₂ + 6O₂ → 6CO₂ + 2H₂O

(b) Heat of combustion calculation

To calculate the heat of combustion of quinone, we will use the equation: q = C × ΔT Where q is the heat released during combustion, C is the heat capacity of the bomb calorimeter, and ΔT is the temperature change in the bomb calorimeter. Given values are: C = 8.5 kJ/ºC ΔT = 29.49ºC - 25.00ºC = 4.49ºC Now we will calculate the heat released during combustion (q): q = C × ΔT q = 8.5 kJ/ºC × 4.49ºC q = 38.165 kJ Now we will find the heat of combustion per gram and per mole of quinone: 1. Heat of combustion per gram (q/g): Divide the heat released during combustion (q) by the mass of the quinone sample. q/g = q / mass q/g = 38.165 kJ / 1.50 g q/g = 25.443 kJ/g 2. Heat of combustion per mole (q/mol): First, we need to determine the molar mass of quinone. Quinone: C₆H₄O₂ Molar mass: (6 × 12.01) + (4 × 1.01) + (2 × 16.00) = 108.05 g/mol Now we will calculate the heat of combustion per mole by dividing the heat released during combustion (q) by the moles of quinone sample. Moles of quinone = mass / molar mass Moles of quinone = 1.50 g / 108.05 g/mol Moles of quinone = 0.01388 mol q/mol = q / moles of quinone q/mol = 38.165 kJ / 0.01388 mol q/mol = 2748.499 kJ/mol So, the heat of combustion per gram of quinone is 25.443 kJ/g, and per mole of quinone is 2748.499 kJ/mol.

Key concepts

Combustion Reaction

A combustion reaction is a chemical process where a substance combines with oxygen, releasing energy in the form of heat and often light. This type of reaction typically results in the formation of carbon dioxide (CO₂) and water (H₂O). In the case of organic compounds, such as quinone, complete combustion involves reacting with oxygen to break down into these end products.
This process is exothermic, meaning it releases energy, essential for tasks like powering engines or heating homes.

• The general form of a combustion reaction is: Hydrocarbon + O₂ → CO₂ + H₂O
• An example with quinone is: C₆H₄O₂ + 6O₂ → 6CO₂ + 2H₂O

During combustion in a calorimeter, the focus is on measuring the heat released to quantify the energy content of the substance.
This gives insight into the efficiency and potential usage of various fuels and materials.

Heat Capacity

Heat capacity is an essential concept in calorimetry. It denotes the amount of heat required to change the temperature of a system by one degree Celsius. In bomb calorimetry, which is used for measuring the heat of combustion reactions, the heat capacity includes both the calorimeter and its contents.

The formula used to calculate the heat involved is: \[ q = C \times \Delta T \]Where:

• \( q \) = heat absorbed or released (in joules or kilojoules)
• \( C \) = heat capacity of the calorimeter (in kJ/°C)
• \( \Delta T \) = change in temperature (°C)

By knowing the heat capacity and measuring the temperature change, we can calculate the heat absorbed or released during a reaction. In the exercise, the calorimeter's heat capacity is provided as 8.5 kJ/°C, meaning it takes 8.5 kJ to raise its temperature by 1°C. The measured temperature change (ΔT) is applied to find the total heat released during quinone's combustion.

Chemical Equation Balancing

Balancing a chemical equation is crucial because it ensures the law of conservation of mass is obeyed. This means that the same number of each type of atom must exist on both sides of the equation. In combustion reactions, balancing involves adjusting coefficients to account for all the atoms of reactants and products, such as carbon (C), hydrogen (H), and oxygen (O).When balancing a chemical equation, follow these steps:

• Write the unbalanced equation.
• Count the number of atoms for each element in the reactants and products.
• Adjust coefficients to balance one element at a time.
• Recount atoms and adjust as needed until the equation is balanced.

For quinone combustion, the unbalanced equation is: \[ \text{C}_6\text{H}_4\text{O}_2 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O} \]Balancing it involves ensuring 6 carbon atoms, 4 hydrogen atoms, and 8 oxygen atoms on each side, resulting in: \[ \text{C}_6\text{H}_4\text{O}_2 + 6\text{O}_2 \rightarrow 6\text{CO}_2 + 2\text{H}_2\text{O} \]This balanced equation represents the stoichiometric relationship in the combustion reaction, essential for accurate calculations of reactants and products in chemical processes.