Question

A chemical engineer burned \(1.520 \mathrm{~g}\) of a hydrocarbon in the bomb of a calorimeter (see Figure 6.10 ). The water temperature rose from \(20.00^{\circ} \mathrm{C}\) to \(23.55^{\circ} \mathrm{C}\). If the calorimeter had a heat capacity of \(11.09 \mathrm{~kJ} / \mathrm{K},\) what was the heat released \(\left(q_{v}\right)\) per gram of hydrocarbon?

Short answer

The heat released per gram of hydrocarbon is 25.88 kJ/g.

Step-by-step solution

Identify Given Values

Start by listing the values provided in the problem:- Mass of hydrocarbon: \(m = 1.520 \text{ g}\)- Initial water temperature: \(T_i = 20.00^{\text{\circ} \text{C}}\)- Final water temperature: \(T_f = 23.55^{\text{\circ} \text{C}}\)- Heat capacity of the calorimeter: \(C = 11.09 \text{ kJ/K}\).

Calculate Temperature Change

Determine the change in temperature using the formula \(\Delta T = T_f - T_i\).Calculate: \[\Delta T = 23.55^{\text{\circ} \text{C}} - 20.00^{\text{\circ} \text{C}} = 3.55^{\text{\circ} \text{C}}\]

Calculate Heat Released

Using the formula \(q_v = C \cdot \Delta T\), where \(q_v\) is the heat released, multiply the heat capacity by the temperature change.Calculate: \[q_v = 11.09 \text{ kJ/K} \cdot 3.55 \text{ K} = 39.34 \text{ kJ}\]

Calculate Heat Released per Gram

Divide the total heat released by the mass of the hydrocarbon to get the heat released per gram.Calculate: \[\text{Heat released per gram} = \frac{39.34 \text{ kJ}}{1.520 \text{ g}} = 25.88 \text{ kJ/g}\]

Key concepts

Heat Capacity

Heat capacity is a measure of the amount of heat energy required to raise the temperature of an object or substance by a certain amount. In our problem, the calorimeter has a heat capacity of 11.09 kJ/K. This means that for every degree Kelvin (or Celsius, since the size of one degree is the same in both scales) increase in temperature, the calorimeter absorbs 11.09 kJ of energy. This concept is important in calorimetry because it allows us to determine the amount of energy transferred during a chemical reaction. Heat capacity can be either specific (per mass unit) or total, as in this problem.

Temperature Change

When we talk about temperature change, we refer to the difference in temperature before and after an event or reaction. In this exercise, the initial temperature (T_i) is 20.00°C and the final temperature (T_f) is 23.55°C. The change in temperature (ΔT) is calculated as: ΔT = T_f - T_i = 23.55°C - 20.00°C = 3.55°C. Knowing the temperature change is crucial because it helps determine the heat energy absorbed or released by the system. In this instance, we need ΔT to find out how much energy was released during the hydrocarbon combustion.

Hydrocarbon Combustion

Combustion of hydrocarbons is a chemical reaction where a hydrocarbon reacts with oxygen to produce carbon dioxide, water, and heat. This type of reaction is highly exothermic, meaning it releases a significant amount of energy. In the given problem, the hydrocarbon combusted produces a temperature rise in the calorimeter, allowing us to measure this release of energy. Understanding hydrocarbon combustion is fundamental not only in calorimetry but also in fields such as energy production, where it is a primary source of heat and power. The general reaction is: CxHy + O2 → CO2 + H2O + heat.

Calorimetry Calculations

Calorimetry involves measuring the heat of chemical reactions or physical changes. Here, it helps us calculate the heat released by the combustion of the hydrocarbon. The steps to do this are:

• Determine the temperature change (ΔT) which was found to be 3.55°C.
• Use the known heat capacity (C) of the calorimeter to find total heat released (q_v) using the formula q_v = C ΔT: q_v = 11.09 kJ/K 3.55 K = 39.34 kJ.
• Lastly, calculate the heat released per gram of hydrocarbon by dividing q_v by the mass of the hydrocarbon: (39.34 kJ) / (1.520 g) = 25.88 kJ/g.

These steps provide a comprehensive way to measure the energy changes in a reaction, helping to understand the energy dynamics of chemical processes.