Question

The following reaction using hydrogen and oxygen is carried out in a bomb calorimeter: \(2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(\ell)\). The following data are recorded: Weight of water in calorimeter = \(2.650 \mathrm{~kg} .\) Initial temperature of water \(=24.442^{\circ} \mathrm{C} .\), Final temperature of water after reaction \(=25.635^{\circ} \mathrm{C}_{.}\), Specific heat of reaction vessel is \(0.200 \mathrm{Kcal}^{1}-\mathrm{kg}\), the weight of the calorimeter is \(1.060 \mathrm{~kg}\), and the specific heat of water is \(1.00\) \(\mathrm{Kcal}^{\circ}-\mathrm{kg}\), calculate the heat of reaction. Assuming that \(0.050\) mole of water was formed in this experiment, calculate the heat of reaction per mole of liquid water formed. Neglect the specific heat of the thermometer and stirrer.

Short answer

The heat of the reaction per mole of liquid water formed is 68.24 \(Kcal/mol\).

Step-by-step solution

Calculate the heat absorbed by the water

The equation for heat gained by water (Q) is given by \[ Q = m \times C \times \Delta T \] where \(m\) = mass of the water in the calorimeter, \(C\) = specific heat of water, and \(\Delta T\) = difference in initial and final temperature. Given that \(m = 2.650 \, kg\), \(C=1.00 \, Kcal^{\circ} kg^{-1}\), and \(\Delta T = 25.635 - 24.442 = 1.193 ^{\circ}C\), we can substitute these values into the equation to get \(Q = 2.650 \times 1.00 \times 1.193 = 3.16 \, Kcal\).

Calculate the heat absorbed by the calorimeter

The equation for heat gained by the calorimeter (Q') is given by \[ Q' = m' \times C' \times \Delta T \] where \(m'\) = mass of the calorimeter, \(C'\) = specific heat of the calorimeter, and \(\Delta T\) = difference in initial and final temperature. Given that \(m' = 1.060 \, kg\), \(C'=0.200 \, Kcal^{\circ} kg^{-1}\), and \(\Delta T = 1.193 ^{\circ}C\), we can substitute these values into the equation to get \(Q' = 1.060 \times 0.200 \times 1.193 = 0.252 \, Kcal\).

Calculate the total heat of reaction

The total heat of reaction (Q_total) is the sum of the heat absorbed by the water and the calorimeter. So, \[ Q_{total} = Q + Q' = 3.16 + 0.252 = 3.412 \, Kcal\]

Calculate the heat of reaction per mole

The heat of reaction per mole is given by \[ Q_{per mole} = Q_{Total} \div number \, of \, moles \] Given that the number of moles of water formed = 0.050, we can substitute these values into the equation to get \[ Q_{per mole} = 3.412 \div 0.050 = 68.24 \, Kcal/mol\]. Therefore, the heat of the reaction per mole of liquid water formed is 68.24 \(Kcal/mol\).

Key concepts

Heat of Reaction

The heat of reaction is crucial in understanding the energy changes during a chemical reaction. It refers to the total amount of heat that is either absorbed or released when a substance undergoes a chemical transformation. In the exercise, we analyzed the reaction of hydrogen and oxygen forming water in a bomb calorimeter. The heat of reaction here is calculated by adding up the heat absorbed by both the water and the calorimeter itself.
This value is expressed in kilocalories (Kcal), which indicates how much energy the reactants either absorb or release. In our case, after performing the calculations for the calorimeter experiment, it was determined that the reaction releases around 3.412 Kcal in total.

• The reaction involves 0.050 moles of water being formed.
• We calculated the heat of reaction per mole of liquid water formed as 68.24 Kcal/mol.

Knowing the heat of reaction is essential for gauging the efficiency and energy needs of chemical processes.

Specific Heat

Specific heat is a measure of how much heat energy is needed to raise the temperature of a specific mass of a substance by one degree Celsius. This property is unique to each material, and it plays a critical role in calorimetry experiments, like the one described in the exercise.
Water, for example, has a specific heat of 1.00 Kcal/kg°C. This means you need 1 Kcal to increase the temperature of one kilogram of water by one degree Celsius. During our calculations, the specific heat helped us determine how much energy was absorbed by the water in the calorimeter.

• The calculation for the heat absorbed used the formula: \( Q = m \times C \times \Delta T \).
• This led to finding that the water absorbed approximately 3.16 Kcal.

The bomb calorimeter had its specific heat too, which was 0.200 Kcal/kg°C. Adding both heats absorbed by the water and the calorimeter allowed us to find the total heat of reaction.

Bomb Calorimeter

A bomb calorimeter is a robust device designed to measure the heat of reaction by absorbing energy released during chemical reactions. It's used when studying exothermic reactions, such as the reaction of hydrogen and oxygen in our exercise.
The bomb calorimeter consists of a sturdy, sealed container where the reaction occurs. This setup ensures no heat escapes, allowing for accurate measurements of the energy changes during the reaction. Several key components contribute to its efficiency:

• The reaction chamber holds the substance.
• The surrounding water absorbs the heat.
• Sensors measure temperature changes accurately.

The calorimeter provides a controlled environment, ensuring that our measurements reflect the energy changes precisely. Calculating the heat absorbed by both the water and the calorimeter's vessel helps us find the total energy change, which is crucial in determining the heat of reaction.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products, often accompanied by energy changes, either as absorption (endothermic) or release (exothermic). In our exercise, hydrogen and oxygen gases undergo a chemical reaction to form liquid water.
Understanding chemical reactions requires knowing:

• Reactants: Hydrogen (\( H_2 \)) and Oxygen (\( O_2 \)).
• Products: Water (\( H_2O \)).
• Reaction type: Exothermic, given that it releases heat.

Such reactions can be influenced by various factors, including temperature, pressure, and catalysts. For instance, the conditions in the bomb calorimeter ensure a closed, controlled environment.
Through these changes, chemical reactions help us understand not just the formation and separation of substances but also the energy dynamics that accompany them. Insight into these dynamics is particularly valuable for students studying thermochemistry and the practical applications of reactions.