The reaction of \(1.40 \mathrm{~g}\) of carbon monoxide with excess water vapor to produce carbon dioxide and hydrogen gases in a bomb calorimeter causes the temperature of the calorimeter assembly to rise from \(22.113^{\circ} \mathrm{C}\) to \(22.799^{\circ} \mathrm{C}\). The calorimeter assembly is known to have a total heat capacity of \(3.00 \mathrm{~kJ} \cdot\left({ }^{\circ} \mathrm{C}\right)^{-1}\). (a) Write a balanced equation for the reaction. (b) Calculate the internal energy change, \(\Delta U\), for the reaction of \(1.00 \mathrm{~mol} \mathrm{CO}(\mathrm{g})\).

Thermochemistry is the branch of chemistry that deals with the heat involved in chemical reactions. It's all about understanding how energy is absorbed or released during a reaction. This includes studying concepts like endothermic and exothermic reactions, which either absorb or release heat, respectively.

In our textbook problem, we analyze a reaction in a bomb calorimeter, a device used to measure the heat of combustion of a substance. By tracking temperature changes, we can determine the heat involved in a chemical reaction. This information, in turn, can be used to calculate the change in internal energy, another key concept in thermochemistry, which we'll look at in more detail.

A balanced chemical equation is fundamental to any study of a chemical reaction. It represents the conservation of mass by ensuring that the same number of atoms of each element is involved in both the reactants and products. Getting this right lets us accurately predict how much of each substance will be consumed or produced.

In the given example, balancing the equation of carbon monoxide reacting with water vapor was the first step before any further calculations could be made. The balanced equation not only guides us through the stoichiometry of the reactants and products but is also crucial when calculating the heat change during the reaction, which ultimately helps determine the internal energy change.

Internal energy change, often denoted as \( \Delta U \), is the total change in energy within a system. In the context of our textbook problem, the system is the reaction mixture within the bomb calorimeter. When a chemical reaction occurs, bonds are broken and formed, which involves either consumption or release of energy.

Since the bomb calorimeter operates at constant volume, no work is done on or by the system, so the internal energy change \( \Delta U \) is simply the amount of heat absorbed or released during the reaction. For our exercise, after finding the amount of heat absorbed by the calorimeter, we use stoichiometry to adjust this value to a per-mole basis, which gives us the internal energy change for the reaction of one mole of CO. This information is critical for anyone studying thermodynamics or involved in energy management within chemical processes.

Heat capacity is a measure of how much heat energy is needed to raise the temperature of a given quantity of substance by a certain temperature interval, typically one degree Celsius or Kelvin. It's expressed in units such as joules per degree Celsius (J/°C) or kilojoules per degree Celsius (kJ/°C).

Every substance has a characteristic heat capacity, which plays a major role in how it responds to heat. For example, water has a high heat capacity, meaning it can absorb a lot of heat without a significant change in temperature. This property is particularly important in bomb calorimetry, as the heat capacity of the calorimeter assembly dictates how much the temperature will change for a given amount of heat produced in the reaction. In our exercise, knowing the calorimeter's heat capacity is essential for accurate calculation of the heat absorbed, which then allows us to determine the internal energy change for the reaction.