A 0.1375 -g sample of solid magnesium is burned in a constant-volume bomb calorimeter that has a heat capacity of \(3024 \mathrm{~J} /{ }^{\circ} \mathrm{C}\). The temperature increases by \(1.126^{\circ} \mathrm{C}\). Calculate the heat given off by the burning \(\mathrm{Mg}\), in \(\mathrm{kJ} / \mathrm{g}\) and in \(\mathrm{kJ} / \mathrm{mol}\).

Heat capacity, a fundamental concept in thermodynamics, refers to the amount of heat energy required to raise the temperature of a substance by one degree Celsius. It's an intrinsic property of matter that varies with the kind and amount of substance. In the context of bomb calorimetry, the heat capacity of the calorimeter is crucial for measuring the heat of combustion. It's the total heat capacity of the calorimeter system, including its water and other components.

In essence, knowing the heat capacity allows us to calculate the total amount of heat absorbed or released during a chemical reaction, simply by observing the temperature change. For example, in our exercise, the calorimeter has a heat capacity of 3024 J/°C, which helps to ascertain the total heat released when the magnesium burns.

The enthalpy of combustion is the change in enthalpy when one mole of a substance burns completely in oxygen under standard conditions. It is usually expressed in kJ/mol and is always negative since combustion is typically exothermic (releases heat).

The measurement of the enthalpy of combustion is vital to understanding how much energy a substance can release, which has practical applications ranging from fuels to food. In bomb calorimetry, precisely measuring the temperature change during the combustion within the calorimeter allows us to calculate the enthalpy of combustion for the reaction. The exercise provided exemplifies this by calculating how much heat is given off per mole of magnesium burned.

Calorimeter calculations are carried out to understand the energy changes during a chemical reaction. In a bomb calorimeter, a sample is burned in an oxygen-rich environment, and the resulting temperature change can be used to determine the amount of heat released using calorimeter calculations.

The equation Q = C × ΔT is essential for these calculations, where Q is the total heat released, C is the calorimeter's heat capacity, and ΔT is the temperature change observed. From the total energy released, you can derive the energy per gram or per mole of the substance combusted, which then provides in-depth information on the energetic efficiency of chemical reactions. Improvements in the explanation of these calculations can aid students in better understanding the relationship between measured physical changes and thermodynamic properties.

Specific heat is closely related to heat capacity but differs in that it's the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius. It's a more precise measurement than heat capacity because it's independent of the amount of substance being measured.

The specific heat value is vital for scientists and engineers because it allows them to predict how different materials will respond to heat. This is important when designing heating and cooling systems, for example. In our problem, calculating the heat given off per gram of magnesium involves understanding specific heat, as it helps determine how much energy is released by the mass of the burned substance. Such understanding allows students to bridge the gap between theoretical concepts and actual physical properties of materials.