Propane is often used as a home fuel in areas where natural...

Propane is often used as a home fuel in areas where natural gas is not available. When $3.00$ grams of propane, $\mathrm{C}_{3} \mathrm{H}_{8}(g)$, are burned in excess oxygen in a bomb calorimeter that has a total heat capacity of $32.7 \mathrm{~kJ} \cdot \mathrm{K}^{-1}$, the temperature of the calorimeter increases by $4.25 \mathrm{~K} .$ Calculate the standard enthalpy of combustion in kilojoules per gram and kilojoules per mole of propane. Assume that $\Delta H_{\mathrm{rxn}} \approx \Delta U_{\mathrm{rxn}}$

Key Concepts

Unit Conversion

Unit conversion is a critical concept in both experimental and theoretical chemistry, as it involves translating measurements from one unit system to another. In the context of combustion and calorimetry, converting energy quantities from per gram to per mole requires the use of the molar mass of the substance, ensuring that the reported energy values can be applied to stoichiometric calculations and comparisons across different substances.

Standard Enthalpy of Combustion

The standard enthalpy of combustion refers to the heat released when one mole of a substance is completely burned in oxygen under standard conditions. It is a thermodynamic quantity that indicates the energy density of a fuel. In bomb calorimetry, which operates at constant volume, the measured change in internal energy is often used as an approximation for the enthalpy change when the pressure-volume work is negligible.

Bomb Calorimetry

Bomb calorimetry is an experimental technique used to measure the energy change of combustion reactions conducted at constant volume. In such a setup, the fuel is burned in a sealed container (the bomb) surrounded by a water bath or another thermal mass with a known heat capacity, and the temperature change is measured. This method is particularly useful for accurately determining the energy content of fuels.

Heat Capacity

Heat capacity is a measure of the amount of energy required to raise the temperature of an object or system by a given temperature interval. In calorimetry, knowing the total heat capacity of the calorimeter allows one to compute the energy released or absorbed during a reaction by relating the temperature change to the stored thermal energy.

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