A 1.103 g sample of a gaseous carbon-hydrogenoxygen compound that occupies a volume of \(582 \mathrm{mL}\) at 765.5 Torr and \(25.00^{\circ} \mathrm{C}\) is burned in an excess of \(\mathrm{O}_{2}(\mathrm{g})\) in a bomb calorimeter. The products of the combustion are \(2.108 \mathrm{g} \mathrm{CO}_{2}(\mathrm{g}), 1.294 \mathrm{g} \mathrm{H}_{2} \mathrm{O}(1),\) and enough heat to raise the temperature of the calorimeter assembly from 25.00 to \(31.94^{\circ} \mathrm{C}\). The heat capacity of the calorimeter is \(5.015 \mathrm{kJ} /^{\circ} \mathrm{C}\). Write an equation for the combustion reaction, and indicate \(\Delta H^{\circ}\) for this reaction at \(25.00^{\circ} \mathrm{C}\).

Step by step solution

01

Calculation of moles of reactants

Start by calculating the amount (mol) of reactant using the ideal gas law: \(PV = nRT\). Where, P is the pressure, V is the volume, n is the number of moles, R is the gas constant and T is the temperature. In this case, we convert pressure from Torr to atm, volume from mL to L, and temperature from Celsius to Kelvin, and use the value of gas constant R = \(0.0821 L·atm/mol·K\). Thus, the moles of the carbon-hydrogen-oxygen compound can be calculated.

02

Calculation of moles of products

Then, we calculate the moles of \(CO_2\) and \(H_2O\) produced from the reaction. We know that 1 mol of \(CO_2\) has a mass of approximately 44.01 g and 1 mol of \(H_2O\) has a mass of approximately 18.015 g. Using the provided masses of \(CO_2\) and \(H_2O\), we can calculate their respective amounts (mol).

03

Formation of combustion equation

Based on the calculated mol of reactants and products, the combustion equation of the carbon-hydrogen-oxygen compound can be established. Assume the chemical formula of the compound is \(C_xH_yO_z\), then the combustion equation is \(C_xH_yO_z + aO_2 -> bCO_2 + cH_2O\), where a, b and c are coefficients determined by the stoichiometry of the reaction (the molar ratio between reactants and products).

04

Calculation of ΔH°

The temperature rise of the calorimeter assembly indicates the amount of heat \(q_p\) produced by the process, which is given by \(q_p= C \Delta T\), where C is the heat capacity of the calorimeter and \(\Delta T\) is the temperature change. Converting q_p to the enthalpy change \(\Delta H^\circ\) per mol of reaction requires the molar quantity of the C_xH_yO_z compound. The result can be obtained through \(\Delta H° = qp / mol(C_xH_yO_z)\).

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