Final answer:
a) The thermal capacity of the calorimeter is approximately 314 kJ/°C. b) The energy of acetylene combustion is approximately -388 kJ/mol.
Step-by-step explanation:
a) To calculate the thermal capacity of the calorimeter, we can use the equation q = mCΔT, where q is the heat absorbed or released, m is the mass of the substance, C is the specific heat capacity, and ΔT is the change in temperature. In this case, we can assume that the whole system (calorimeter and sample) is at the same temperature, so the heat released by the sample is equal to the heat absorbed by the calorimeter. The heat released by the sample can be calculated using the equation q = nΔH, where n is the number of moles and ΔH is the enthalpy change. Let's solve for the thermal capacity (C) using the given values:
a) q_sample = q_calorimeter => n_sample * ΔH_sample = C_calorimeter * ΔT_calorimeter
Given: mass_sample = 6.79 g, ΔH_sample = -802 kJ/mol, ΔT_calorimeter = 10.8 °C
To find C_calorimeter, we need to calculate the number of moles in the sample:
Number of moles = mass_sample / molar_mass_methane = 6.79 g / 16.04 g/mol = 0.4234 mol
Now we can plug in the values and solve for C_calorimeter:
0.4234 mol * -802 kJ/mol = C_calorimeter * 10.8 °C
C_calorimeter = (0.4234 mol * -802 kJ/mol) / 10.8 °C
C_calorimeter = -314.0944 kJ/°C
Therefore, the thermal capacity of the calorimeter is approximately 314 kJ/°C.
b) To find the energy of acetylene combustion, we can use the same equation q = nΔH. Since acetylene (C2H2) has a different molar mass than methane (CH4), we need to recalculate the number of moles in the sample:
Given: mass_acetylene = 12.6 g, molar_mass_acetylene = 26.038 g/mol
Number of moles = mass_acetylene / molar_mass_acetylene = 12.6 g / 26.038 g/mol = 0.4839 mol
Now we can plug in the values and solve for the energy of acetylene combustion:
q_acetylene = n_acetylene * ΔH_methane = 0.4839 mol * -802 kJ/mol = -387.5 kJ/mol
Therefore, the energy of acetylene combustion is approximately -388 kJ/mol.