Final answer:
The heat of reaction for the combustion of a mole of titanium in the given calorimeter setup is approximately 14765.89 kJ/mol, as determined by calculating the total heat absorbed using the calorimeter's heat capacity and the mass and molar mass of titanium.
Step-by-step explanation:
When 1.640 g of titanium is combusted in a bomb calorimeter, the resulting temperature increase from 25.00 °C to 76.50 °C can be used to calculate the heat of reaction for the combustion of a mole of titanium. Given that the heat capacity of the calorimeter is 9.84 kJ/°C, we can determine the total heat absorbed by the calorimeter during the reaction.
First, we calculate the total heat absorbed (q) by multiplying the heat capacity (C) by the change in temperature (ΔT):
q = C × ΔT
q = 9.84 kJ/°C × (76.50 °C - 25.00 °C)
q = 9.84 kJ/°C × 51.50 °C
q = 506.34 kJ
Next, to find the heat of reaction per mole of titanium, we convert the mass of titanium to moles using its molar mass (47.87 g/mol):
Number of moles = mass / molar mass
Number of moles = 1.640 g / 47.87 g/mol
Number of moles ≈ 0.0343 mol
Now, we can determine the heat of reaction per mole:
Heat of reaction per mole = q / Number of moles
Heat of reaction per mole ≈ 506.34 kJ / 0.0343 mol
Heat of reaction per mole ≈ 14765.89 kJ/mol
The heat of reaction for the combustion of a mole of Ti in this calorimeter is approximately 14765.89 kJ/mol.