Question

The combustion of titanium with oxygen produces titanium dioxide:

Ti _(s) + O_{2 (g)} → TiO_{2 (s)}

When 2.060 g of titanium is combusted in a bomb calorimeter, the temperature of the calorimeter increases from 25.00 °C to 91.60 °C. In a separate experiment, the heat capacity of the calorimeter is measured to be 9.84 kJ/K. The heat of reaction for the combustion of a mole of Ti in this calorimeter is __________ kJ/mol.

Ti = 47.867 amu

O₂ = 31.9988 amu

TiO₂ = 79.8650 amu

Report answer in scientific notation use En rather than x 10ⁿ

Answer 1

The standard heat capacity equation is:
Q = (C)(Tf - Ti)
Where Q = molar heat ,

C= the molar heat capacity, 9.84 kJ/K

But, the Kelvin units are the exact same magnitude as Celcius means 1K=1C therefore, the heat capacity of the calorimeter = 9.84 kJ/C.

(Tf - Ti) is the temperature change = 91.60 °C -25.00 °C = 66.6 °C

Then

Q = 9.84 kJ/C*66.6 °C

Q = 655.344 kJ total energy

Now determine the moles of titanium as follows:

the molar mass of titanium = (47.867g/mol)

2.060g / 47.867g/mol = 0.0430 moles.

To calculate the energy which was realesed per mole of reactant use the following expression:

total energy / number of mole = 655.344 kJ /0.0430 moles =1.524 x 10^4 kJ / mol