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.

Answer 1

Answer: The heat of reaction for the combustion of titanium is 15240 kJ/mol

Explanation:

The quantity of heat required to raise the temperature of a substance by one degree Celsius is called the specific heat capacity.

$Q=C\times \Delta T$

Q = Heat absorbed by calorimeter =?

C = heat capacity of calorimeter = 9.84 kJ/K

Initial temperature of the calorimeter  = $T_i$ = $25.00^0C=(25.00+273)=298.00K$

Final temperature of the calorimeter  = $T_f$  = $91.60^0C=(91.60+273)K=364.6K$

Change in temperature ,$\Delta T=T_f-T_i=(364.6-298.0)K=66.60K$

Putting in the values, we get:

$Q=9.84kJ/K\times 66.60K=655.3kJ$

As heat absorbed by calorimeter is equal to heat released by combustion of titanium

$Q=q$

$\text{Moles of titanium}=\frac{\text{given mass}}{\text{Molar Mass}}=\frac{2.060g}{47.8g/mol}=0.0430mol$  

Heat released by 0.0430 moles of titanium = 655.3 kJ

Heat released by 1 mole of titanium = $\frac{655.3}{0.0430}\times 1=15240kJ$

The heat of reaction for the combustion of titanium is 15240 kJ/mol