Question

The combustion of titanium with oxygen produces titanium dioxide: Ti(s) + O2(g) → TiO2(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: 64800 kJ/mol

Explanation:

Heat gained by bomb calorimeter =Q

Heat capacity of bomb calorimeter , C =9.84 kJ/K =

Change in temperature = ΔT= (91.60-25.00) °C = 66.6°C  = 66.6 K

$Q=C\times \Delta T=9.84KJ\times 66.6K= 655.34kJ$

Let the heat released during reaction be q.

$q=m\times c\times \Delta T$

Total heat released during reaction is equal to total heat gained by water and bomb calorimeter.

$q=Q=655.34kJ$

Thus 2.060 g of titanium releases = 655.34 kJ of heat

1 g of titanium releases =$\frac{655.34}{2.060}\times 1=1350kJ$ of heat

1 mole or 48 g of titanium releases =$\frac{1350}{1}\times 48=64800kJ$ of heat

Thus heat given off by the burning titanium, in kJ/mol is 64800.