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

Step-by-step 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* \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* 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}}=(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 =
`(655.3)/(0.0430)* 1=15240kJ`

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