contestada

When 1.960 g of titanium is combusted in a bomb calorimeter, the temperature of the calorimeter increases from 25.00 °C to 86.98 °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.

Respuesta :

Answer : The heat of combustion of one mole of Ti is -14897.4 kJ/mole

Explanation :

First we have to calculate the heat gained by the calorimeter.

[tex]q=c\times (T_{final}-T_{initial})[/tex]

where,

q = heat gained by calorimeter = ?

c = specific heat = [tex]9.84kJ/K[/tex]

[tex]T_{final}[/tex] = final temperature = [tex]25.00^oC=273+25.00=298.00K[/tex]

[tex]T_{initial}[/tex] = initial temperature = [tex]86.98^oC=273+86.98=359.98K[/tex]

Now put all the given values in the above formula, we get:

[tex]q=9.84kJ/K\times (359.98-298.00)K[/tex]

[tex]q=609.9kJ[/tex]

Heat released by the reaction = - Heat gained by calorimeter = -609.9 kJ

Now we have to calculate the heat of combustion of one mole of Ti.

To calculate the number of moles of Ti:

Molar mass of Ti = 47.87 g/mole

Number of moles Ti = [tex]\frac{\text{Mass of Ti}}{\text{Molar mass of Ti}}=\frac{1.960g}{47.87g/mol}=0.04094mole[/tex]

Heat of combustion of one mole of Ti = [tex]-\frac{609.9kJ}{0.04094mole}=-14897.4kJ/mole[/tex]

Therefore, the heat of combustion of one mole of Ti is -14897.4 kJ/mole