A gas (Molar mass = 280 g mol$$^{-1}$$) was burnt in excess $$O_2$$ in a constant volume calorimeter and during combustion the temperature of calorimeter increased from 298.0 K to 298.45 K. If the heat capacity of calorimeter is 2.5 kJ K$$^{-1}$$ and enthalpy of combustion of gas is 9 kJ mol$$^{-1}$$ then amount of gas burnt is _____ g.

We need to find the amount of gas burnt in a constant volume calorimeter.

The molar mass of the gas is 280 g mol$$^{-1}$$, the observed temperature rise is $$\Delta T = 298.45 - 298.0 = 0.45$$ K, the heat capacity of the calorimeter is $$C = 2.5$$ kJ K$$^{-1}$$, and the enthalpy of combustion is $$\Delta_c H = 9$$ kJ mol$$^{-1}$$.

The heat released is calculated by multiplying the calorimeter heat capacity by the temperature change:

$$q = C \times \Delta T = 2.5 \times 0.45 = 1.125 \text{ kJ}$$

This heat corresponds to the moles of gas burnt times the magnitude of the enthalpy of combustion:

$$q = n \times |\Delta_c H|$$

$$1.125 = n \times 9$$

$$n = \frac{1.125}{9} = 0.125 \text{ mol}$$

The mass of gas consumed follows from the number of moles and the molar mass:

$$\text{Mass} = n \times M = 0.125 \times 280 = 35 \text{ g}$$

Hence, the answer is 35 g.