The standard enthalpy of combustion of methane ( CH ₄ ) at 300 K is -895 kJ mol ⁻¹ . When 3.2 g of methane is burnt in a bomb calorimeter at 300 K , the temperature of the calorimeter system increases by 4 K . The heat capacity of the calorimeter system is ________ J K ⁻¹ . (Nearest integer) [Given: R = 8.3 J K ⁻¹ mol ⁻¹ , molar mass of C and H are 12 and 1 g mol ⁻¹ respectively. Assume ideal gas behaviour.]

Step-by-step solution

The combustion reaction of methane is: CH ₄( g ) + 2 O ₂( g ) CO ₂( g ) + 2 H ₂ O ( l ) The change in the number of gaseous moles is: n_g = 1 - (1 + 2) = -2 The relationship between enthalpy change ( H ) and internal energy change ( U ) is: H = U + n_g RT Substituting the given values: -895 = U + -2 8.3 300 1000 -895 = U - 4.98 U = -890.02 kJ mol ⁻¹ The molar mass of CH ₄ is 16 g mol ⁻¹ . Moles of methane burnt = 3.2 16 = 0.2 mol The heat released at constant volume ( q_v ) for 0.2 mol is: q_v = 0.2 890.02 = 178.00