Heat Capacity and Specific Heat

The heat capacity (C) of a sample of substance is the quantity of heat needed to raise the temperature of the sample of substance by one degree Celsius (or Kelvin).  

q = cΔt  

Heat capacity is directly proportional to the amount of substance.  

The specific heat capacity is the quantity of heat required to raise the temperature of one gram of a substance by one degree Celsius at constant pressure.  

q = s × m × Δt  

where q is the heat required to raise temperature  

            m = mass in grams  

            s = specific heat of the substance  

            Δt = temperature difference    

VARIATION OF HEAT OF REACTION WITH TEMPERATURE  

The heat of reaction depends on the temperature. The relation between the two is known asKirchoff’s equation.  

(i) ΔH₂ – ΔH₁ / T₂ – T₁ = ΔC_P                     (ii) ΔE₂ – ΔE₁ / T₂ – T₁ = ΔC_V 

ΔC_P = molar heat capacity of products – molar heat capacity of reactants (at constant pressure)  

ΔC_v = molar heat capacity of products – molar heat capacity of reactants (at constant volume)    

Sample problem: The standard heat of formation listed for gaseous NH₃ is -11.02 kcal/mol at 

298 K. Given that at 298 K, the constant pressure heat capacities of gaseous N₂, H₂ and NH₃ are respectively 6.96, 6.89, 8.38 cal/mol. Determine ΔH⁰_298K and ΔH_{773 K} for the reactions,      

                  1/2 N₂ (g) + 3/2 H₂ (g) ——> NH₃(g)       

Solution: 1/2 N₂ (g) + 3/2 H₂ (g) ——> NH₃(g)       

             ΔH_298K = Σ(H_f)_p – Σ(H_f)_R = –(11.02 – 0)

                       = -11.02 kcal mol^-1  

                        ΔH₂ = -13.6 kcal mol^-1  

Exercise:       

The specific heats of iodine vapour and solid are 0.031 and 0.055 cals/g respectively. If heat of sublimation of iodine is 24 cals/g at 200°C, Calculate its value at 250 °C.