Question

How much heat is lost when 575 grams molten iron at 1825 k becomes solid iron at 293 k? The melting point or iron is 1811 k.​

Answer 1

Answer:

146 kJ  

Explanation:

There are two heat flows in this question.  

Heat lost on cooling + heat lost on solidifying = 0  

                 q₁              +                 q₂                   = 0  

              mCΔT          +             nΔHsol              = 0  

Data:  

       m = 575 g  

       C = 0.449 J·K⁻¹g⁻¹  

    T_i = 1825 K  

    T_f = 1811 K  

ΔHsol = -13.8 kJ·mol⁻¹  

Calculations:  

(a) Heat lost on cooling  

ΔT = T_f - T_i = 1811 K - 1825 K = -14 K  

q₁ = mCΔT = 575 g × 0.449 J·K⁻¹g⁻¹ × (-14 K) = -361 J = -3.61 kJ  

(b) Heat lost on solidifying  

$n = \text{575 g} \times \dfrac{\text{1 mol}}{\text{55.84 g}} = \text{10.30 mol}\\\\q_{2} = n\Delta_{\text{sol}}H = \text{10.30 mol} \times \dfrac{\text{-13.8 kJ}}{\text{1 mol}}= \text{-142.1 kJ}$

(c) Total heat lost  

q = q₁ + q₂ = -3.61 kJ - 142.1 kJ = -146 kJ  

The heat lost was 146 kJ.