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

146 kJ

Step-by-step 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} * \frac{\text{1 mol}}{\text{55.84 g}} = \text{10.30 mol}\\\\q_(2) = n\Delta_{\text{sol}}H = \text{10.30 mol} * \frac{\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.