\(\text{H}^+ + \text{OH}^- \rightarrow \text{H}_2\text{O}\)
m moles 120 40 – 80 – 40
Heat liberated from reaction
= 40 × 10–3× 57 × 103 J …(1)
Heat gained by solution = \(mC\Delta T\)
Mass of solution \(m = V × d = 1000 × 1 = 1000 g\)
Heat gained by solution \(= 1000 × 4.2 × ΔT …(2)\)
From eq (1) and eq (2)
Heat liberated = Heat gained
\(40 × 10–3 × 57 × 103 = 1000 × 4.2 × ΔT\)
\(ΔT = 54 ×\) 10–2 \(°C\)
\(ΔT = 54°C\) (Rounded off to the nearest integer)
So, the answer is 54°C.
The freezing point depression constant (\( K_f \)) for water is \( 1.86 \, {°C·kg/mol} \). If 0.5 moles of a non-volatile solute is dissolved in 1 kg of water, calculate the freezing point depression.