Chapter 15.3, Problem 23PP

Interpretation Introduction

Interpretation: The heat required to melt 25.7 g of solid methanol at its melting point is to be calculated.

Concept introduction:

Heat of fusion: The energy needed to melt 1g of a substance.

Answer to Problem 23PP

2.576 kJ

Explanation of Solution

The following steps are needed to calculate the heat required to melt solid methanol:

• Calculate the molar mass of methanol.
• Calculate the number of moles contained in 25.7g of solid methanol.
• Calculate the heat required to melt the solid methanol using the formula,

  $\text{Q}=\text{N}\times \text{Δ}{\text{H}}_{\text{fusion}}$

The heat of fusion, $\text{Δ}{\text{H}}_{\text{fusion}}$ , for methanol ${\text{CH}}_3\text{O}\text{H}=3.22\raisebox{1ex}{$\text{k}\text{J}$}\!\left/ \!\raisebox{-1ex}{$\text{m}\text{o}\text{l}$}\right.$ .

Molar mass of methanol ${\text{CH}}_3\text{O}\text{H}=12\times 1+1\times 3+16\times 1+1\times 1=32\raisebox{1ex}{$\text{g}$}\!\left/ \!\raisebox{-1ex}{$\text{m}\text{o}\text{l}$}\right.$ .

  $\text{Q}=\text{N}\times \text{Δ}{\text{H}}_{\text{fusion}}$ (N in moles)

  $\text{N}=\frac{\text{mass}}{32\raisebox{1ex}{$\text{g}$}\!\left/ \!\raisebox{-1ex}{$\text{m}\text{o}\text{l}$}\right.}=\frac{25.7}{32}\approx 0.8$

  $\text{Q}=0.8\times 3.22\raisebox{1ex}{$\text{k}\text{J}$}\!\left/ \!\raisebox{-1ex}{$\text{m}\text{o}\text{l}$}\right.=2.5\text{76 kJ}$

Conclusion

The heat required to melt 25.7 g of solid methanol is 2.576 kJ.