Question

Methanol and ethanol form a nearly ideal solution at 300K.A solution is made by mixing 32 g of methanol and 23 g of ethanol at 300 K .Calculate the partial pressure of its constituents and the total pressure of the solution.( At 300 K p0 CH3OH = 90 mm Hg p0 C2H5OH = 51 mm Hg

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{Moles}\mathrm{of}\mathrm{methanol}=\frac{\mathrm{Mass}}{\mathrm{Molar}\mathrm{mass}}=\frac{32\mathrm{g}}{32{\mathrm{gmol}}^{-1}}=1\mathrm{mol} \\ \mathrm{Moles}\mathrm{of}\mathrm{ethanol}=\frac{\mathrm{Mass}}{\mathrm{Molar}\mathrm{mass}}=\frac{23\mathrm{g}}{46{\mathrm{gmol}}^{-1}}=0.5\mathrm{mol} \\ \mathrm{Mole}\mathrm{fraction}\mathrm{of}\mathrm{methanol},{\mathrm{X}}_{{\mathrm{CH}}_3\mathrm{OH}}=\frac{\mathrm{Moles}\mathrm{of}\mathrm{methanol}}{\mathrm{Total}\mathrm{moles}} \\ \mathrm{or},{\mathrm{X}}_{{\mathrm{CH}}_3\mathrm{OH}}=\frac{1}{1+0.5}=\frac{1}{1.5}=0.67 \\ \mathrm{Mole}\mathrm{fraction}\mathrm{of}\mathrm{ethanol},{\mathrm{X}}_{{\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH}}=1-{\mathrm{X}}_{{\mathrm{CH}}_3\mathrm{OH}}=1-0.67=0.33 \\ \mathrm{Applying}\mathrm{Raoult}\text{'}\mathrm{s}\mathrm{law}, \\ \mathrm{Partial}\mathrm{Vapour}\mathrm{pressure}\mathrm{of}\mathrm{methanol}=0.67\times 90=60.3\mathrm{mm} \\ \mathrm{Partial}\mathrm{Vapour}\mathrm{pressure}\mathrm{of}\mathrm{ethanol}=0.33\times 51=16.83\mathrm{mm} \\ \mathrm{Total}\mathrm{pressure}=60.3\mathrm{mm}+16.82\mathrm{mm}=77.12\mathrm{mm} \end{gathered}$$