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Raoult’s law and vapor pressure (8282)
Viernes 9 de agosto de 2024, por
Calculate the vapor pressure at 
of a solution containing 150 grams of glucose dissolved in 140 grams of ethyl alcohol. The vapor pressure of ethyl alcohol at is 43 mm Hg.
Glucose is 
and has a molecular mass of 180 g/mol. Ethyl alcohol is 
and has a molecular mass of 46 g/mol. Using this data, calculate the moles of each substance and determine the mole fraction of alcohol in the mixture.
![150\ \cancel{g}\ \ce{C6H12O6}\cdot \frac{1\ \text{mol}}{180\ \cancel{g}} = \color[RGB]{0,112,192}{\textbf{0.833\ mol\ \ce{C6H12O6}}}](local/cache-vignettes/L437xH52/fd9d7256ed701275e28a18d4b2a24909-cd4bd.png?1733069638 "150\ \cancel{g}\ \ce{C6H12O6}\cdot \frac{1\ \text{mol}}{180\ \cancel{g}} = \color[RGB]{0,112,192}{\textbf{0.833\ mol\ \ce{C6H12O6}}}")
![140\ \cancel{g}\ \ce{C2H6O}\cdot \frac{1\ \text{mol}}{46\ \cancel{g}} = \color[RGB]{0,112,192}{\textbf{3.043\ mol\ \ce{C2H6O}}}](local/cache-vignettes/L403xH52/8459314dac433cb5b7765e119baad222-dba0d.png?1733069638 "140\ \cancel{g}\ \ce{C2H6O}\cdot \frac{1\ \text{mol}}{46\ \cancel{g}} = \color[RGB]{0,112,192}{\textbf{3.043\ mol\ \ce{C2H6O}}}")
The mole fraction of alcohol is:
![x_{\ce{C2H6O}} = \frac{n_{\ce{C2H6O}}}{n_{\ce{C2H6O}} + n_{\ce{C6H12O6}}} = \frac{3.043\ \cancel{\text{mol}}}{(0.833 + 3.043)\ \cancel{\text{mol}}} = \color[RGB]{0,112,192}{\bf 0.785}](local/cache-vignettes/L555xH53/d684317ff9259ce1be15344d83f7b7b2-7a205.png?1733069638 "x_{\ce{C2H6O}} = \frac{n_{\ce{C2H6O}}}{n_{\ce{C2H6O}} + n_{\ce{C6H12O6}}} = \frac{3.043\ \cancel{\text{mol}}}{(0.833 + 3.043)\ \cancel{\text{mol}}} = \color[RGB]{0,112,192}{\bf 0.785}")
Now calculate the vapor pressure using Raoult’s law:
![P_{\ce{C2H6O}} = x_{\ce{C2H6O}}\cdot P_T = 0.785\cdot 43\ \text{mm Hg} = \fbox{\color[RGB]{192,0,0}{\textbf{33.75\ \ce{mm\ Hg}}}}](local/cache-vignettes/L568xH32/cd3edf3caa7b39581176da0db7a77539-71988.png?1733069638 "P_{\ce{C2H6O}} = x_{\ce{C2H6O}}\cdot P_T = 0.785\cdot 43\ \text{mm Hg} = \fbox{\color[RGB]{192,0,0}{\textbf{33.75\ \ce{mm\ Hg}}}}"){kind=small}