What mass of ethanol in g must be added to 1. | vedclass

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(C) Let the mass of ethanol be $w \, g$. The molar mass of ethanol $(C_2H_5OH)$ is $46 \, g/mol$. The number of moles of ethanol is $n_{ethanol} = \fr

Vedclass · Accepted Answer

$638.89$

Vedclass · Answer

(C) Let the mass of ethanol be $w \, g$. The molar mass of ethanol $(C_2H_5OH)$ is $46 \, g/mol$. The number of moles of ethanol is $n_{ethanol} = \frac{w}{46}$.Water has a mass of $1.0 \, kg = 1000 \, g$. The molar mass of water $(H_2O)$ is $18 \, g/mol$. The number of moles of water is $n_{water} = \frac{1000}{18} \approx 55.56 \, mol$.The mole fraction of ethanol is given by $x_{ethanol} = \frac{n_{ethanol}}{n_{ethanol} + n_{water}} = 0.2$.Substituting the values: $\frac{w/46}{w/46 + 55.56} = 0.2$.$w/46 = 0.2 	imes (w/46 + 55.56)$.$w/46 = 0.2(w/46) + 11.112$.$0.8(w/46) = 11.112$.$w/46 = 13.89$.$w = 13.89 	imes 46 = 638.94 \, g \approx 638.89 \, g$.

What mass of ethanol in $g$ must be added to $1.0 \, kg$ of water to have a mole fraction of ethanol equal to $0.2$?

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