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  • Calculate the molarity of a solution of ethanol in water, in which the mole fraction of ethanol is 0.040 (assume the density of water to be one).

1.29    Calculate the molarity of a solution of ethanol in water, in which the mole fraction of ethanol is 0.040 (assume the density of water to be one).

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Given that the mole fraction of ethanol in water is 0.040.

Mole\ fraction\ of\ ethanol\ = \frac{Number\ of\ moles\ of\ ethanol}{Total\ number\ of\ moles\ of\ solution}

\Rightarrow X_{ethanol} = \frac{n_{ethanol}}{n_{water}+n_{ethanol}} = 0.040

To find the molarity we must have to find the number of moles of ethanol present in 1litre of solution.

Assuming the density of water to be 1 kg\ m^3.

Therefore, water is approximately equal to 1Litre.

The number of moles in 1L of water:

= \frac{1000g}{18g}\ mol^{-1} = 55.55\ moles

So, substituting in place of n_{water} = 55.55 in above equation we get,

\Rightarrow X_{ethanol} = \frac{n_{ethanol}}{55.55+n_{ethanol}} = 0.040

\Rightarrow 0.96\times n_{ethanol} = 55.55\times0.040

n_{ethanol} = 2.31\ mol

So, 2.31\ moles are present in 1L of solution.

Hence, the molarity of the solution is 2.31\ M

Posted by

Divya Prakash Singh

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