Question

What mass of ethanol be added to 1.0Kg water to have the mole fraction of ethanol equal to 0.20?

Answer 1

Let the mass of Ethanol be 'x' g.

We need the mole fraction of ethanol to be equal to 0.2.

Thus, no. of moles of ethanol / no. of moles of ethanol + water = 0.2

First, let us calculate the no. of moles of Water.
We are given that the mass of water is 1 kg, i.e. 1000 g.

No. of moles = Gram Mass/ Molar Mass

Molar Mass of Water ( $H_{2} O$ ) is 18.
Thus, no. of moles = 1000/18 = 55.55

We know that the molar mass of Ethanol ($C_{2} H_{5} OH$) is 46.

Thus,
$\frac{x/46}{x/46 + 55.55}$ = 0.2

x/46 = x/230 + 11.11
x/46 - x/230 = 11.11
Simplifying further, we get

5x/230 - x/230 = 11.11
4x/230 = 11.11
4x = 230 * 11.11
4x = 2555.3
x = 2555.3 / 4
x = 638.825

Thus, approximately 638.825 g of Ethanol must be added to make its mole fraction 0.2.

Answer 2

Answer:

638.825

Explanation:

Let the mass of Ethanol be 'x' g.

We need the mole fraction of ethanol to be equal to 0.2.

Thus, no. of moles of ethanol / no. of moles of ethanol + water = 0.2

First, let us calculate the no. of moles of Water.

We are given that the mass of water is 1 kg, i.e. 1000 g.

No. of moles = Gram Mass/ Molar Mass

Molar Mass of Water ( H_{2} OH

2

O ) is 18.

Thus, no. of moles = 1000/18 = 55.55

We know that the molar mass of Ethanol (C_{2} H_{5} OHC

2

H

5

OH ) is 46.

Thus,

\frac{x/46}{x/46 + 55.55}

x/46+55.55

x/46

= 0.2

x/46 = x/230 + 11.11

x/46 - x/230 = 11.11

Simplifying further, we get

5x/230 - x/230 = 11.11

4x/230 = 11.11

4x = 230 * 11.11

4x = 2555.3

x = 2555.3 / 4

x = 638.825

Thus, approximately 638.825 g of Ethanol must be added to make its mole fraction 0.2.

I hope that it will help you.