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Question

Mole fraction of A in H2O is 0.2 . The molarity of A in water is....?

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Solution

Density of water in g/ml is 1. It is a standard value

However for doing the problem we do not require density value and hence the statement is not necessary.


Given

Mole fraction of A = 0.2

decimal 0.2 is same as fraction 1 fifth.

Mole fraction of A = 1 fifth

And here the mixture contains A and H subscript 2 O
Therefore
mole fraction of H subscript 2 O
equals 1 minus 1 fifth equals fraction numerator 5 minus 1 over denominator 5 end fraction equals 4 over 5
That is if we take 5 moles of mixture we have 1 open parentheses 5 cross times 1 fifth close parentheses moles of A and 4 open parentheses 5 cross times 4 over 5 close parentheses moles of H subscript 2 O

Moles = fraction numerator m a s s over denominator m o l a r space m a s s end fraction

Molar mass of water is 18

4 equals fraction numerator m a s s over denominator 18 end fraction m a s s equals 18 cross times 4 equals 72 g

4 moles of water means it weigh 72g or 72mL (since 1g = 1mL)

1 mole of A is present in 72 mL of water.

Molarity is no. of moles of solute present in 1 L of solution.

1 mL = 1 over 1000 L

72 mL=72 over 1000 equals 72 cross times 10 to the power of negative 3 end exponent L

So molarity = fraction numerator 1 over denominator 72 cross times 10 to the power of negative 3 end exponent end fraction equals 1000 over 72
= 13.9 M










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