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Calculate the mole percentage of CH3OH  and H2O  respectively in 60 (by mass) aqueous Solution of CH3OH .
A.45.8,54.2
B.54.2,45.8
C.50,50
D.60,40

Answer
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Hint: Mole percentage of any component in a given sample is the amount of that component present in the total volume of the sample.
-After calculating the number of moles of each component present in the sample, the total number of moles in the sample could be calculated by simply adding the number of moles of both.
-Then we divide the individual number of moles with the total number of moles and multiply with hundred in order to get the mole percentage.

Complete step by step answer:
In order to calculate the mole percentage of the water and methanol present in the Solution, we will first calculate the number of moles of methanol and water individually, then we will add the total number of moles present in the Solution. Then we will calculate the mole percentage using the calculated values.
Given are the values of percentage by mass Solution of methanol.
60 by mass Solution of methanol. This means in 100gm total Solution 60gm of methanol is dissolved in 40gm of water H2O 
We know that the Molar mass of methanol is 32g/mol
And the Molar mass of water is 18g/mol
We know that the number of moles of solute is, given mass of solute, per molar mass of the Solution.
Which means No. of moles of CH3OH=60gm32g/mol=1.875 mol 
So the number of moles of methanol is 1.875moland, we will calculate the number of moles of water,
And No. of moles of H2O=40gm18gm/mol=2.222 mol 
The number of moles of water is turned out to be 2.222mol

Now we will calculate the total number of moles present in the Solution, that is
Total no. of moles =1.875+2.222=4.097 moles 
Now from this value we will calculate the mole percentage of both methanol and water separately, the mole percentage of a substance can be calculated by the following mathematical situation,
 Molepercentage= Moles of compoundTotal no. of moles×100
So we will calculate the mole percentage of methanol,
Mole
And similarly, now we will calculate the mole percentage of water
Mole
So the mole percentage of methanol is 45.8 and the mole percentage of water is turned out to be 54.23. These values correspond to the values which are given in the option A.

So the correct option is option A.

Note: The percentage by mass ratio of methanol was given in the question, we used it to calculate the number of moles of methanol. And since the sample of mixture contained only two components, the remaining percentage of mass ratio would be of water.
-So we calculated the number of moles of water as well. Next we add up both the calculated number of moles to get the total number of moles in the sample.
-Then using this value, we calculate individual mole percentages of the component by simply dividing their number of moles with the total number of moles and multiplying it with hundred.