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What are the mole fractions of hydrochloric acid (HCl) and water in a 20% w/w aqueous HCl solution?

Answer
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Hint: As we know that mole fraction can be described as the number of molecules or moles of a particular component in a mixture divided by the total number of moles present in the given mixture. It is also a way of expressing the concentration of a solution.
Formula used:
We will require the following formula to calculate the mole fraction:-
xA=number of moles of Atotal moles present in the mixture

Complete answer:
Let us begin with the definition of mole fraction as follows:-
-Mole fraction: It can be defined as the number of molecules or moles of a particular component in a mixture divided by the total number of moles present in the given mixture. It is denoted by ‘x’.
It can be calculated by the following formula:-
xA=number of moles of Atotal moles present in the mixture
-As we have been given that 20% w/w aqueous HCl solution which means that out of 100 grams of solution, the mass of HCl present is 20 grams. So the mass of water present = (100 - 20) grams = 80 grams.
-Calculation of moles of HCl and water:-
Molar mass of H = 1g/mol
Molar mass of Cl = 35.5g/mol
Molar mass of O = 16g/mol
So the molar mass of HCl = (1+35.5)g/mol = 36.5g/mol
And molar mass of H2O = ( 2(1) + 16 )g/mol = 18g/mol
As we know that moles (n) = given massmolar mass
Moles of HCl (nHCl) = 20g36.5g/mol= 0.547moles
Moles of H2O(nH2O) = 80g18g/mol= 4.444moles
-Calculation of mole fractions of hydrochloric acid (HCl) and water in a 20% w/w aqueous HCl solution:-
Mole fraction of HCl:-
xHCl=number of moles of HCltotal moles present in the mixturexHCl=0.547moles0.547moles+4.444molesxHCl=0.547moles4.991molesxHCl=0.1090.1(approximately)
Mole fraction ofH2O:-
xH2O=number of moles of H2Ototal moles present in the mixturexH2O=4.444moles0.547moles+4.444molesxH2O=4.444moles4.991molesxH2O=0.8900.9(approximately)
Hence, the mole fraction of HCl is 0.1 and mole fraction of water is 0.9 in a 20% w/w aqueous HCl solution.

Note:
-Remember that the sum of mole fractions of all the components of mixture or a solution is always equal to 1. So the moles fraction of water can also be directly calculated as follows:-
Mole fraction of HCl + Mole fraction of water = 1
Mole fraction of water = 1 – 0.1 = 0.9
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