Question

Define mole fraction. A solution of sucrose in water is labelled as 20% w/w. What would be the mole fraction of each component in the solution?

Answer 1

Hint: The number of moles of a component can be calculated by the equation-
Mole fraction of x = number of moles of x / total number of moles in the mixture.
- The number of moles of a component can be found using the equation-
Number of moles = given mass / molar mass

Complete step by step solution:
- Mole fraction, also known as molar fraction is defined as the number of moles of a constituent divided by the total number of moles in the mixture.
- If no of moles of a constituent is taken to be x, then the mole fraction of that constituent will be given by the equation,
Mole fraction of x = number of moles of x / total number of moles in the mixture. – (equation 1)
- In the question, it is given that the solution of sucrose in water is labelled as 20% w/w. This means that for every 100g of the sucrose solution, there will be 20g of water.
- Hence, out of 100g, the amount of water will be 100 – 20 = 80g.
- In the given question, we have only two components.
- So, in order to find the mole fraction of water and sucrose in the sucrose solution, we can modify the equation 1 as -
Mole fraction of sucrose = number of moles of sucrose / (number of moles of sucrose + number of moles of water) – (equation 2)
Mole fraction of water = number of moles of water / (number of moles of sucrose + number of moles of water) – (equation 3)

- To find the mole fraction of each component, we have to now find the number of moles of each component.
- The number of moles of a component can be found out by the equation –
Number of moles = given mass / molar mass. – (equation 4)
- We know that the given mass of sucrose and water is 20g and 80g respectively.
- Also, the molar mass of water and sucrose can be found out as-
Molar mass of water (${{H}_{2}}O$) = (2x1) + (1x16) = 18g/mol.
Molar mass of sucrose (${{C}_{12}}{{H}_{22}}{{O}_{11}}$ ) = (12x12) + (22x1) + (11x16) = 342g/mol.
- Substituting the values of given mass and molar mass of sucrose and water in equation 4, we get
Number of moles of water = 80/18 = 4.44 mol
Number of moles of sucrose = 20/342 = 0.585 mol.
- Now that we have the number of moles of sucrose and water, we can substitute them in equations 2 and 3 to obtain the answer.
Mole fraction of sucrose = 0585 / (0585+4.44) = 0.013
Mole fraction of water = 4.44 / (0585+4.44) = 0.987
- Hence the mole fraction of sucrose and water in the sucrose solution are 0.013 and 0.987 respectively.

Note: In a mixture of 2 substances, if we find the mole fraction of one substance, we can easily predict the mole fraction of the other substance. In such cases, the mole fraction of one component will be equal to one minus the mole fraction of the other component.