a solution of A (molar mass 100g/mol) and B (molar mass 1.10 x 10^2 g/mol) is prepared by mixing equal masses of the two. Find the mole fractions of each component in solution
To find the mole fractions of each component in the solution, we need to first determine the number of moles of A and B present in the solution.
Let's assume that the solution contains a total mass of x grams.
Since the masses of A and B are equal, each component will have a mass of x/2 grams in the solution.
To find the number of moles of A, we divide the mass of A by its molar mass:
Number of moles of A = (mass of A) / (molar mass of A) = (x/2) / 100 g/mol = x / 200
Similarly, the number of moles of B can be calculated as follows:
Number of moles of B = (mass of B) / (molar mass of B) = (x/2) / (1.10 x 10^2 g/mol) = (x / 220)
The total number of moles in the solution is the sum of the moles of A and B:
Total number of moles = Number of moles of A + Number of moles of B
= x/200 + x/220
Now, we can calculate the mole fraction of A and B in the solution:
Mole fraction of A = Number of moles of A / Total number of moles
= (x/200) / (x/200 + x/220)
= (x/200) / (11x/2200 + 10x/2200)
= (x/200) / (21x/2200)
= x / (200 * 21)
Similarly, the mole fraction of B can be calculated as follows:
Mole fraction of B = Number of moles of B / Total number of moles
= (x/220) / (x/200 + x/220)
= (x/220) / (11x/2200 + 10x/2200)
= (x/220) / (21x/2200)
= x / (220 * 21)
Therefore, the mole fractions of component A and component B in the solution are x / (200 * 21) and x / (220 * 21), respectively.