In this question, we have to find out the mole fraction of silver nitrate, AgNO3 based on the value of molality that it presents. In order to do that, we need to use the molality information, which is:
2.81 m
Molality is = moles of solute/mass of the solvent
We have a salt in an aqueous solution, therefore we have salt in water, to be more specific, we have 2.81 moles of AgNO3 in 1000 grams of water (1 kg of water)
Assuming 1000 grams of water, now we have to find out how many moles of water we have in 1000 grams, based on its molar mass, 18.015g/mol
18.015g = 1 mol
1000g = x moles
18.015x = 1000
x = 1000/18.015
x = 55.402 moles of H2O in 1000 grams
Now, the formula for mole fraction is:
Mole fraction = number of moles of solute/total number of moles in the solution
Using the number of moles we found:
nAgNO3 = 2.81
nH2O = 55.402
We now can calculate it:
Mole fraction = 2.81/2.81+55.402
Mole fraction = 0.048
The value for the mole fraction of an aqueous solution of AgNO3 is 0.048