Hello!
a) The
mole fraction of solute of a 15% NaOH aqueous solution can be calculated in the following way:
First, we have to assume that we have
100 grams of solution. This will simplify the calculations.
Now, we know that this solution has 15 grams of NaOH and 85 grams of water. We can calculate the number of moles of each one in the following way:

To finish, we calculate the
mole fraction by dividing the moles of NaOH between the total moles:

So, the mole fraction of NaOH is
0,073
b) The
molality (moles NaOH/ kg of solvent) of a 15% NaOH aqueous solution can be calculated in the following way:
First, we have to assume that we have
100 grams of solution. This will simplify the calculations.
Now, we know that this solution has 15 grams of NaOH and 85 grams
(0,085 kg) of water. We can calculate the moles of NaOH in the following way:

Now, we apply the definition of molality to calculate the molality of the solution:

So, the molality of this solution is
4,41 mHave a nice day!