To determine the mole fraction of urea in a solution where the molality is
4.44 m , we first need to understand the definitions and relationships involved.
Molality (
) is given by:
m=mass of solvent in kgmoles of solute
Here, the molality is
4.44 m , which means there are
moles of urea (solute) per kilogram of water (solvent).
The next step involves calculating the mole fraction. Mole fraction (
) of urea is given by:
Xurea=moles of urea+moles of watermoles of urea
Since we have
moles of urea, let's determine the moles of water. The molar mass of water (
) is approximately
18 g/mol . Therefore, the moles of water in
(or
1000 g ) of water are:
Moles of water=18 g/mol1000 g≈55.56 moles
We then substitute these values into the mole fraction formula:
Xurea=4.44+55.564.44
Simplifying the expression inside the denominator first:
4.44+55.56=60
So, the mole fraction of urea becomes:
Xurea=604.44
Dividing the values gives us:
Xurea≈0.074
The problem asks for the mole fraction in the form
x×10−3 , so we convert our result to this form:
Xurea=74×10−3
Therefore, the value of
is:
