A `5%` solution of cane sugar is isotonic with `0.877%` solution of urea. Calculate the molecular mass of urea if the molecular mass of cane sugar is `342`.

Options

A. `68.4 u`
B. `136.8 u`
C. `171.2 u`
D. `34.24 u`

Answer

1

Explanation

By definition, isotonic solution possess same molar concentration.
5% cane sugar solution means (here) 5 g of sugar is dissolved per `100 mL` of solution. Thus,
`M_(sugar)=(5g//342 g mol^(-1))/(100 mL)xx(1000 mL)/L …(1)`
`1%` solution of substance `X` means (here) 1 g of `X` is dissolved per `100 mL` of solution. Thus,
`M_(x)=(1g//mm_(x))/(100 mL)xx(1000 mL)/L ...(2)`
Equating (1) and (2), we get
`5/342 mol=(1 g)/(mm_(solute))`
Thus, `mm_(solute)=22.4/68 g mol^(-1)`
`=68.4 g mol^(-1)`
Thus, molecular mass of `X` is `68.4 u`.
Note that, we can also get the same result by just equation the number of moles of sugar of sugar and `X`.