Question

What is the molar mass of a non-ionizing solid if $10g$ of this solid, dissolved in $100g$ of water, formed a solution that froze at $-{1.21}^{o}C$?

• A. $0.65g/mol$
• B. $6.5g/mol$
• C. $130g/mol$
• D. $154g/mol$
• E. $265g/mol$

Answer 1

The correct option is D $154g/mol$

Let $M$ g/mol be the molar mass of solid.

The number of moles of solid $=\frac{10g}{Mg/mol}=\frac{10}{M}mol$

The mass of water $=100g\times \frac{1kg}{1000g}=0.1kg$

The molality $m=\frac{10}{M\times 0.1}=\frac{100}{M}$

The freezing point of pure water is 0 deg C. The freezing point of the solution is $-1.21{}^{0}C$.

The depression in the freezing point

$\Delta T_f=0{}^{0}C-(-1.21{}^{0}C)=1.21{}^{0}C$

$\Delta T_f=K_f\times m$

$1.21=1.86\times \frac{100}{M}$

The molar mass of solid $M\approx 154g/mol$