Question

If $1$ mole of ethyl alcohol in $1,000$ grams of water depresses the freezing point by ${1.86}^{o}C$, what will be the freezing point of a solution of $1$ mole of ethyl alcohol in $500$ grams of water?

• A. $-{0.93}^{o}C$
• B. $-{1.86}^{o}C$
• C. $-{2.79}^{o}C$
• D. $-{3.72}^{o}C$
• E. $-{5.58}^{o}C$

Answer 1

Answer: (D)

$-{3.72}^{o}C$

1 mole of ethyl alcohol in 1,000 grams of water corresponds to molality
$m=1$ m (as per the definition of molality).
1 mole of ethyl alcohol in 500 grams of water corresponds to molality
$m=2$
When molality is doubled, the depression in the freezing point is also doubled. Hence, the depression in the freezing point will be $2\times -{1.86}^{o}C=-{3.72}^{o}C$