Question

The elements ${}^{\prime }{X}^{\prime }$ and ${}^{\prime }{Y}^{\prime }$ form two different binary compounds $X{Y}_2$ and $X{Y}_4$. When dissolved in $20gm$ of $C{S}_2$ solvent, $1gm$ of $X{Y}_2$ lowers the freezing point by ${2.5}^{o}C$, whereas $1gm$ of $X{Y}_4$ lowers the freezing point by ${1.5}^{o}C$. The molal depression constant for $C{S}_2$ is $5$. The atomic mass of element ${}^{\prime }{Y}^{\prime }$ will be :

• A. $42.64$
• B. $64.42$
• C. $33.34$
• D. $12.8$

Answer 1

The correct option is C $33.34$

$\Delta T_{f_1}=-k_f{m}_1$

$2.5=5\times \frac{1}{(M.wt)}\times \frac{1000}{20}$

$(M.wt{)}_1=100$

$X+2Y=100--\left(1\right)$

$\Delta T_{f_2}=k_f{m}_2$

$1.5=5\times \frac{1}{{(M.wt)}_2}\times \frac{1000}{20}$

${(M.wt)}_2=166.66$

$X+4Y=166.66--\left(2\right)$

$Now\left(2\right)-\left(1\right)$

$2Y=66.66$

$Y=33.33$