Question

in a very dilute solution the number of moles of solvent are 10 times more than that of the solute if vapour pressure of the solvent is 80 mm of Mercury find the vapour pressure of the solution​

Answer 1

Answer: The vapor pressure of the solution is 88.0 mmHg

Explanation:

Mole fraction is defined as the moles of a component present in the total moles of a solution. It is represented by the symbol $\chi$. Suppose two components A and B are present a solution. The mole fraction of component A will be:

$\chi_A=\frac{n_A}{n_A+n_B}$                ...(1)

where,

n = number of moles  

Given values:

$n_{solvent}=10\times n_{solute}$

Using equation 1:

$\chi_{solvent}=\frac{10\times n_{solute}}{[10\times n_{solute}]+n_{solute}}\\\\\chi_{solvent}=\frac{10}{11}\\\\\chi_{solvent}=0.9091$

Raoult's law is the law that is used to calculate the vapor pressure of the individual gases present in a solution. The equation for this follows:

$p_A=\chi_A\times p_T$                 ...(2)

where,

$p_A$ = vapor pressure of substance A in the solution

$p_T$ = total pressure of the solution

Given values:

$p_{solvent}=80 mmHg\\\chi_{solvent}=0.9091$

Plugging values in equation 2:

$80mmHg=0.9091\times p_T\\\\p_T=\frac{80 mmHg}{0.9091}\\\\p_T=88.0 mmHg$

Hence, the vapor pressure of the solution is 88.0 mmHg