Question

The vapor pressure of water at${{23}^{\circ }}C$is $\text{19}\cdot \text{8mm}$. $\text{0}\text{.1}$glucose is dissolved in $178\cdot 2g$ water. What is the vapor pressure (in mm) of the resultant solution?
A. 19
B. 19.602
C. 19.402
D. 19.202

Answer 1

Hint: Vapor pressure of a solution can be found using Raoult’s Law. According to this law, the partial vapor pressure of a component in a mixture is equal to the vapor pressure of the pure component at that temperature multiplied by its mole fraction in the mixture.

Formula used:$p={{p}_{o}}{{x}_{A}}$
$p\to $vapor pressure of solution
${{p}_{0}}\to $vapor pressure of pure component
${{\text{x}}_{A}}\to \text{ }$mole fraction
${{\text{x}}_{A}}=\dfrac{{{n}_{A}}}{{{n}_{B}}+{{n}_{B}}}$
Where ${{n}_{A}}\to $no. of moles of pure component (water)
Where ${{n}_{B}}\to $no. of moles of glucose



Complete answer:
 Vapor Pressure: It is a measure of the tendency of a material to change into gaseous or vapor state.
Mole fraction: It is defined as the unit of amount of constituents divided by the total amount of all constituents in a mixture.
Given,
${{n}_{B}}$(number of moles of glucose)$=0\cdot 1$
${{n}_{B}}$(number of moles of water)$=\dfrac{\text{Given weight of substance}}{\text{Molar mass}}$
Molar mass for water$\left( {{\text{H}}_{2}}\text{O} \right)=2\times 1$(for${{\text{H}}_{2}})+16$(for O)
$=2+16=18$
So,
${{n}_{A}}=\dfrac{178\cdot 2}{18}=9\cdot 9$
${{x}_{A}}=\dfrac{{{n}_{A}}}{{{n}_{A}}+{{n}_{B}}}=\dfrac{9.9}{9\cdot 9+0\cdot 1}=\dfrac{9.9}{10\cdot 0}=0\cdot 99$

$\begin{align}
& \text{So, vapour pressure of solution (p)=}{{\text{p}}_{0}}{{x}_{A}} \\
 & \\
\end{align}$
 $=19\cdot 8\times 0\cdot 99$
  $=19\cdot 602mm$ .

So, the correct answer is “Option B”.

Additional Information:
 Raoult’s law was given by Francois-Marie Raoult in 1887. It is used to estimate the contribution of individual components of a liquid or solid mixture to the total pressure exerted by the system, especially for discrete mixtures where the quantity of each component is known.

Note:
 Study about Raoult’s Law, mole fraction and the partial vapor pressure of mixtures. Ideal Solution is the solution in which molecular interactions between solute molecules are absolutely zero, and it follows Raoult’s Law. Positive Deviation from Raoult’s Law occurs when the vapor pressure of the components is greater than what is expected in Raoult’s Law. Negative Deviation in Raoult’s Law means that we find a lower than expected vapor pressure for the solution.