Question:

The vapour pressure of pure benzene at a certain temperature is $0.850$ bar. A non-volatile, nonelectrolyte solid weighing $0.5\,g$ is added to $39.0\, g$ of benzene (molar mass 78 g/mol). The vapour pressure of the solution then is 0.845 bar. What is the molecular mass of the solid substance?

Updated On: Jun 23, 2023
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The Correct Option is C

Solution and Explanation

$P^{\circ}_{A}=0.850\,bar,\, P_{s}=0.845\,bar$ $w=0.5\,g, \,m=?$ weight of solvent (benzene) $= 39.0\, g$ and molecular weight of benzene $= 78\, g$ As we know, $\frac{P^{\circ}_{A}-P_{s}}{P^{\circ}_{A}}=x_{B}=\frac{n_{B}}{n_{A}}$ $\frac{0.850-0.845}{0.850}=\frac{\frac{w_{B}}{M_{B}}}{\frac{w_{A}}{M_{A}}}=\frac{\frac{0.5}{m}}{\frac{39}{78}}$ On solving, we get molecular mass of solid structure $(m) = 170\, g.$
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Concepts Used:

Solutions

A solution is a homogeneous mixture of two or more components in which the particle size is smaller than 1 nm.

For example, salt and sugar is a good illustration of a solution. A solution can be categorized into several components.

Types of Solutions:

The solutions can be classified into three types:

  • Solid Solutions - In these solutions, the solvent is in a Solid-state.
  • Liquid Solutions- In these solutions, the solvent is in a Liquid state.
  • Gaseous Solutions - In these solutions, the solvent is in a Gaseous state.

On the basis of the amount of solute dissolved in a solvent, solutions are divided into the following types:

  1. Unsaturated Solution- A solution in which more solute can be dissolved without raising the temperature of the solution is known as an unsaturated solution.
  2. Saturated Solution- A solution in which no solute can be dissolved after reaching a certain amount of temperature is known as an unsaturated saturated solution.
  3. Supersaturated Solution- A solution that contains more solute than the maximum amount at a certain temperature is known as a supersaturated solution.