Question

Mole fraction of urea in a solvent is 0.1. If morality of solution is 10/9m then molar mass of solvent (in g/mol ) is

Answer 1

Answer: The molar mass of the solvent is 100 g/mol.

Explanation:

We are given:

Mole fraction of urea is 0.1. This means that 0.1 moles of urea is present in 1 mole of solution.

Mole fraction of solvent = (1 - 0.1) = 0.9

This means that 0.9 moles of solvent is present in 1 mole of solution.

To calculate the molality, we use the equation:  

$\text{Molality}=\frac{\text{Moles of solute}}{\text{Mass of solvent (in kg)}}$

Molality of the solution = $\frac{10}{9}$

Moles of solute (urea) = 0.1

Putting values in above equation, we get:

$\frac{10}{9}=\frac{0.1}{\text{Mass of solvent (in kg)}}$

Mass of solvent = 0.09kg = 90 g        (Conversion factor: 1 kg = 1000 g)

To calculate the molar mass of solvent, we use the equation:

$\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}$

Moles of solvent = 0.9

Mass of solvent = 90 g

Putting values in above equation, we get:

$0.9mol=\frac{90g}{\text{Molar mass of solvent}}\\\\\text{Molar mass of solvent}=100g/mol$

Hence, the molar mass of the solvent is 100 g/mol.

Answer 2

Answer:

Answer: The molar mass of the solvent is 100 g/mol.

Explanation:

We are given:

Mole fraction of urea is 0.1. This means that 0.1 moles of urea is present in 1 mole of solution.

Mole fraction of solvent = (1 - 0.1) = 0.9

This means that 0.9 moles of solvent is present in 1 mole of solution.

To calculate the molality, we use the equation:

\text{Molality}=\frac{\text{Moles of solute}}{\text{Mass of solvent (in kg)}}Molality=

Mass of solvent (in kg)

Moles of solute

Molality of the solution = \frac{10}{9}

9

10

Moles of solute (urea) = 0.1

Putting values in above equation, we get:

\begin{gathered}\frac{10}{9}=\frac{0.1}{\text{Mass of solvent (in kg)}}\\\\\end{gathered}

9

10

=

Mass of solvent (in kg)

0.1

Mass of solvent = 0.09kg = 90 g (Conversion factor: 1 kg = 1000 g)

To calculate the molar mass of solvent, we use the equation:

\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}Number of moles=

Molar mass

Given mass

Moles of solvent = 0.9

Mass of solvent = 90 g

Putting values in above equation, we get:

\begin{gathered}0.9mol=\frac{90g}{\text{Molar mass of solvent}}\\\\\text{Molar mass of solvent}=100g/mol\end{gathered}

0.9mol=

Molar mass of solvent

90g

Molar mass of solvent=100g/mol

Hence, the molar mass of the solvent is 100 g/mol.