Chapter 12, Problem 12.99QE

(a)

Interpretation Introduction

Interpretation:

The molar mass of the gas using the ideal gas law has to be calculated.

Concept Introduction:

Ideal gas law:  The molar mass of a gas can be derived from the ideal gas law,

  $\text{PV=nRT}$

Here,    $\text{P=}$ Pressure of the gas (in atm)

    $\text{V=}$ Volume of the solution (in liters)

    $\text{R=}$ Universal gas constant

    $\text{T=}$ Temperature (in kelvin)

    $\text{n=}$ Number of moles

The number of moles n, is replaced by the mass of the gas in grams and the equation becomes,

  $\text{M=m×}\frac{\text{RT}}{\text{PV}}$

Here.    $\text{M=}$ Molar mass of the gas

    $\text{m=}$ Mass of the gas

(b)

Interpretation Introduction

Interpretation:

The molar mass from the freezing point of the solution has to be calculated.

Concept Introduction:

Freezing point depression:  The freezing point depression is proportional to the concentration of the solute particles and is given by the equation,

  ${\text{ΔT}}_{\text{f}}{\text{=mk}}_{\text{f}}$

Here,

  ${\text{ΔT}}_{\text{f}}\text{=}$ Freezing point of the solution

  $\text{m=}$ Molal concentration

  ${\text{k}}_{\text{f}}\text{=}$ Freezing point depression constant (depends on the solvent used).

(c)

Interpretation Introduction

Interpretation:

The difference in values found in the molar mass of the gas calculated from the freezing point of the solution and from ideal gas law has to be explained.