Chapter 16, Problem 97A

Interpretation Introduction

Interpretation: The molarity of the acid is to be calculated when an excess of zinc is added to $800\text{mL}$ of hydrochloric acid solution.

Concept Introduction:

Among the three states of matter, gases are a little complicated with millions and billions of energetic molecules. Therefore, scientist has come across these concepts of ideal gas as an approximate model to describe gas behavior.

According to the above statement, an ideal gas equation is been derived as:

  $PV=n\text{R}T$

Here, $P$ is the vapor pressure, $V$ is the volume of solvent, $R$ is the gas constant $\left(8.31\frac{\text{J}}{\text{Kmol}}\right)$ , $n$ is the volume of solute, and $T$ is the temperature.

The formula to calculate the molarity of the solution is given as:

  $\text{Molarity}=\frac{\text{Moles solute}}{\text{Litre solution}}$

Answer to Problem 97A

The molarity of $\text{HCl}$ is solution is $0.34\text{M}$ .

Explanation of Solution

Given:

Volume of $\text{HCl}$ is $800\text{mL}$ .

Volume of $\text{HCl}\left(\text{gas}\right)$ is $1.21\text{L}$ .

Temperature is $21°\text{C}$

Pressure is $747\text{mmHg}$

The vapor pressure is $18.6\text{mmHg}$

Convert $\text{mL}$ to $\text{L}$ .

  $\begin{array}{c}800\text{mL}=800\times \frac{1\text{L}}{1000\text{mL}}\\ =0.80\text{L}\end{array}$

Convert temperate from degree into Kelvin.

  $\begin{array}{c}T=21+274\cdot 15\\ =294\cdot 15\text{K}\end{array}$

Substitute $0.80$ for $n$ , $18.6\text{mmHg}$ for $P$ , $\left(8.31\frac{\text{J}}{\text{Kmol}}\right)$ for $R$ and $294\cdot 15\text{K}$ for $T$ in the equation of the ideal gas equation.

  $\begin{array}{c}PV=n\text{R}T\\ V=\frac{0.8\times 8.31\times 294.15}{\begin{array}{c}18.6\\ =105.13\text{L}\end{array}}\end{array}$

Substitute $36.6$ for moles solute and $105.13$ for the volume of solution in the equation of molarity.

  $\begin{array}{c}\text{Molarity}=\frac{36.5}{105.13}\\ =0.34\text{M}\end{array}$

Conclusion

The molarity of $\text{HCl}$ is solution is $0.34\text{M}$ .