Chapter 17, Problem 130AP

Interpretation Introduction

Interpretation:

$\text{pH}$

of the solution prepared by mixing HCl gas and ammonia liquid is to be determined with given volume of HCl, volume and concentration of ammonia, and pressure.

Concept introduction:

$\text{pH}$

is a measure to specify the acidity or basicity of an aqueous solution. $\text{pH}$ of a solution is determined as follows:

$\text{pH}=-\log \left[\text{acid}\right]$

The number of moles of a gas is determined as follows:

$PV=nRT$

Here, $P$

is the pressure of gas, $V$

is the volume of gas, $n$ is the number of moles, $R$ is the gas constant, and $T$

is the temperature.

The relationship between $\text{atm}$ and $\text{mm}\text{Hg}$ can be expressed as:

$\text{1}\text{atm=}\text{760}\text{mm}\text{Hg}$

To convert $\text{mm}\text{Hg}$

to $\text{atm}$, conversion factor is $\frac{1\text{ atm}}{760\text{ mm Hg}}$

The number of moles of compound is calculated by the equation:

$M=\frac{m}{V}$

Here, M is the concentration of solution in molarity, m is the number of moles of solute, and V is the volume of the solution.

${\text{K}}_{\text{a}}$ is the acid-ionization constant, which is a measure of the extent to which an acid dissociates in an aqueous solution.

The dissociation of a weak acid in an aqueous solution :

$HA\left(aq\right)+H_{2}O\left(l\right)\rightleftharpoons H_3{O}^{+}\left(aq\right)+A^{-}\left(aq\right)$

The acid ionization constant for a weak acid is as:

${\text{K}}_a=\frac{{\text{[H}}^{+}][{\text{A}}^{-}]}{\text{[HA]}}$

The pH of the solution can be calculated as: $\text{pH}=-\text{log}\left[{\text{H}}^{\text{+}}\right]$