Chapter 2, Problem 23RE

MATHEMATICAL Calculate the hydrogen ion concentration, $\left[{\text{H}}^{+}\right]$, for each of the following materials:

(a) Blood plasma, pH 7.4

(b) Orange juice, pH 3.5

(c) Human urine, pH 6.2

(d) Household ammonia, pH 11.5

(e) Gastric juice, pH 1.8

Interpretation Introduction

Interpretation:

The hydrogen ion concentration for each of the following materials:

(a) Blood plasma, pH 7.4

(b) Orange juice, pH 3.5

(c) Human urine, pH 6.2

(d) Household ammonia, pH 11.5

(e) Gastric juice, pH 1.8

Concept introduction:

The pH (potential of hydrogen) can be mathematically defined as the negative logarithm of the H⁺ (hydrogen ion) concentration within an aqueous solution. In chemistry, it is used to determine the acidity or the basicity of a solution.

Answer to Problem 23RE

Solution:

a. $\text{4}\times {\text{10}}^{-\text{8}}\text{ Molar}$

b. $\text{3}\text{.2}\times {\text{10}}^{-4}\text{ Molar}$

c. $\text{6}\text{.3}\times {\text{10}}^{-7}\text{ Molar}$

d. $\text{3}\text{.2}\times {\text{10}}^{-12}\text{ Molar}$

e. $\text{4}\times {\text{10}}^{-\text{8}}\text{ Molar}$

Explanation of Solution

(a) The pH of blood plasma is 7.4. The concentration of H⁺ in blood plasma can be calculated as follows:

$\begin{array}{c}\text{pH}=-\text{log}{\left[\text{H}\right]}^{\text{+}}\\ \text{7}\text{.4}=-\text{log}{\left[\text{H}\right]}^{\text{+}}\\ {\left[\text{H}\right]}^{\text{+}}=\text{antilog}-\text{7}\text{.4}\\ {\left[\text{H}\right]}^{\text{+}}=\text{4}\times {\text{10}}^{-\text{8}}\text{ Molar}\end{array}$

So, the hydrogen ion concentration of blood plasma will be $\text{4}\times {\text{10}}^{-\text{8}}\text{ Molar}$.

(b) The pH of orange juice is 3.5. The hydrogen ion concentration of orange juice can be calculated as follows:

$\begin{array}{c}\text{pH}=-\text{log}{\left[\text{H}\right]}^{\text{+}}\\ 3.5=-\text{log}{\left[\text{H}\right]}^{\text{+}}\\ {\left[\text{H}\right]}^{\text{+}}=\text{antilog}-3.5\\ {\left[\text{H}\right]}^{\text{+}}=3.2\times {\text{10}}^{-4}\text{ Molar}\end{array}$

So, the hydrogen ion concentration of blood plasma will be $\text{3}\text{.2}\times {\text{10}}^{-4}\text{ Molar}$.

(c) The pH of human urine is 6.2. The hydrogen ion concentration of human urine can be calculated as follows:

$\begin{array}{c}\text{pH}=-\text{log}{\left[\text{H}\right]}^{\text{+}}\\ 6.2=-\text{log}{\left[\text{H}\right]}^{\text{+}}\\ {\left[\text{H}\right]}^{\text{+}}=\text{antilog}-6.2\\ {\left[\text{H}\right]}^{\text{+}}=6.3\times {10}^{-7}\text{ Molar}\end{array}$

So, the hydrogen ion concentration of human urine will be $\text{6}\text{.3}\times {\text{10}}^{-7}\text{ Molar}$.

(d) The pH of household ammonia is 11.5. The hydrogen ion concentration of household ammonia can be calculated as follows:

$\begin{array}{c}\text{pH}=-\text{log}{\left[\text{H}\right]}^{\text{+}}\\ 11.5=-\text{log}{\left[\text{H}\right]}^{\text{+}}\\ {\left[\text{H}\right]}^{\text{+}}=\text{antilog}-11.5\\ {\left[\text{H}\right]}^{\text{+}}=3.2\times {\text{10}}^{-12}\text{ Molar}\end{array}$

So, the hydrogen ion concentration of household ammonia will be $\text{3}\text{.2}\times {\text{10}}^{-12}\text{ Molar}$.

(e) The pH of gastric juice is 1.8. The hydrogen ion concentration of gastric juice can be calculated as follows:

$\begin{array}{c}\text{pH}=-\text{log}{\left[\text{H}\right]}^{\text{+}}\\ 1.8=-\text{log}{\left[\text{H}\right]}^{\text{+}}\\ {\left[\text{H}\right]}^{\text{+}}=\text{antilog}-1.8\\ {\left[\text{H}\right]}^{\text{+}}=1.6\times {\text{10}}^{-2}\text{ Molar}\end{array}$

So, the hydrogen ion concentration of gastric juice will be $\text{4}\times {\text{10}}^{-\text{8}}\text{ Molar}$.

Conclusion

Therefore, it can be concluded that the H⁺ concentration of blood plasma will be $\text{4}\times {\text{10}}^{-\text{8}}\text{ Molar}$, the hydrogen ion concentration of blood plasma will be $\text{3}\text{.2}\times {\text{10}}^{-4}\text{ Molar}$, and the H⁺ concentration of human urine will be $\text{6}\text{.3}\times {\text{10}}^{-7}\text{ Molar}$. The hydrogen ion concentration of household ammonia will be $\text{3}\text{.2}\times {\text{10}}^{-12}\text{ Molar}$ and the hydrogen ion concentration of gastric juice will be $\text{4}\times {\text{10}}^{-\text{8}}\text{ Molar}$.