Q.10.44 - An Introduction to General, Organic, and Biological Chemistry

Question

A patient with respiratory alkalosis has a blood plasma pH of 7.58. What is the $\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]$ pf the blood plasma?

Step-by-Step Solution

Answer

The concentration of $\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]$ is $3.80\times {10}^{-7} \mathrm{M}$.

Step 1: Given information

The pH of the blood sample is $7.58$.

Step 2: Explanation

pH or "potential of hydrogen" is a scale used to specify the acidity or basicity of a watery solution. Acidic solutions are estimated to have lower pH values than basic or alkaline solutions. 

The pH of the blood sample is 7.58.

Therefore,

$$\begin{gathered} \mathrm{pH}=-{\log }_{10}\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right] \\ \Rightarrow \left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]={10}^{-\mathrm{pH}} \\ \Rightarrow \left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]={10}^{-7.58} \\ \left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]=3.80\times {10}^{-7} \mathrm{M} \end{gathered}$$

Thus, the $\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]$ concentration is $3.80\times {10}^{-7} \mathrm{M}$.