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?

Short answer

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

Step-by-step solution

Given information

The pH of the blood sample is$7.58$.

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$3.80\times {10}^{-7}\mathrm{M}$.