Q. 10.87 - An Introduction to General, Organic, and Biological Chemistry

Question

Determine the pH for the follow ing solutions: $(10,6)$

a. $\left[\mathrm{OH}\right]=1.0\times {10}^{-7}\mathrm{M}$

b.$\left[{\mathrm{H}}_2{\mathrm{O}}^{\text{'}}\right]=4.2\times {10}^{-3}\mathrm{M}$

c. $\left[{\mathrm{H}}_2{\mathrm{O}}^{+}\right]=0.0001\mathrm{M}$

d. $\left[\mathrm{OH}\right]=8.5\times {10}^{-9}\mathrm{M}$

Step-by-Step Solution

Answer

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Step 1 Introduction

The $\mathrm{pH}$ scale relates to the logarithmic scale. $\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]$of aqueous solutions.

Mathematically expression of $\mathrm{pH}$ is the negative logarithmic  of the $\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]$

$Kw=\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]\left[{\mathrm{OH}}^{-}\right]$

$\mathrm{pH}=-\log \left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]$

$\mathrm{pOH}=-\log \left[{\mathrm{OH}}^{-}\right]$

Acidic solution $=\mathrm{pH}<7.0\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]>1.0\times {10}^{-7}\mathrm{M}$

Neutral solution $=\mathrm{pH}=7.0\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]=1.0\times {10}^{-7}\mathrm{M}$

Basic solution $=\mathrm{pH}>7.0\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]<1.0\times {10}^{-7}\mathrm{M}$

Step 2 Explantion part (a)

Given acid concentration of the solution is  $1.0\times {10}^{-11}\mathrm{M}$  . Calculate the $\mathrm{pH}$of the solution by using the following formula:

$pH=-\log \left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]$

$=-\log \left[1.0\times {10}^{-11}\right]$

$=11-\log (1.0)$

$=11$