Chapter U4.20, Problem 5E

Interpretation Introduction

Interpretation:

The reason for the pH of a ${\text{1×10}}^{\text{-9}}\text{M}$ HCl to be 7 though the exponent is -9 should be explained.

Concept introduction:

  ${\text{1×10}}^{\text{-9}}\text{M}$ HCl solution is very dilute in which contribution of [H+] from water can’t be neglected.

Answer to Problem 5E

As total [H⁺] is close to 10-7 so pH of a ${\text{1×10}}^{\text{-9}}\text{M}$ HCl is 7.

Explanation of Solution

From HCl, $\left[{\text{H}}^{\text{+}}\right]{\text{=10}}^{\text{-9}}$ .

From water, $\left[{\text{H}}^{\text{+}}\right]{\text{=10}}^{\text{-7}}$ as for water $\left[{\text{H}}^{\text{+}}\right]\text{=}\left[{\text{OH}}^{\text{-}}\right]{\text{=10}}^{\text{-7}}$ at 298 K.

So total concentration of hydrogen ion will be:

  $\begin{array}{l}\left[{\text{H}}^{\text{+}}\right]={10}^{-9}+{10}^{-7}={10}^{-9}\left(1+100\right)=101\times {10}^{-9}\\ =1.01\times {10}^{-7}\end{array}$

Now,

  $\text{pH=-log}\left[{\text{H}}^{\text{+}}\right]\text{=-log}\left(\text{1}{\text{.01×10}}^{\text{-7}}\right)\text{=7-log1}\text{.01=7}\text{.}$

Conclusion

Thus pH of a ${\text{1×10}}^{\text{-9}}\text{M}$ HCl is 7.