Question

The concentration of ${\mathit{H}}_{\mathbf{3}}{\mathit{O}}^{\mathbf{+}}$ in a sample of wine is $\mathbf{2}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{4}}\mathit{M}$.Calculate the pH of the wine.

Short answer

The pH of the wine is 3.70

Step-by-step solution

Understanding the concept of amphoteric oxides

The negative logarithm of $H^{+}$ion concentration is used to calculate pH. It’s a scale that is used to measure acids and bases.

$pH=-\log \left[H_3{O}^{+}\right]$

Applying the concept and calculation of pH.

By definition the mathematical expression of pH could be written as:

$pH=-log\left[H_3{O}^{+}\right]$

Given concentration of$H_3{O}^{+}$in the sample of wine is$2\times {10}^{-4}M$, and after applying the value in the mathematical expression written above,

$pH=-\log \left[2\times {10}^{-4}M\right]$

Now apply the properties of the logarithm,

$$\begin{gathered} \log \left(a\times b\right)=\log \left(a+b\right) \\ \log a^x=x.\log a \end{gathered}$$

The above expression could be rewritten as:

$$\begin{gathered} pH=-\log 2+\left(-\log {10}^{-4}\right) \\ pH=3.70 \end{gathered}$$

The value of pH here is less than 7 which means the sample is acidic in nature.