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What will be the pH of a soft drink if hydrogen ion concentration in the sample is $3.8\times {{10}^{-3}}M$?
A. 3.8
B. 5.04
C. 2.42
D. 9.2

Last updated date: 17th Jun 2024
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Hint: As only the concentration of hydrogen is given, try to find an equation that relates the pH and the concentration of hydrogen. The equation was given by S.P Sorensen in the 1900’s.

Complete Solution :
- In order to answer our question, we need to study about the pH of solutions. The nature of solution whether neutral, acidic or basic is expressed in terms of ${{[{{H}_{3}}O]}^{+}}$ by scientific notation as $1.0\times {{10}^{-x}}$. Here, x may have varying from 0 to 14 at 298K. But the way of expressing concentration is quite inconvenient.
- For example, if the ${{[{{H}_{3}}O]}^{+}}$ of a solution is $3.5\times {{10}^{-4}}M$, this means that actually it is 0.00035M. In order to simplify it, there is another method for expressing the concentration of the hydronium ion. It is called pH and it is measured in the pH scale. Mathematically,
\[pH=-{{\log }_{10}}{{[{{H}_{3}}O]}^{+}}\]
Thus, the pH of a solution may be defined as the logarithm of the reciprocal hydrogen ion concentration.

\[pOH=-\log {{[OH]}^{-}}\]
- Let us learn about the pH scale. The pH scale is the range for expressing the nature of any solution. We know that at 298K, hydronium ion ranges from ${{10}^{0}}M$ to ${{10}^{-14}}M$. The corresponding pH range is from 0 to 14.

- Now, let us come to our question. We have been provided with the concentration of hydrogen in the soft drink and we are expected to find out the pH. So, from the above equation, we can write the pH of the soft drink as:
\[pH = -\log (3.8\times {{10}^{-3}})\]

- Now, an important property of logarithm is that $\log (a\times b) = \log a+\log b$. Now applying this property, we have
\[pH = -[\log 3.8+\log {{10}^{-3}}]=2.42\]
So, the correct answer is “Option C”.

Note: Following are the points to be noted:
For a neutral solution,${{[{{H}_{3}}O]}^{+}}={{10}^{-7}}$and pH = 7
For an acidic solution,${{[{{H}_{3}}O]}^{+}}>{{10}^{-7}}$and pH < 7
For a basic solution,${{[{{H}_{3}}O]}^{+}}<{{10}^{-7}}$ and pH > 7