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What is the formula for calculating pH?

A.${\rm{pH = }} - {\rm{log}}\left[ {{{\rm{H}}_{\rm{3}}}{{\rm{O}}^ + }} \right]$

B. ${\rm{pH/log = }} - {\rm{log}}\left[ {{{\rm{H}}_{\rm{3}}}{{\rm{O}}^ + }} \right]$

C. ${\rm{pH = }} - {\rm{log}}\left[ {{\rm{O}}{{\rm{H}}^ - }} \right]$

D. ${\rm{pH = }} - {\rm{log/}}\left[ {{{\rm{H}}_3}{{\rm{O}}^ + }} \right]$

E. ${\rm{pH = log}}\left[ {{{\rm{H}}_3}{{\rm{O}}^ - }} \right]$

Last updated date: 29th Feb 2024
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IVSAT 2024
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Hint: We know that the nature of the solution whether neutral, basic or acidic is expressed in terms of hydronium ion $\left( {{{\rm{H}}_{\rm{3}}}{{\rm{O}}^ + }} \right)$ concentration. The measurement of concentration of hydrogen or hydronium ion in a solution is termed as pH.

Complete step by step solution:
Let’s discuss pH in detail. The pH of a solution is defined as the negative logarithm of its hydronium ion concentration.

${\rm{pH}} = - \log \left[ {{{\rm{H}}_{\rm{3}}}{{\rm{O}}^ + }} \right] = \log \dfrac{1}{{\left[ {{{\rm{H}}_{\rm{3}}}{{\rm{O}}^ + }} \right]}}$

We can also say that the pH of a solution is the logarithm of the reciprocal of hydrogen ion concentration. That means, the concentration of hydronium ion is inversely proportional to the pH of the solution. Increasing the concentration of hydronium ion lowers the pH of the solution.
Therefore, the formula to measure pH is ${\rm{pH = }} - {\rm{log}}\left[ {{{\rm{H}}_{\rm{3}}}{{\rm{O}}^ + }} \right]$.

So, the correct answer is Option A.

Additional Information:
Let’s understand pH scale in detail. pH scale is the range for expressing the nature of any solution. We know that at 298 K, hydrogen ion ranges from ${10^0}$ M to ${10^{ - 14}}$M . The corresponding pH range is from zero to fourteen.
1. For a neutral solution, $\left[ {{{\rm{H}}_{\rm{3}}}{{\rm{O}}^ + }} \right]$=${10^{ - 7}}$
and pH=7
2. For an acidic solution, $\left[ {{{\rm{H}}_{\rm{3}}}{{\rm{O}}^ + }} \right]$>${10^{ - 7}}$
and pH<7
3. For an basic solution, $\left[ {{{\rm{H}}_{\rm{3}}}{{\rm{O}}^ + }} \right]$<${10^{ - 7}}$
and pH>7

The nature of the solution can also be expressed in terms of pOH value. For a neutral solution value of pOH is 7, for an acidic solution value of pOH is more than 7 and for a basic solution, its value is less than 7.

Note: Always remember that an acid is a substance that releases hydrogen ion $\left( {{{\rm{H}}^ + }} \right)$ in aqueous solution and a base is a substance that releases hydroxide ion $\left( {{\rm{O}}{{\rm{H}}^ - }} \right)$in a solution. It is also to be noted that releasing of ${{\rm{H}}^ + }$ or ${\rm{O}}{{\rm{H}}^ - }$ is possible only in liquid state.
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