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The ${{K}_{a}} $ of propionic acid is $1.34\times {{10} ^ {-5}} $. What is the pH of a solution containing 0.5M propionic acid and 0.5M sodium propionate?

Last updated date: 22nd Jun 2024
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Hint: For calculating pH we need to find:
$p{{K}_{a}} $, by using the formula: $p{{K}_{a}} =-\log {{K}_{a}} $,
Then, after finding $p{{K}_{a}} $, pH can be calculated by: $pH=p{{K}_{a}} +\log \left (\dfrac {\left [ salt \right]} {\left [ acid \right]} \right) $.

Complete step by step solution:
We have been provided that ${{K}_{a}} $ of propionic acid is $1.34\times {{10} ^ {-5}} $,
An acid dissociation constant (${{K}_{a}} $) is a quantitative measure of the strength of an acid in solution. It is the equilibrium constant for a chemical reaction known as dissociation in the context of acid–base reactions.
We know that $p{{K}_{a}} =-\log {{K}_{a}} $,
Now, keeping the values in the above equation we would get: $p{{K}_{a}} =-\log (1.34\times {{10} ^ {-5}}) $,
Solving it further: $p{{K}_{a}} =5-0.127$,
Value of $p{{K}_{a}} $ comes out to be: $p{{K}_{a}} =4.873$,
Now, we need to calculate the pH,
 We know that pH is a scale used to specify the acidity or basicity of an aqueous solution. Acidic solutions are measured to have lower pH values than basic or alkaline solutions. The pH scale is logarithmic and inversely indicates the concentration of hydrogen ions in the solution.
So, we will be calculating the value of pH by using the formula: $pH=p{{K}_{a}} +\log \left (\dfrac {\left [ salt \right]} {\left [ acid \right]} \right) $,
Now, as we have been given the value of: $\left [ salt \right] =\left [ acid \right] =0.5M$,
Keeping these values in $pH=p{{K}_{a}} +\log \left (\dfrac {\left [ salt \right]} {\left [ acid \right]} \right) $,
We would get: $pH=4.87+\log \left (\dfrac {0.5} {0.5} \right) $,

So, the value of pH comes out to be: 4.873.

Note: pH is important because substances such as our stomach acids tend to be at a certain pH in order to work properly. pH is also important because it must be at certain levels in order for living organisms to survive.