Question

The pH of a sample of Vinegar is 3.76. Calculate the concentration of Hydrogen ions in it.

Answer 1

Hint:
- Vinegar is a commercial name used for Acetic acid. With pH of the solution given, we can easily find the concentration of hydrogen ions present in the solution. Formula to find pH is \[pH = - \log \left[ {{H^ + }} \right]\]

Complete step-by-step answer:
We know that Acetic acid is known as Vinegar. Here, the pH of the sample of Vinegar is given. So, we can find out the concentration of Hydrogen ions simply by using pH formula.
One molecule of Acetic acid dissociates and gives only one Hydrogen ion as shown below.
\[C{H_3}COOH \to C{H_3}CO{O^ - } + {H^ + }\]
Formula Used: \[pH = - \log \left[ {{H^ + }} \right]\]………………….(1)
Here it is given that \[pH = 3.76\]
Put the value of pH in equation (1), so
\[3.76 = - \log \left[ {{H^ + }} \right]\]…………………(2)
We need to Find value of \[\left[ {{H^ + }} \right]\], So we will use the fundamental equation from the logarithm given Below.
If \[A = \log \left[ B \right]\] then \[B = anti\log \left[ A \right]\].
So, we can write eq. (2) as
\[ - 3.76 = \log \left[ {{H^ + }} \right]\]
\[\left[ {{H^ + }} \right] = anti\log \left[ { - 3.76} \right]\]
Now use either a Log-Table or Scientific Calculator to find out antilog value of (-3.76).
\[\left[ {{H^ + }} \right] = 0.00017378\]M
Writing the value in Proper form,
\[\left[ {{H^ + }} \right] = 1.74 \times {10^{ - 4}}\]M
So, concentration of Hydrogen ions in given sample is \[1.74 \times {10^{ - 4}}\]M

Additional Information:
- In the formula \[pH = - \log \left[ {{H^ + }} \right]\], concentration of Hydrogen ion is always expressed in Molarity.
- The concept and formula of pH was given by Sorenson. We can find pH of any solution by the concentration of Hydrogen ions present in the solution and Concentration of Hydrogen ions can be found by pH of the solution.

Note:
- Do not forget the Minus sign of the value while finding out the antilog value as it may lead to error in solution.
e.g. antilog(3.0) is equal to 3000 and antilog(-3.0) is equal to 0.001.
- While finding out the concentration of Hydrogen ions, knowledge of fundamental Logarithmic equations like how to simplify a fractional number and how to get the logarithmic value of any number by its power to 10.