Question

The pH of milk, black coffee, tomato juice, lemon juice and egg white are 6.8, 5.0, 4.2, 2.2 and 7.8 respectively. Calculate corresponding hydrogen ion concentration in each.

Answer 1

Hint: The ‘potential of hydrogen’ or ‘power of hydrogen’ is referred as pH in chemistry and the pH of the solution determines whether the given solution is acidic, basic or neutral in nature. It also tells us how acidic or alkaline the given solution is.

Formula used:
The pH of solution is calculated as the minus log of hydrogen ion concentration of that solution.
The formula used for determining pH is:
\[pH = \dfrac{1}{{\log \left[ {{H^ + }} \right]}} = - \log \left[ {{H^ + }} \right]\]
The hydrogen ion concentration is denoted by \[\left[ {{H^ + }} \right]\].

Complete step by step answer:
The pH of the solution is determined by measuring the hydrogen ion concentration of that solution. The solution with pH below 7 is considered as acidic in nature and the solutions with pH higher than that of 7 are considered as alkaline in nature. The solution with pH 7 is neutral in nature.
Here, we will determine hydrogen ion concentration based on the pH given.
To determine the hydrogen ion concentration, we need to rearrange the above formula.
On rearranging the formula, we will get:
\[\left[ {{H^ + }} \right] = anti\log \left[ { - pH} \right]\]
Now, we will calculate hydrogen ion concentration for each substance based on its pH.

1. The pH of milk is 6.8.
The formula for calculating hydrogen ion concentration of the milk is:
\[\left[ {{H^ + }} \right] = anti\log \left[ { - pH} \right]\]
On substituting the respective value, we will get:
\[\left[ {{H^ + }} \right] = anti\log \left[ { - 6.8} \right]\]
\[\Rightarrow \left[ {{H^ + }} \right] = 1.584 \times {10^{ - 7}}M\]
Therefore, the hydrogen ion concentration of milk is \[1.584 \times {10^{ - 7}}M\].

2. The pH of black coffee is given as 5.0.
The formula for calculating hydrogen ion concentration of the black coffee is:
\[\left[ {{H^ + }} \right] = anti\log \left[ { - pH} \right]\]
On substituting the respective value, we will get:
\[\left[ {{H^ + }} \right] = anti\log \left[ { - 5.0} \right]\]
\[\Rightarrow \left[ {{H^ + }} \right] = 1 \times {10^{ - 5}}M = {10^{ - 5}}M\]
Therefore, the hydrogen ion concentration of black coffee is \[{10^{ - 5}}M\].

3. The pH of tomato juice is 4.2.
The formula for calculating hydrogen ion concentration of the tomato juice is:
\[\left[ {{H^ + }} \right] = anti\log \left[ { - pH} \right]\]
On substituting the respective value, we will get:
\[\left[ {{H^ + }} \right] = anti\log \left[ { - 4.2} \right]\]
\[\Rightarrow \left[ {{H^ + }} \right] = 6.309 \times {10^{ - 5}}M\]
Therefore, the hydrogen ion concentration of tomato juice is\[6.309 \times {10^{ - 5}}M\].

4. The pH of lemon juice is 2.2.
The formula for calculating hydrogen ion concentration of the lemon juice is:
\[\left[ {{H^ + }} \right] = anti\log \left[ { - pH} \right]\]
On substituting the respective value, we will get:
\[\left[ {{H^ + }} \right] = anti\log \left[ { - 2.2} \right]\]
\[\Rightarrow \left[ {{H^ + }} \right] = 6.30 \times {10^{ - 3}}M\]
Therefore, the hydrogen ion concentration of\[6.30 \times {10^{ - 3}}M\].

5. The pH of egg white is 7.8.
The formula for calculating hydrogen ion concentration of the egg white is:
\[\left[ {{H^ + }} \right] = anti\log \left[ { - pH} \right]\]
On substituting the respective value, we will get:
\[\left[ {{H^ + }} \right] = anti\log \left[ { - 7.8} \right]\]
\[\Rightarrow \left[ {{H^ + }} \right] = 1.584 \times {10^{ - 8}}M\]
Therefore, the hydrogen ion concentration of \[1.584 \times {10^{ - 8}}M\].

Additional information:
The pH scale, used for determining the acidic or basic nature of the aqueous solution, ranges from 0 to 14.
The solution with pH ranging from 0 to 3 are considered as strong acids whereas, the solution with pH 4 to just below 7 are weak acids. The solutions with pH ranging from 12 to 14 are strong bases and those falling in the range of 7 to 10 are weak bases.

Note: To calculate the hydrogen ion concentration of a solution, we need to rearrange the formula used for calculating pH. We can also use the following formula to calculate the hydrogen ion concentration of solution based on its pH.
\[\left[ {{H^ + }} \right] = {10^{ - pH}}\]
While calculating hydrogen ion concentration using pH of the solution, the antilog of the pH is taken. While calculating the antilog of the pH, keep in mind that we must take antilog of negative value of pH.