Question

When equal volumes of pH=4 and pH=6 are mixed together then the pH of the resulting solution will be: [log 5=0.7]
A) 4.3
B) 4.7
C) 5
D) 5.3

Answer 1

Hint: pH of the solution is equal to the negative logarithm of hydrogen ion concentration.
Hydrogen ion concentration is equal to the ratio of the number of moles of hydrogen ions to the volume of solution in liters. When you multiply hydrogen ion concentration with volume of solution, you obtain the number of moles of hydrogen ions present in the solution.

Complete step by step answer:
Assume that 1 L of each solution is mixed.
Calculate the hydrogen ion concentration of solution having pH of 4.
\[\Rightarrow \left[ {{{\text{H}}^ + }} \right] = {10^{ - 4}}M\]
Calculate the number of moles present in one liter of \[{10^{ - 4}}M\] solution.
\[\Rightarrow{10^{ - 4}}{\text{mol/LL}} \times 1 = {10^{ - 4}}{\text{mol}}\]
Calculate the hydrogen ion concentration of solution having pH of 6.
\[\Rightarrow \left[ {{{\text{H}}^ + }} \right] = {10^{ - 6}}M\]
Calculate the number of moles present in one liter of \[{10^{ - 6}}M\] solution.
\[\Rightarrow{10^{ - 6}}{\text{mol/LL}} \times 1 = {10^{ - 6}}{\text{mol}}\]
Calculate total number of moles of hydrogen ions present when two solutions are mixed.
\[\Rightarrow{10^{ - 4}}{\text{mol}} + {10^{ - 6}}{\text{mol}} = 1.01 \times {10^{ - 4}}{\text{mol}}\]
Calculate total volume when two solutions are mixed.
\[\Rightarrow{\text{1 L + 1 L = 2 L}}\]
Calculate the hydrogen ion concentration when two solutions are mixed.
\[\Rightarrow \left[ {{{\text{H}}^ + }} \right]{\text{ = }}\dfrac{{1.01 \times {{10}^{ - 4}}{\text{mol}}}}{{{\text{2 L}}}}\]
\[\Rightarrow \left[ {{{\text{H}}^ + }} \right]{\text{ = 5}}{\text{.05}} \times {10^{ - 5}}{\text{M}}\]
pH of the solution is equal to the negative logarithm of hydrogen ion concentration.
\[\Rightarrow{\text{pH}} = - {\log _{10}}\left[ {{{\text{H}}^ + }} \right]\]
Substitute value of the hydrogen ion concentration and calculate the pH of the resulting solution when two solutions are mixed.
\[\Rightarrow{\text{pH}} = - {\log _{10}}{\text{5}}{\text{.05}} \times {10^{ - 5}}{\text{M}}\]
\[\Rightarrow{\text{pH}} = 4.3\]

Hence, the option (A) is the correct option.

Note: Do not write the option (C) 5 as the write answer by simply adding 4 and 6 and then by dividing it with 2. This is because pH is based on the logarithm of hydrogen ion concentration. So, you cannot add two pH values to obtain the pH of the resulting solution.