Question

A beer has a pH of 4.30. What is the \[\left[ {{H_{3}}{O^ + }} \right]?\]
A. \[3.0 \times {1O^ - }^4\]
B. \[2.0 \times {1O^{ - 4}}\]
C. \[2.0 \times {1O^{ - 5}}\]
D. \[5.0 \times {1O^{ - 5}}\]

Answer 1

Hint:when we calculate the pH of an aqueous solution to know the concentration of the hydronium ion in moles per liter (molarity). The pH is calculated using the expression: \[pH\; = - {\text{ }}log{\text{ }}\left[ {{H_3}{O^ + }} \right].\] Now as per question pH value is given with help of formula easily calculate the value of hydronium ion.

Complete answer:
As we know pH is a value that expresses the concentration of hydrogen in solution. The pH scale ranges from \[0{\text{ }}to{\text{ }}14\;\], pH scale is a tool for measuring acids and bases. Litmus paper is an indicator used to tell if a substance is an acid or a base, pure water is neutral and has a pH of\[7\]. Solutions with a pH lower than \[7\] are acidic, while solutions with a pH higher than \[7\] are alkaline, or basic.
Beer has acidic pH because during fermentation not only ethanol is produced by the yeast. They produce organic acids and other metabolites like glycerol esters, higher alcohols, ketones as well.
Here we determine the value of hydronium ion, As it is well known that pH is negative logarithm of hydronium in concentration.
Now we can use the formula of pH
\[\Rightarrow pH\; = \; - log\left[ {{H_3}{O^ + }} \right]\]
\[\Rightarrow 4.30 = \; - {\text{ }}log\left[ {{H_3}{O^ + }} \right]\]
By solving log we get,
\[\Rightarrow log{10^{4{\text{ }}}} + log2 = \;log\dfrac{1}{{\left[ {{H_3}{O^ + }} \right]}}\]
\[\Rightarrow log\left( {2{\text{ }} \times {{10}^{4\;}}} \right) = \;log\;\dfrac{1}{{\left[ {{H_3}{O^ + }} \right]}}\]
\[\Rightarrow \dfrac{1}{{\left[ {{H_3}{O^ + }} \right]}} = \;2 \times {10^4}\]
\[\Rightarrow \left[ {{H_3}{O^ + }} \right] = {\text{ }}\dfrac{1}{{2 \times {{10}^4}}}\]
\[\Rightarrow \left[ {{H_3}{O^ + }} \right] = 5{\text{ }} \times {10^{ - 5}}mol/L\]

Therefore option (D) is the correct answer.

Note:
1. pH is a function of the acid / basic water content. Water with more free hydrogen ions is acidic and water with more free hydroxyl ions is basic. pH to determine the strength of the solution and
2. The pH can also control the availability of nutrients, biological functions, microbial activity, and the behavior of chemicals, it is used for environmental monitoring.