Question

What is the pH of a solution whose ${H^ + }$ ion concentration is $2 \times {10^{ - 5}}$ions/litre?
A.$4.7$
B.$6.7$
C.$9.3$
D.None of these

Answer 1

The pH scale is logarithmic and inversely indicates the concentration of hydrogen ions in the solution. This is because the formula used to calculate pH approximates the negative of the base 10 logarithm of the molar concentration of hydrogen ions in the solution. Here we use the formula of $pH$ which is $pH\; = - \log [{H_3}{O^ + }]$

Complete answer:
$pH$ 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 range goes from $0$ to $14$, with $7$ being neutral. pH of less than $7$ indicates acidity, whereas a $pH$ of greater than $7$ indicates a base. $pH$ is really a measure of the relative amount of free hydrogen and hydroxyl ions in the water.
To calculate the pH of an aqueous solution you need to know the concentration of the hydronium ion in moles per liter (molarity). $pH$ is then calculated using the expression:
$\Rightarrow pH\; = - \log [{H_3}{O^ + }]$
$\Rightarrow [{H^ + }] = 2 \times {10^{ - 5}} \\\ \Rightarrow pH = - \log (2 \times {10^{ - 5}}) \\\ \Rightarrow 5 - \log 2 \\\ \Rightarrow 4.7 \\\$
So, the correct answer is (A) $4.7$.

Note:
Indicators may be used to measure $pH$, by making use of the fact that their color changes with $pH$. Visual comparison of the color of a test solution with a standard color chart provides a means to measure accurately to the nearest whole number. More precise measurements are possible if the color is measured spectrophotometrically, using a colorimeter or spectrophotometer. Universal indicator paper is made from absorbent paper that has been impregnated with universal indicator. Another method of measuring $pH$ is using an electronic $pH$ meter.