Question

What is the pH of $0.45M$ ${H_2}S{O_4}$ ?

Answer 1

pH of a solution is the negative logarithm of concentration of ${H^ + }\;$ ions. pH helps to identify whether a solution is acidic, basic or neutral. In the question molarity of sulphuric acid is given, from this molarity find out the ${H^ + }\;$ ion concentration and then using the formula pH can be found out. The formula for pH is: $pH = - log[{H^ + }]$

Complete Step By Step Answer:
pH is defined as the negative logarithm of ${H^ + }\;$ ion concentration. It is a measure of how acidic/basic water or any solution is.
The measurement was originally used by the Danish biochemist S.P.L. Sorensen to represent the hydrogen ion concentration, expressed in equivalents per litre, of an aqueous solution. Its formula is given as:
$pH = - log[{H^ + }]$
In the question given above we have to determine the pH of $0.45M$ of strong acid ${H_2}S{O_4}$ . It is known that the sulphuric acid ${H_2}S{O_4}$ is a strong acid as it dissociates completely in water. And this ionization is hardly affected by the presence/absence of other solutes present in the same solution. Therefore dissociation occurs like,
${H_2}S{O_4} \to 2{H^ + } + SO_4^{(2 - )}$
The concentration of ${H_2}S{O_4}$ is given as $0.45M$ . So it can be written as:
$[{H_2}S{O_4}] = 0.45M$
Now we know that pH is also the concentration of hydrogen ions in the solution. and also you should know that $1$ mole of ${H_2}S{O_4}$ gives $2$ mole of ${H^ + }\;$ ions therefore its concentration will be double the concentration of ${H_2}S{O_4}$ and thus:
$[{H^ + }] = 2{\text{ }}[{H_2}S{O_4}]$
$\Rightarrow [{H^ + }] = 2 \times 0.45$
$\Rightarrow [{H^ + }] = 0.9M$
Now that we have found out the value of ${H^ + }\;$ we can substitute this value in the formula to find out the pH of the sulphuric acid.
Thus, $pH = - log[{H^ + }]$
$\Rightarrow pH = - log[0.9]$
$\Rightarrow pH = - \left( { - 0.04575} \right)$
$\Rightarrow pH = + 0.04575$
Therefore the value of pH is $+ 0.04575$ .

Note:
The full form of pH is the potential of hydrogen. It ranges from $0 - 14$ . When a solution is acidic, its pH will be less than $7$ , and when a solution is basic or alkaline, its pH will be greater than $7$ . pH $7$ is considered neutral. Pure water has a pH of $7$ .