Question

The pH of the solution is 2. If its pH is to be raised to 4 then the \[[{{\text{H}}^ + }]\] of the original solution has to be:
A. Doubled
B. Halved
C. Increased by 100 times
D. Decreased by 100 times

Answer 1

Hint: pH and the concentration of hydrogen ion has an inverse relation. If the pH increases then the concentration of \[[{{\text{H}}^ + }]\] will decrease and vice versa. We need to calculate the concentration of \[[{{\text{H}}^ + }]\] on the pH value given to determine the decrease in concentration, using the formula.

Formula used: \[{\text{pH}} = - \log [{{\text{H}}^ + }]\]

Complete step by step solution:
Let us first calculate the concentration of \[[{{\text{H}}^ + }]\] using the formula for pH 2 and 4.
For pH 2, we will get
\[{\text{2}} = - \log [{{\text{H}}^ + }]\]
We can rewrite it as:
$\Rightarrow$\[ - {\text{2}} = \log [{{\text{H}}^ + }]\]
Since the log has a base 10 so we can raise the power of 10 at each side. 10 will cancel the log as follow
$\Rightarrow$\[{\text{1}}{{\text{0}}^{ - 2}} = {10^{\log [{{\text{H}}^ + }]}}\]
After canceling log and 10 we will get,
$\Rightarrow$\[{\text{1}}{{\text{0}}^{ - 2}} = [{{\text{H}}^ + }]\]
For pH 4,
\[4 = - \log [{{\text{H}}^ + }]\]
We can rewrite it as:
$\Rightarrow$\[ - 4 = \log [{{\text{H}}^ + }]\]
Since the log has a base 10 so we can raise the power of 10 at each side. 10 will cancel the log as follow
$\Rightarrow$\[{\text{1}}{{\text{0}}^{ - 4}} = {10^{\log [{{\text{H}}^ + }]}}\]
After canceling log and 10 we will gte,
$\Rightarrow$\[{\text{1}}{{\text{0}}^{ - 4}} = [{{\text{H}}^ + }]\]

Hence, the concentration of hydrogen ion changes from \[{\text{1}}{{\text{0}}^{ - 2}}\] to \[{\text{1}}{{\text{0}}^{ - 4}}\]. The concentration decreases 100 times, because a higher number in negative means decrease in quantity.

The correct option is, (D).

Note: pH is the power of hydrogen. We have seen the concentration of hydrogen is very small, in the negative power of 10 and it is difficult to study this low concentration of hydrogen and hence to make the study easier we introduced the concept of Ph. pH value lies within 0 to 14 with 7 being the neutral pH. The substances with pH below 7 are acidic and substances with pH above 7 are basic.