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Question: If \( {{10}^{-6}} \) M HCl is diluted to \( 100 \) times. Its pH is: (A) \( 6 \) (B) \( 8 \) ...

If 10−6{{10}^{-6}} M HCl is diluted to 100100 times. Its pH is:
(A) 66
(B) 88
(C) 6⋅956\cdot 95
(D) 9⋅59\cdot 5

Explanation

Solution

10−6{{10}^{-6}} M HCl is diluted to 100100 times means water is added to it or we can say that due to addition of water the concentration of HCl decreases. So, we will find the new concentration for HCl after the dilution. But here the effect of hydrogen ions of water will also be included along with hydrogen ions of hydrochloric acid because water also gets dissociated into H+{{H}^{+}} and OH−O{{H}^{-}} ions. Then find the resulting pH value at this concentration.

Formula Used: pH=−log⁡[H+]\text{pH}=-\log \left[ {{\text{H}}^{+}} \right]

Complete Step By Step Solution
When HCl is diluted to 100 times its concentration decreases so the new concentration becomes - 10−6100=10−6102=10−6−2=10−8M\dfrac{{{10}^{-6}}}{100}=\dfrac{{{10}^{-6}}}{{{10}^{2}}}={{10}^{-6-2}}={{10}^{-8}}M
HCl being strong acid dissociates into hydrogen and chloride ions on other hand water also dissociates as- H2O⇌H++OH−{{\text{H}}_{2}}\text{O}\rightleftharpoons {{\text{H}}^{+}}+\text{O}{{\text{H}}^{-}} . For water the pH value is 7 and the corresponding concentration is 10−7M{{10}^{-7}}M .
So, the pH for the diluted HCl becomes:
pH=−log⁡[H+]\text{pH}=-\log \left[ {{\text{H}}^{+}} \right]
pH=−log⁡(10−8+10−7)\text{pH}=-\log \left( {{10}^{-8}}+{{10}^{-7}} \right)
pH=−log⁡(10−7(10−1+1))\text{pH}=-\log \left( {{10}^{-7}}\left( {{10}^{-1}}+1 \right) \right)
pH=−log⁡(10−7(0⋅1+1))\text{pH}=-\log \left( {{10}^{-7}}\left( 0\cdot 1+1 \right) \right)
pH=−log⁡(10−7(1⋅1))\text{pH}=-\log \left( {{10}^{-7}}\left( 1\cdot 1 \right) \right)
pH=−log⁡(1⋅1×10−7)\text{pH}=-\log \left( 1\cdot 1\times {{10}^{-7}} \right)
Using identity: -
log⁡(a×b)=log⁡a+log⁡b\log (\text{a}\times \text{b})=\log \text{a}+\log \text{b}
pH=−log⁡1⋅1+(−log⁡10−7)\text{pH}=-\log 1\cdot 1+(-\log {{10}^{-7}})
pH=−0⋅04−(−7)log⁡10\text{pH}=-0\cdot 04-(-7)\log 10
pH=−0⋅04+7\text{pH}=-0\cdot 04+7
pH=−0⋅04+7log⁡10\text{pH}=-0\cdot 04+7\log 10
pH=6⋅96\text{pH}=6\cdot 96
So, the correct choice is (C).

Additional Information
The pH is defined as the potential of hydrogen which tells us about the concentration of hydrogen ions in the aqueous solution. It tells us whether the given solution is acidic or basic. The pH scale ranges from 0−140-14 , pH less than 7 specifies acidity and pH greater than 7 specifies basicity, pH of 7 comes under neutral i.e. at this pH value there are equal no. of hydrogen and hydroxyl ions.
The acid with high dissociation constant means that it will dissociate highly into its ions in the aqueous solution. The pH value for a strong acid will be less than that for a weak acid which indicates that as the pH value approaches 7 the strength of acid keeps on decreasing. After crossing the value 7 the acidic character is lost and basicity comes into action. The pH scale is logarithmic due to which each whole pH value below 7 is ten times more acidic than the next higher value.

Note
Do add the concentration of hydrogen ions due to water as it will also dissociate into its respective ions. If you do not add this then the calculated answer will be wrong. Similarly if a strong base is diluted instead of acid then one has to take care of the hydroxyl ions for water along with the base. The process of dilution simply means increasing the amount of water or solvent without increasing the amount of solute which will result in the decrease of concentration of given solute.