Question

A solution of \[pH\text{ }9\] is one thousand times as basic as a solution of pH___.
A.\[4\]
B.\[7\]
C.\[~10\]
D.\[6\]

Answer 1

Hint: In order to solve this question we will establish a relationship between the pH values and the concentration of protons present in the solution
Then using that relationship we will try to find out the pH of solution given in the question.

Complete step by step answer:
The concentration of hydrogen ion in one molar hydrochloric acid, distilled water and one molar solution of sodium hydroxide are \[1\], \[{{10}^{-7}}\]and \[{{10}^{-14}}mol\text{ }d{{m}^{-3}}\] respectively. It is suitable to construct a scale of simpler numbers for representation of these values. This can be done by taking the reciprocal of the logarithm to the base ten of the concentration of hydrogen ions in the solution.
When\[\left[ {{H}_{3}}{{O}^{+}} \right]\text{ }=\text{ }1\text{ }mol\text{ }d{{m}^{-3}}\],
\[pHvalue=\dfrac{1}{\log 10[H_3{{O}^{+}}]}=-\log [H_3{{O}^{+}}]=-\log {{10}^{-7}}=7\]
Here we equate the pH value of the solution and the reciprocal of concentration of hydronium ion present in the solution. The proton exists in the form of hydronium ion in the solution. This is because the water present in the solution takes up the proton from the acid and becomes positively charged. If we could imagine the structure of water we could see that the water has a lone pair, and because of those it is a bent structure. So when those lone pairs are taken up by the proton in the solution, that is when the water becomes hydronium ion.
In the example we took the concentration of hydronium ion to be \[\left[ {{H}_{3}}{{O}^{+}} \right]\text{ }=\text{ }1\text{ }mol\text{ }d{{m}^{-3}}\], so now when we put this value in the relationship we have, we get \[7\] as the pH value. This indicates the solution was neutral to begin with.
Now consider the pH value given in the question is \[9\],
So the concentration of \[{{H}^{+}}\]will be
$pH=-\log {{H}^{+}}=9$
Hence $[{{H}^{+}}]={{10}^{-9}}$
So the proton concentration turned out to be \[{{10}^{-9~}}\]
The question says one thousand as basic as the a solution of pH, so the proton concentration is increased by \[1000\]
So we get,
$[{{H}^{+}}]={{10}^{-6}}$
So the now the pH would be
$pH=-\log {{H}^{+}}=6$

Hence, the correct option is D.

Note:
The pH and pOH of a water solution at \[25{}^\circ C\] are related by the following equation.
\[pH\text{ }+\text{ }pOH\text{ }=\text{ }14\]
If either the pH or the pOH of a solution is known, the other can be quickly calculated from the above formula.