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Question: How many times more basic is a solution with pH of \( 10 \) than a solution with a pH of \( 8 \) ? ...

How many times more basic is a solution with pH of 1010 than a solution with a pH of 88 ?
a. A pH of 1010 is two times as basic
b. A pH of 88 is two times as basic
c. A pH of 1010 is 2.0002.000 times as basic
d. A pH of 1010 is 100100 times as basic

Explanation

Solution

In chemistry, pH is a scale which is specifically used for measuring the strength of acidity or basicity of a solution. In general, the lower the value of pH, the higher will be the acidity of solution whereas higher the value of pH, the higher will be the basicity of the solution.

Complete answer:
The pH of a solution is defined as per following equation:
pH=−log⁡[H]+   −(i)pH = - \log {[H]^ + }\,\,\, - (i)
Where, [H]+{[H]^ + } is the molar concentration of hydrogen ions. The value of pH lies from 00 to 1414 in which if the value of pH is less than 77 , then the solution is acidic. If the value of pH is greater than 77 , then the solution is basic and if its value is exactly equal to 77 , then the solution is said to be neutral.
Now, for the given question we need to compare the molar concentrations of hydrogen ion for both the values of pH which is calculated as follows:
Case-1: the value of pH is 1010 :
Substituting value in equation (i)-
10=−log⁡[H]+10 = - \log {[H]^ + }
⇒[H]+=10−10\Rightarrow {[H]^ + } = {10^{ - 10}}
Case-2: the value of pH is 88 :
Substituting value in equation (1)-
8=−log⁡[H]+8 = - \log {[H]^ + }
⇒[H]+=10−8\Rightarrow {[H]^ + } = {10^{ - 8}}
Comparing the values of concentration of hydrogen ion in both the cases and the finding the ratio as follows:
[H+]1[H+]2=10−1010−8\dfrac{{{{[{H^ + }]}_1}}}{{{{[{H^ + }]}_2}}} = \dfrac{{{{10}^{ - 10}}}}{{{{10}^{ - 8}}}}
⇒[H+]1[H+]2=10−2\Rightarrow \dfrac{{{{[{H^ + }]}_1}}}{{{{[{H^ + }]}_2}}} = {10^{ - 2}}
⇒[H+]2=100×[H+]1\Rightarrow {[{H^ + }]_2} = 100 \times {[{H^ + }]_1}
Hence, a solution of pH of 1010 is 100100 times as basic as the solution of pH 88 .
Thus, option (d) is the correct answer.

Note:
It is important to note that to compare the strength of acidity or basicity of a solution, just look for the value of pH and pOH associated with the solution. pOH is the negative logarithm of hydroxide ion and is related to pH by the expression pH+pOH=14pH + pOH = 14