Select the correct answer.

The pH scale measures the acidity of a liquid as a function of its hydrogen ion [tex]\([H^+]\)[/tex] concentration.

[tex]\[ pH = -\log \left[ H^+ \right] \][/tex]

How does the [tex]\([H^+]\)[/tex] concentration of a solution with a pH of 4 compare with that of a solution with a pH of 2?

A. The [tex]\([H^+]\)[/tex] concentration in a solution with a pH of 4 is 0.1 times that of a solution with a pH of 2.

B. The [tex]\([H^+]\)[/tex] concentration in a solution with a pH of 4 is 100 times that of a solution with a pH of 2.

C. The [tex]\([H^+]\)[/tex] concentration in a solution with a pH of 4 is 0.01 times that of a solution with a pH of 2.

D. The [tex]\([H^+]\)[/tex] concentration in a solution with a pH of 4 is 10 times that of a solution with a pH of 2.



Answer :

To determine how the [tex]\( H^{+} \)[/tex] concentration of a solution with a pH of 4 compares with that of a solution with a pH of 2, we use the relationship given by the pH scale:
[tex]\[ pH = -\log \left[ H^{+} \right] \][/tex]

Let's begin by finding the hydrogen ion concentration for each pH value.

1. Hydrogen ion concentration for pH 4:
[tex]\[ pH = 4 \implies 4 = -\log \left[ H^{+} \right] \][/tex]
Solving for [tex]\( H^{+} \)[/tex]:
[tex]\[ \left[ H^{+} \right] = 10^{-4} \][/tex]

2. Hydrogen ion concentration for pH 2:
[tex]\[ pH = 2 \implies 2 = -\log \left[ H^{+} \right] \][/tex]
Solving for [tex]\( H^{+} \)[/tex]:
[tex]\[ \left[ H^{+} \right] = 10^{-2} \][/tex]

Next, we find the ratio of the hydrogen ion concentrations:

3. Ratio of hydrogen ion concentrations:
[tex]\[ \text{Ratio} = \frac{\left[ H^{+} \right]_{\text{pH 4}}}{\left[ H^{+} \right]_{\text{pH 2}}} = \frac{10^{-4}}{10^{-2}} = 10^{-4 - (-2)} = 10^{-4 + 2} = 10^{-2} = 0.01 \][/tex]

Thus, the [tex]\( H^{+} \)[/tex] concentration in a solution with a pH of 4 is [tex]\( 0.01 \)[/tex] times that of a solution with a pH of 2.

This corresponds to option C:
C. The [tex]\( H^{+} \)[/tex] concentration in a solution with a pH of 4 is 0.01 times that of a solution with a pH of 2.