the ph of a solution decreases by 2.0. how does the hydronium ion concentration of the solution change…

Answer:

B. increases to 100 times the original concentration

Explanation:

Step1: Recall pH formula

The pH is defined as $pH = -\log[H_3O^+]$, where $[H_3O^+]$ is the hydronium - ion concentration.

Step2: Let the initial pH be $pH_1$ and final pH be $pH_2$

We know that $pH_2=pH_1 - 2$.

Step3: Express hydronium - ion concentrations in terms of pH

If $pH_1=-\log[H_3O^+]_1$ and $pH_2 = -\log[H_3O^+]_2$, then $-\log[H_3O^+]_2=-\log[H_3O^+]_1 - 2$.

Step4: Rearrange the equation

$\log[H_3O^+]_2=\log[H_3O^+]_1 + 2$.

Step5: Use the property of logarithms

Since $a=\log b$ implies $b = 10^a$, we have $[H_3O^+]_2 = 10^{\log[H_3O^+]_1+2}$. Using the property $a^{m + n}=a^m\times a^n$, we get $[H_3O^+]_2=10^{\log[H_3O^+]_1}\times10^2$. Since $10^{\log[H_3O^+]_1}=[H_3O^+]_1$, then $[H_3O^+]_2 = 100[H_3O^+]_1$. So the hydronium - ion concentration increases to 100 times the original concentration.