Question

5
select the correct answer.
the ph scale measures the acidity of a liquid as a function of its hydrogen ion (h⁺) concentration
ph = -log h⁺
how does the h⁺ concentration of a solution with a ph of 4 compare with that with a ph of 2?
○ a. the h⁺ concentration in a solution with a ph of 4 is 10 times that of a solution with a ph of 2
○ b. the h⁺ concentration in a solution with a ph of 4 is 100 times that of a solution with a ph of 2
○ c. the h⁺ concentration in a solution with a ph of 4 is 0.01 times that of a solution with a ph of 2
○ d. the h⁺ concentration in a solution with a ph of 4 is 0.1 times that of a solution with a ph of 2

Explanation:

Step1: Find $[H^+]$ for pH = 4

Given $pH=-\log[H^+]$, when $pH = 4$, we have $4=-\log[H^+_1]$, then $\log[H^+_1]= - 4$. By the definition of logarithm, $[H^+_1]=10^{-4}$.

Step2: Find $[H^+]$ for pH = 2

When $pH = 2$, we have $2=-\log[H^+_2]$, then $\log[H^+_2]= - 2$. By the definition of logarithm, $[H^+_2]=10^{-2}$.

Step3: Calculate the ratio

Find the ratio $\frac{[H^+_1]}{[H^+_2]}=\frac{10^{-4}}{10^{-2}}$. Using the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$, we get $\frac{10^{-4}}{10^{-2}}=10^{-4+2}=10^{-2}=0.01$.

Answer:

C. The $H^+$ concentration in a solution with a pH of 4 is 0.01 times that of a solution with a pH of 2.