Question

the equation for the ph of a substance is ph = -logh+, where h+ is the concentration of hydrogen ions. a basic solution has a ph of 11.2. an acidic solution has a ph of 2.4. what is the approximate difference in the concentration of hydrogen ions between the two solutions?
1.6×10^(-9)
4.0×10^(-3)
6.7×10^(-1)
1.6×10^(11)

Explanation:

Step1: Find hydrogen - ion concentration of basic solution

Given $pH =-\log[H^{+}]$, for basic solution with $pH = 11.2$, we can rewrite the formula as $[H^{+}]_{basic}=10^{-pH}$. So $[H^{+}]_{basic}=10^{- 11.2}$.

Step2: Find hydrogen - ion concentration of acidic solution

For acidic solution with $pH = 2.4$, using the formula $[H^{+}]=10^{-pH}$, we get $[H^{+}]_{acidic}=10^{-2.4}$.

Step3: Calculate the difference

The difference $\Delta[H^{+}]=[H^{+}]_{acidic}-[H^{+}]_{basic}=10^{-2.4}-10^{-11.2}$. Since $10^{-11.2}$ is extremely small compared to $10^{-2.4}$, we can approximate $\Delta[H^{+}]\approx10^{-2.4}$.
$10^{-2.4}=\frac{1}{10^{2.4}}\approx\frac{1}{251.19}\approx4.0\times10^{-3}$.

Answer:

$4.0\times10^{-3}$