Calculate [H3O^+] of an aqueous solution that is 1.8 × 10^-9 M in OH^- Round your answer to 2 significant figures.

Question

Note: Reference the Fundamental constants table for additional information.

Answer 1

To find the concentration of \([H_3O^+]\) in an aqueous solution given the concentration of \([OH^-]\), we can use the ion product of water at 25°C, which is:

\[ K_w = [H_3O^+][OH^-] = 1.0 \times 10^{-14} \]

Given that the concentration of hydroxide ions \([OH^-]\) is \(1.8 \times 10^{-9} , \text{M}\), we can rearrange the equation to find \([H_3O^+]\):

\[ [H_3O^+] = \frac{K_w}{[OH^-]} = \frac{1.0 \times 10^{-14}}{1.8 \times 10^{-9}} \]

Now, calculate \([H_3O^+]\):

\[ [H_3O^+] = \frac{1.0 \times 10^{-14}}{1.8 \times 10^{-9}} \approx 5.56 \times 10^{-6} , \text{M} \]

Rounding to 2 significant figures:

\[ [H_3O^+] \approx 5.6 \times 10^{-6} , \text{M} \]

Thus, the concentration of \([H_3O^+]\) in the solution is \( \boxed{5.6 \times 10^{-6}} , \text{M} \).