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Chapter 15: Problem 70

What is \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) in a solution whose pH is 1.9\(?\)

Short Answer

Expert verified
The concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions in the solution is \(1.26 \times 10^{-2} M\).

Step by step solution

01

Understand the pH formula

The formula that relates pH and the concentration of hydronium ions (\(\mathrm{H}_{3} \mathrm{O}^{+}\)) in a solution is \(pH = -\log_{10}[\mathrm{H}_{3} \mathrm{O}^{+}]\). In this problem, we are given the pH (1.9) and we need to find \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration.
02

Rearrange the formula to solve for [\(\mathrm{H}_{3} \mathrm{O}^{+}\)]

The pH formula can be rearranged to solve for the concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\). This can be done by applying 10 to the power of both sides of the equation, inverting the minus sign on RHS, this will give: \([\mathrm{H}_{3} \mathrm{O}^{+}] = 10^{-pH}\)
03

Substitute the given pH value into the rearranged equation

Now substitute the given pH value (1.9) into the equation above: \([\mathrm{H}_{3} \mathrm{O}^{+}] = 10^{-1.9}\)
04

Evaluate the expression

Calculate the value of the equation to get the concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\) in the solution: \([\mathrm{H}_{3} \mathrm{O}^{+}] = 1.26 \times 10^{-2} M\)

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Most popular questions from this chapter

What kind of an electrolyte is a weak base?

Why is water considered amphoteric?

Calculate the \(\mathrm{pH}\) of a 0.0316 \(\mathrm{M}\) solution of the strong base RbOH.

What are the components of a buffer solution? Give an example.

A solution of acetic acid had the following solute concentrations: \(\left[\mathrm{CH}_{3} \mathrm{COOH}\right]=\) \(0.035 \mathrm{M},\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=7.4 \times 10^{-4} \mathrm{M},\) and \(\left[\mathrm{CH}_{3} \mathrm{COO}^{-}\right]=7.4 \times 10^{-4} \mathrm{M} .\) Calculate the \(K_{a}\) of acetic acid based on these data.
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