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Chapter 15: Problem 32

What is the \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration in a solution that is 100 times less acidic than one having a \(\mathrm{pH}\) of \(2.56 ?\)

Short Answer

Expert verified
The concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions in the less acidic solution is approximately \(2.75 \times 10^{-5}\mathrm{M}\).

Step by step solution

01

Determine the concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions in the given solution

Using the pH formula, we can calculate the concentration of hydronium ions in the given solution. The pH formula is given by: \[ \mathrm{pH} = -\log_{10} [\mathrm{H}_{3} \mathrm{O}^{+}] \] Given the pH value is 2.56, we can rearrange the formula to solve for the concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions: \[ [\mathrm{H}_{3} \mathrm{O}^{+}] = 10^{-\mathrm{pH}} \] Substitute the given pH value of 2.56 into the formula: \[ [\mathrm{H}_{3} \mathrm{O}^{+}] = 10^{-2.56} \]
02

Calculate the concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions in the given solution

Now, let's evaluate the expression: \[ [\mathrm{H}_{3} \mathrm{O}^{+}] = 10^{-2.56} \approx 2.75 \times 10^{-3} \mathrm{M} \] So, the concentration of hydronium ions in the given solution is approximately \(2.75 \times 10^{-3}\mathrm{M}\).
03

Determine the concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions in the less acidic solution

As the less acidic solution is 100 times less acidic than the given solution, we can divide the concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions in the given solution by 100 to find the concentration in the less acidic solution: \[ [\mathrm{H}_{3} \mathrm{O}^{+}]_{\text{less acidic}} = \frac{[\mathrm{H}_{3} \mathrm{O}^{+}]_{\text{given solution}}}{100} \] Now, let's substitute the value previously calculated for the given solution into the above formula: \[ [\mathrm{H}_{3} \mathrm{O}^{+}]_{\text{less acidic}} = \frac{2.75 \times 10^{-3}\mathrm{M}}{100} \]
04

Calculate the concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions in the less acidic solution

Finally, we can evaluate the expression: \[ [\mathrm{H}_{3} \mathrm{O}^{+}]_{\text{less acidic}} = \frac{2.75 \times 10^{-3}\mathrm{M}}{100} \approx 2.75 \times 10^{-5} \mathrm{M} \] Therefore, the concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions in the less acidic solution is approximately \(2.75 \times 10^{-5}\mathrm{M}\).

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Most popular questions from this chapter

When ammonia gas is dissolved in water, is the water behaving as an acid, as a base, or neither? Explain.

Perchloric acid, \(\mathrm{HClO}_{4}\), is a strong acid. (a) Write the chemical equation for the reaction between perchloric acid and water. (b) List all species present in an aqueous solution of perchloric acid in order of concentration, highest to lowest. (c) Calculate the concentration of all species (except \(\mathrm{H}_{2} \mathrm{O}\) ) present in a \(0.100 \mathrm{M} \mathrm{HClO}_{4}\) solution. (d) What is the \(\mathrm{pH}\) of this solution?

True or false? As a solution's acidity increases, its pH decreases.

What is the \(\mathrm{pH}\) of a solution whose hydronium ion concentration is \(0.0010 \mathrm{M?}\) Is the solution acidic or basic?

A solution is prepared by dissolving \(2.50\) moles of \(\mathrm{LiOH}\) in enough water to get \(4.00 \mathrm{~L}\) of solution. What are the \(\mathrm{OH}^{-}\) and the \(\mathrm{H}_{3} \mathrm{O}^{+}\) molar concentrations?
See all solutions

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