Question

An aqueous solution has an OH concentration of \(1.0 \times 10^{-11} \mathrm{M}\). What is the \(\mathrm{H}_{3} \mathrm{O}\) concentration? Is this solution acidic or basic? Justify your answer

Short answer

The H3O⁺ concentration is \(1.0 \times 10^{-3} M\), and the solution is acidic.

Step-by-step solution

Understand what is given

The OH⁻ concentration of the aqueous solution is given as \(1.0 \times 10^{-11} M\).

Apply the water ion product formula

The water ion product formula, \(K_w = [H_3O^+][OH^-]\), where \(K_w\) represents the ion product constant for water and has a value of \(1.0 \times 10^{-14}\) at 25°C, can be used to find the H3O⁺ concentration if the OH⁻ concentration is known.

Calculate the H3O⁺ concentration

To find the H3O⁺ concentration, we need to rearrange the water ion product formula and replace \(K_w\) with the given value: \[H_3O^+ =\frac{K_w}{OH^-}\] Plug in the values, \(K_w= 1.0 \times 10^{-14} \) and \(OH^- = 1.0 \times 10^{-11} M\): \(H_3O^+ =\frac{1.0 \times 10^{-14}}{1.0 \times 10^{-11}}\) \(H_3O^+ = 1.0 \times 10^{-3} M\)

Determine whether the solution is acidic or basic

To determine whether the solution is acidic or basic, we need to compare the H3O⁺ concentration with the neutral value. For a neutral solution, \(H_3O^+ = OH^-\), and the typical value is \(1.0 \times 10^{-7} M\). 1. If \(H_3O^+ > 1.0 \times 10^{-7} M\), the solution is acidic. 2. If \(H_3O^+ < 1.0 \times 10^{-7} M\), the solution is basic.

Justify the answer

In our case, the H3O⁺ concentration is \(1.0 \times 10^{-3} M\). As this value is greater than \(1.0 \times 10^{-7} M\), the solution is acidic. Final answer: The H3O⁺ concentration is \(1.0 \times 10^{-3} M\), and the solution is acidic.

Key concepts

Hydronium Ion Concentration

In acid-base chemistry, understanding the hydronium ion concentration, represented as \([H_3O^+]\), is crucial. Hydronium ions are formed when water molecules gain a proton. This occurs in aqueous solutions when an acid dissolves in water.

For the given problem, you start with a known hydroxide ion concentration, \([OH^-]\). Thanks to the water ion product equation, if you know the hydroxide ion concentration, you can find the concentration of hydronium ions. The water ion product equation, \(K_w = [H_3O^+][OH^-]\), allows us to calculate unknown quantities in the equation.

By rearranging this formula, it becomes \([H_3O^+] = \frac{K_w}{[OH^-]}\), making it easy to find \([H_3O^+]\) if \([OH^-]\) is known. In this exercise, plugging \(1.0 \times 10^{-14}\) as \(K_w\) and \(1.0 \times 10^{-11} M\) for \([OH^-]\) gives the heightened \([H_3O^+]\) concentration of \(1.0 \times 10^{-3} M\). Thus, this solution is distinctly acidic.

pH and pOH

The pH and pOH scales are essential tools in measuring the acidity and basicity of solutions. The pH scale, specifically, quantifies the concentration of hydronium ions (\([H_3O^+]\))in a solution.

The relationship is given by the formula: \(pH = -\log_{10}(\text{[H}_3\text{O}^+\text{]})\). This logarithmic scale means that even small changes in hydronium ion concentration result in significant pH shifts.

Likewise, pOH measures the hydroxide ion concentration. The formula for pOH is similarly structured: \(pOH = -\log_{10}([OH^-])\). Importantly, in aqueous solutions, pH and pOH are interrelated, following the equation \(pH + pOH = 14\). Therefore, determining one allows for calculation of the other.

In the given problem, after calculating the hydronium ion concentration, you could find the pH by using the concentration in the pH formula. Knowing \([H_3O^+] = 1.0 \times 10^{-3} M\), one finds \(pH = 3\), again confirming an acidic solution since acidic solutions have a pH less than 7.

Water Ion Product

The water ion product, \(K_w\), plays a crucial role in determining the concentrations of hydronium and hydroxide ions in aqueous solutions. At 25°C, \(K_w\) is consistently valued at \(1.0 \times 10^{-14}\). This value represents the product of the concentrations of \([H_3O^+]\) and \([OH^-]\).

This constant results from the dissociation of water molecules into hydronium and hydroxide ions: \(2H_2O \rightleftharpoons H_3O^+ + OH^-\). Yet, how does this relate to determining if a solution is acidic or basic?

When the temperature remains at 25°C, the relationship between \([H_3O^+]\) and \([OH^-]\) is always governed by \(K_w = 1.0 \times 10^{-14}\). If \([H_3O^+] > [OH^-]\), there is an acidic environment, and conversely, if \([OH^-] > [H_3O^+]\), the solution becomes basic. For neutral solutions, \([H_3O^+] = [OH^-] = 1.0 \times 10^{-7}\) M.

Thus, \(K_w\) is not just a number; it is the key to understanding the fundamental nature of any aqueous solution.