Question

Calculate the \(\mathrm{H}_{3} \mathrm{O}^{*}\) ion concentration from the \(\mathrm{OH}^{-}\)ion concentration. Then identify the solution as acidic, basic, or neutral. (a) \(\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-3} \mathrm{M}\) (b) \(\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-11} M\) (c) \(\left[\mathrm{OH}^{-}\right]=3.2 \times 10^{-8} M\)

Short answer

(a) The solution is basic with a H3O* concentration of 1.0 x 10^-11 M. (b) The solution is acidic with a H3O* concentration of 1.0 x 10^-3 M. (c) The solution is acidic with a H3O* concentration of 3.125 x 10^-7 M.

Step-by-step solution

Calculate the H3O* ion concentration

Using the equation, [H3O*] = Kw / [OH-], calculate [H3O*] for each solution. \n(a) For [OH-] = 1.0 x 10^-3 M, [H3O*] = (1.0 x 10^-14) / (1.0 x 10^-3) = 1.0 x 10^-11 M \n(b) For [OH-] = 1.0 x 10^-11 M, [H3O*] = (1.0 x 10^-14) / (1.0 x 10^-11) = 1.0 x 10^-3 M \n(c) For [OH-] = 3.2 x 10^-8 M, [H3O*] = (1.0 x 10^-14) / (3.2 x 10^-8) = 3.125 x 10^-7 M.

Identify the nature of the solution

Compare [H3O*] and [OH-] to determine whether each solution is acidic, basic, or neutral. \n(a) For [OH-] = 1.0 x 10^-3 M, [H3O*] = 1.0 x 10^-11 M, so the solution is basic because [OH-] > [H3O*]. \n(b) For [OH-] = 1.0 x 10^-11 M, [H3O*] = 1.0 x 10^-3 M, so the solution is acidic because [OH-] < [H3O*]. \n(c) For [OH-] = 3.2 x 10^-8 M, [H3O*] = 3.125 x 10^-7 M, so the solution is acidic because [OH-] < [H3O*].

Key concepts

Acid and Base Concentration

Understanding the concentration of acids and bases is fundamental in chemistry, especially when studying the behavior of solutions. The concentration is typically measured in molarity (M), which is moles of solute per liter of solution. When looking into acids and bases, it's essential to know that acid solutions have a higher concentration of hydrogen ions, denoted as \( \[H_3O^+\] \), and base solutions have a higher concentration of hydroxide ions, \( \[OH^-\] \).

The strength of an acid or a base depends on its ability to donate or accept \( \[H^+\] \) ions, which is reflected in its concentration in a solution. By understanding the molarity of these ions, we can calculate the pH or pOH of a solution, revealing its acidity or basicity respectively. It is also helpful for predicting the outcome of chemical reactions, as the concentration of these ions can drive the reaction in one direction or another.

Hydroxide Ion Concentration

The hydroxide ion concentration in a solution tells us how basic the solution is. It is often represented by \( \[OH^-\] \). A high concentration of hydroxide ions suggests that the solution is a strong base. Conversely, a low concentration of hydroxide ions would make the solution weakly basic or even acidic if the hydrogen ion concentration is higher by comparison.

For instance, pure water has a hydroxide ion concentration of \( 1.0 \times 10^{-7} \ M \), making it neutral. Solutions with higher \( \[OH^-\] \) concentrations than this are considered basic, while those with lower concentrations are acidic. This parameter is an integral part of understanding the balance between acids and bases in a chemical context, and it has a direct relationship with pH, as both scale inversely to each other.

Calculating H3O+ Concentration

To determine the hydrogen ion concentration, \( \[H_3O^+\] \), in a solution, we can use the ion product constant of water, \( K_w \), which is \( 1.0 \times 10^{-14} \ M^2 \). This expression is based on the autoionization of water, where one water molecule donates a proton to another, generating one hydroxide ion, \( \[OH^-\] \), and one hydronium ion, \( \[H_3O^+\] \).

The formula \( \[H_3O^+\] = \frac{K_w}{\left[OH^-\right]} \) allows us to calculate the hydrogen ion concentration from a known hydroxide ion concentration, aiding in characterizing the solution's acidity. This relationship highlights the inversely proportional nature of \( \[H_3O^+\] \) and \( \[OH^-\] \) in a solution, a concept that's at the core of acid-base chemistry.

Acidity and Basicity of Solutions

The acidity or basicity of a solution is a measure of its pH level, directly tied to the concentration of \( \[H_3O^+\] \) ions for acidity and \( \[OH^-\] \) ions for basicity. Solutions with a pH less than 7 are acidic, while those with a pH greater than 7 are basic. The pH scale is logarithmic, meaning each whole pH value below 7 is ten times more acidic than the next higher value.

When given the concentration of hydroxide ions, as we are in the exercise, we can calculate the corresponding \( \[H_3O^+\] \) ion concentration and then use the pH scale to determine the solution's character. This process is a routine part of chemical analysis, allowing for the prediction and control of reactions, preserving the stability of chemical compounds, and understanding biological systems.