Problem 43 - Chemistry

Question

Calculate the \(\left[\mathrm{OH}^{-}\right]\) of each of the following solutions at \(25^{\circ} \mathrm{C}\). Identify each solution as neutral, acidic, or basic. a. \(\left[\mathrm{H}^{+}\right]=1.0 \times 10^{-7} M\) c. \(\left[\mathrm{H}^{+}\right]=12 \mathrm{M}\) b. \(\left[\mathrm{H}^{+}\right]=8.3 \times 10^{-16} M\) d. \(\left[\mathrm{H}^{+}\right]=5.4 \times 10^{-5} M\)

Step-by-Step Solution

Answer

a. \([\mathrm{OH}^-] = 1.0 \times 10^{-7} M\) (Neutral) b. \([\mathrm{OH}^-] \approx 1.20 \times 10^{-1} M\) (Basic) c. \([\mathrm{OH}^-] \approx 8.33 \times 10^{-16} M\) (Acidic) d. \([\mathrm{OH}^-] \approx 1.85 \times 10^{-10} M\) (Acidic)

Step 1: a. Calculate the concentration of OH⁻ ions

Given the concentration of H⁺ ions as \(1.0 \times 10^{-7} M\), we can find the concentration of OH⁻ ions using the Kw value and the formula mentioned above. \(K_w = [\mathrm{H}^+][\mathrm{OH}^-]\) Rearranging for [OH⁻]: \([\mathrm{OH}^-] = \frac{K_w}{[\mathrm{H}^+]}\) Plug in the values: \([\mathrm{OH}^-] = \frac{1.0 \times 10^{-14}}{1.0 \times 10^{-7}}\) \([\mathrm{OH}^-] = 1.0 \times 10^{-7} M\) Since [H⁺] = [OH⁻], the solution is neutral.

Step 2: b. Calculate the concentration of OH⁻ ions

Given the concentration of H⁺ ions as \(8.3 \times 10^{-16} M\), we can find the concentration of OH⁻ ions using the Kw value and the formula mentioned above. \([\mathrm{OH}^-] = \frac{K_w}{[\mathrm{H}^+]}\) Plug in the values: \([\mathrm{OH}^-] = \frac{1.0 \times 10^{-14}}{8.3 \times 10^{-16}}\) \([\mathrm{OH}^-] \approx 1.20 \times 10^{-1} M\) Since [OH⁻] > [H⁺], the solution is basic.

Step 3: c. Calculate the concentration of OH⁻ ions

Given the concentration of H⁺ ions as \(12 M\), we can find the concentration of OH⁻ ions using the Kw value and the formula mentioned above. \([\mathrm{OH}^-] = \frac{K_w}{[\mathrm{H}^+]}\) Plug in the values: \([\mathrm{OH}^-] = \frac{1.0 \times 10^{-14}}{12}\) \([\mathrm{OH}^-] \approx 8.33 \times 10^{-16} M\) Since [OH⁻] < [H⁺], the solution is acidic.

Step 4: d. Calculate the concentration of OH⁻ ions

Given the concentration of H⁺ ions as \(5.4 \times 10^{-5} M\), we can find the concentration of OH⁻ ions using the Kw value and the formula mentioned above. \([\mathrm{OH}^-] = \frac{K_w}{[\mathrm{H}^+]}\) Plug in the values: \([\mathrm{OH}^-] = \frac{1.0 \times 10^{-14}}{5.4 \times 10^{-5}}\) \([\mathrm{OH}^-] \approx 1.85 \times 10^{-10} M\) Since [OH⁻] < [H⁺], the solution is acidic.

Key Concepts

Acidic Solutions

In chemistry, an acidic solution is one where the concentration of hydrogen ions (\[\left[\mathrm{H}^{+}\right]\]) is greater than the concentration of hydroxide ions (\[\left[\mathrm{OH}^{-}\right]\]). This situation arises when the solution's pH is below 7. Understanding acidity involves recognizing that more hydrogen ions mean a higher level of acidity.
An easy way to remember this is that in acidic solutions:

• \( [\mathrm{H}^+] > [\mathrm{OH}^-] \)
• pH < 7

In the provided problem, part c gives an example of an acidic solution where \([\mathrm{H}^{+}]=12\,\text{M}\), yielding an \([\mathrm{OH}^{-}]\) of approximately \(8.33 \times 10^{-16} \text{M}\). Clearly, \([\mathrm{OH}^{-}]\) is much smaller than \([\mathrm{H}^{+}]\), indicating an acidic solution.
It's essential to observe that even a slight deviation of pH below 7 can classify a solution as acidic. Acids are generally known to give a sour taste and can be found in substances like vinegar and citrus fruits.

Basic Solutions

Basic solutions, also known as alkaline solutions, occur when the concentration of hydroxide ions (\(\left[\mathrm{OH}^{-}\right]\)) exceeds that of the hydrogen ions (\(\left[\mathrm{H}^{+}\right]\)). This condition results in a pH greater than 7. Bases are often slippery or soapy to the touch and have a bitter taste.
To determine if a solution is basic, check for the following:

• \( [\mathrm{OH}^-] > [\mathrm{H}^+] \)
• pH > 7

In the step-by-step solution, part b illustrates a basic solution situation with \([\mathrm{H}^{+}]=8.3 \times 10^{-16} \text{M}\), resulting in an \([\mathrm{OH}^{-}]\) of approximately \(1.20 \times 10^{-1} \text{M}\). Here, the \([\mathrm{OH}^{-}]\) is greater than the \([\mathrm{H}^{+}]\), hence the basic nature of the solution.
Common basic substances include baking soda and household ammonia. Understanding basic solutions is key in tasks like neutralizing acids or cleaning, where a higher pH is desirable.

Neutral Solutions

Neutral solutions are unique in that the concentration of hydrogen ions is equal to that of hydroxide ions, resulting in a balanced pH of 7. This equilibrium means the solution is neither acidic nor basic. The most common example of a neutral solution is pure water.
Key points to identify a neutral solution include:

• \( [\mathrm{H}^+] = [\mathrm{OH}^-] \)
• pH = 7

In the given exercise, part a showcases a neutral solution where both \([\mathrm{H}^{+}]\) and \([\mathrm{OH}^{-}]\) are \(1.0 \times 10^{-7} \text{M}\). This complete balance is what defines neutrality in solutions.
Neutral solutions, like water, are pivotal in maintaining life-supporting environments and are used widely in laboratories for chemical reactions that require a non-reactive background.