Question

What is \(\mathrm{pOH}\) of an aqueous solution with hydrogen ion concentration equal to \(3 \times 10^{-5} \mathrm{~mol} \mathrm{~L}^{-1}\) ? (a) \(9.47\) (b) \(4.52\) (c) \(12.69\) (d) \(11.69\)

Short answer

The pOH of the solution is 9.52, which is not listed in the options provided.

Step-by-step solution

Calculate the pH

Use the formula for pH, which is pH = -log[H+], where [H+] is the concentration of hydrogen ions. For [H+] of \(3 \times 10^{-5} M\), the pH is calculated as pH = -log(3 \times 10^{-5}).

Calculate the pOH

Knowing that pH + pOH = 14 for aqueous solutions at 25°C, you can rearrange the equation to find pOH: pOH = 14 - pH. After calculating the pH from the first step, subtract this value from 14 to find the pOH.

Find the numerical value of pH and pOH

Using a calculator, find the pH from Step 1, and then use this value to calculate pOH from Step 2. The final result will be the pOH of the solution.

Key concepts

pH and pOH Relationship

Understanding the relationship between pH and pOH is crucial for students studying chemistry, particularly in the realm of acid-base chemistry. These two concepts are linked by a simple mathematical relationship: the sum of the pH and pOH of an aqueous solution is always 14 at 25°C. This is due to how these values are defined. The pH is a measure of the acidity of a solution, representing the negative logarithm of the hydrogen ion concentration. On the other hand, pOH measures the alkalinity and represents the negative logarithm of the hydroxide ion concentration.

This inverse relationship is essential in the study of acid-base equilibrium because if you know the value of one (either the pH or the pOH), you can easily determine the other. In practice, this means that in a neutral solution where the pH is 7, the pOH is also 7, and any shift in pH due to added acid or base will correspondingly alter the pOH to maintain their sum as 14.

Hydrogen Ion Concentration

The hydrogen ion concentration in a solution is foundational to understanding acid-base chemistry. It is usually denoted as \[ \left[\text{H}^+\right] \] and refers to the amount of hydrogen ions (protons) per unit volume in the solution. This concentration is a direct determinant of a solution's pH value; the higher the hydrogen ion concentration, the more acidic the solution is, and thus, the lower the pH value.

In the context of the provided exercise, the hydrogen ion concentration is given, and it is this value that sets the stage for calculating the pH. The negative logarithm of the hydrogen ion concentration gives the pH value, which is a clear and intuitive scale for comparing the acidity of different solutions. For instance, a higher value of \[ \left[\text{H}^+\right] \] will consequently produce a lower pH value.

pH Calculation

The pH calculation is a straightforward yet vital process in quantifying the acidity of a solution. The formula \( \text{pH} = -\log\left[\text{H}^{+}\right] \) is used, where \( \left[\text{H}^{+}\right] \) is the hydrogen ion concentration. To apply this formula, one starts with determining the hydrogen ion concentration of the solution, which can be provided directly or calculated from the properties of the solute.

The use of logarithms in this calculation compresses the wide range of hydrogen ion concentrations into a manageable scale; pH generally ranges from 0 (highly acidic) to 14 (highly basic). This is invaluable for scientists and students alike, providing an easier means to discuss and compare the acidity of different solutions. In the coursework exercise, the given \( \left[\text{H}^{+}\right] \) is plugged into this formula, allowing one to calculate the pH as the first step towards finding the pOH.

Acid-base Equilibrium

In chemistry, acid-base equilibrium is a central concept that explains how acids and bases interact in a solution to establish a state of balance. At this equilibrium, the rate of the forward reaction (where the acid donates a proton to water) equals the rate of the reverse reaction (where the conjugate base accepts a proton from water). The equilibrium is governed by the constant \( K_a \) for acids and \( K_b \) for bases, and it can be shifted by changes in concentration or by the addition of other substances.

In relation to pH and pOH, acid-base equilibrium provides the backdrop for why these values change the way they do. When an acid is added to water, it increases the hydrogen ion concentration, promoting a decrease in pH. Conversely, when a base is present, it decreases the hydrogen ion concentration, thereby increasing pH. These changes are mirrored in the pOH values as they must always add up to 14 in an aqueous solution at 25°C. These principles help students predict the behavior of acids and bases in various scenarios, enhancing their understanding of chemical reactions and solution chemistry.