Question

Given the following \(\left[\mathrm{OH}^{-}\right]\) values, determine the pH of each solution. a. \(1.0 \times 10^{-6} \mathrm{M}\) b. \(1.0 \times 10^{-9} \mathrm{M}\) c. \(1.0 \times 10^{-2} \mathrm{M}\) d. \(1.0 \times 10^{-7} \mathrm{M}\)

Short answer

a. pH = 8, b. pH = 5, c. pH = 12, d. pH = 7

Step-by-step solution

- Understand the Relationship between \(\text{pH}\) and \(\text{pOH}\)

The pH and pOH of a solution are related by the equation: \[\text{pH} + \text{pOH} = 14\]. Hence, we can find the pH if we know the pOH.

- Calculate the pOH

To find the pOH, use the formula: \(\text{pOH} = -\text{log}[\text{OH}^{-}]\). Apply this formula to each given \(\text{OH}^{-}\) concentration.

- Calculate pH for part (a)

For \([\text{OH}^{-}] = 1.0 \times 10^{-6} \text{M}\), calculate the pOH: \(\text{pOH} = -\text{log}(1.0 \times 10^{-6}) = 6\). Then, find the pH: \(\text{pH} = 14 - 6 = 8\).

- Calculate pH for part (b)

For \([\text{OH}^{-}] = 1.0 \times 10^{-9} \text{M}\), calculate the pOH: \(\text{pOH} = -\text{log}(1.0 \times 10^{-9}) = 9\). Then, find the pH: \(\text{pH} = 14 - 9 = 5\).

- Calculate pH for part (c)

For \([\text{OH}^{-}] = 1.0 \times 10^{-2} \text{M}\), calculate the pOH: \(\text{pOH} = -\text{log}(1.0 \times 10^{-2}) = 2\). Then, find the pH: \(\text{pH} = 14 - 2 = 12\).

- Calculate pH for part (d)

For \([\text{OH}^{-}] = 1.0 \times 10^{-7} \text{M}\), calculate the pOH: \(\text{pOH} = -\text{log}(1.0 \times 10^{-7}) = 7\). Then, find the pH: \(\text{pH} = 14 - 7 = 7\).

Key concepts

pOH

The concept of pOH is crucial when dealing with the acidity or basicity of a solution. pOH is a measure of the concentration of hydroxide ions (OH⁻) in a solution. It is derived from the formula: \(\text{pOH} = -\text{log}[\text{OH}^-]\). This means the pOH value is calculated by taking the negative logarithm (base 10) of the hydroxide ion concentration. If you know the hydroxide concentration, you can easily determine the solution's pOH, which then helps you find other properties like pH.

concentration of hydroxide ions

The concentration of hydroxide ions in a solution is represented by \([\text{OH}^-]\). This concentration helps in determining the pOH of the solution. Different concentrations of hydroxide ions will result in different pOH values, thus affecting the pH of the solution as well. In chemistry, concentrations like \(1.0 \times 10^{-6} \text{ M}\) or \(1.0 \times 10^{-9} \text{ M}\) are common, signifying how many moles of hydroxide ions are present in one liter of solution. Calculating pOH from these concentrations helps in further calculations to find the solution's pH.

logarithms in chemistry

Logarithms play a significant role in chemistry, especially when dealing with pH, pOH, and ion concentrations. The logarithmic scale compresses the range of values a lot, making it easier to manage. For instance, the formula for pOH, \(\text{pOH} = -\text{log}[\text{OH}^-]\), uses the logarithm to convert the often very small numbers associated with concentrations into more manageable values. Understanding how to use logarithms is crucial for accurately determining pOH and consequently pH.

relationship between pH and pOH

The relationship between pH and pOH is given by the simple equation: \( \text{pH} + \text{pOH} = 14\). This means that if you know the pOH, you can find the pH by subtracting the pOH value from 14, and vice versa. This relationship is vital because it links the acidity (pH) and the basicity (pOH) of a solution, helping you understand the overall behavior of the solution. For example, if the pOH of a solution is 6, the pH would be \(14 - 6 = 8\), indicating the solution is slightly basic.