Question

A sample of Windex had a \(\left[\mathrm{OH}^{-}\right]=6.3 \times 10^{-5} \mathrm{~mol} \mathrm{~L}^{-1}\) What is the \(\mathrm{oH}\) of the sample?

Short answer

The pOH of the sample is -log(6.3 × 10⁻⁵), which is approximately 4.20.

Step-by-step solution

Recall the formula for pOH

The pOH of a solution is calculated using the formula: pOH = -log[OH⁻], where [OH⁻] is the concentration of hydroxide ions in moles per liter.

Use the given hydroxide ion concentration

Substitute the given hydroxide ion concentration into the formula: pOH = -log(6.3 × 10⁻⁵ M).

Calculate pOH

Calculate the pOH by evaluating the logarithm of the hydroxide ion concentration: pOH = -log(6.3 × 10⁻⁵).

Key concepts

Hydroxide Ion Concentration

Hydroxide ions (\text{OH}^-) play a vital role in acid-base chemistry. These ions are formed when a base dissolves in water, resulting in an increase in the hydroxide ion concentration, which can be expressed in moles per liter (\text{mol/L} or \text{M}). This value denotes how many moles of hydroxide ions are present in one liter of solution. It is an important metric used to calculate the strength of a base.

For instance, if a cleaning solution like Windex has a hydroxide ion concentration of \(6.3 \times 10^{-5} \text{M}\), it suggests that in every liter of Windex, there are \(6.3 \times 10^{-5}\) moles of hydroxide ions. Understanding this concentration helps chemists to predict the behavior of bases in reactions and to classify their strength.

pOH Formula

The pOH of a solution is a measure of the basicity of a solution. It is calculated using the pOH formula, which is \(\text{pOH} = -\log[\text{OH}^-]\). This formula provides a direct relationship between the hydroxide ion concentration and the pOH value. To make sense of the negative logarithm, remember that a higher hydroxide ion concentration, which corresponds to a stronger base, results in a lower pOH value.

Continuing with the Windex example, you would input the hydroxide ion concentration into the pOH formula like so: \(\text{pOH} = -\log(6.3 \times 10^{-5})\). The logarithm scales down the typically small hydroxide ion concentration to a more manageable number, which in this case corresponds to the basicity of the cleaning solution.

Acid-Base Chemistry

Acid-base chemistry is a fundamental concept that deals with the substances that can donate protons (acids) and accept protons (bases). Water (\text{H2O}) can both accept and donate protons, acting as both an acid and a base. The balance between hydroxide ions (\text{OH}^-) and hydronium ions (\text{H3O}^+) in a solution determines its pH and pOH, which are related by the equation \(\text{pH} + \text{pOH} = 14\) at 25°C in pure water.

Understanding how to manipulate pH and pOH is critical in various processes from industrial applications to biological systems. For example, ensuring the correct pOH of a cleaning solution, like in our Windex example, is necessary for effectiveness and safety. The relationship between pH, pOH, and the corresponding ion concentrations is essential for predicting the outcomes of many chemical reactions.