Question

The pOH of a solution is \(9.40 .\) Calculate the hydrogen ion concentration of the solution.

Short answer

The concentration of hydrogen ions (\([H^+]\)) in the solution is \(10^{-4.6}\) M.

Step-by-step solution

Calculate the Hydroxide Ion Concentration

pOH is calculated by the formula, pOH = \( -\log[OH^-] \). Therefore, the hydroxide ion concentration can be calculated by rearranging this formula as, \([OH^-] = 10^{-pOH}\). Given that the pOH of the solution is 9.40, the concentration of OH- ions becomes \([OH^-] = 10^{-9.40}\).

Calculate the Hydrogen Ion Concentration

Next, the hydrogen ion concentration can be calculated using the ion product of water (\(K_w\)), which is given as \(K_w = [H+][OH^-]\). By substituting our calculated \([OH^-]\) into this formula, the hydrogen ion concentration can be found: \([H+] = \frac{K_w}{[OH^-]}\) = \(\frac{1.0 \times 10^{-14}}{10^{-9.40}}\).

Key concepts

Hydrogen Ion Concentration

The hydrogen ion concentration, often denoted as \([H^+]\), is a crucial measure of the acidity or basicity of a solution. When you know the pOH of a solution, you can easily find the concentration of hydrogen ions using the relationship between pOH, \([OH^-]\), and \([H^+]\).

This relationship is revealed by the ion product of water, \(K_w\), which connects \([H^+]\) and \([OH^-]\) in an aqueous solution. To calculate \([H^+]\), first calculate the hydroxide ion concentration as \[ [OH^-] = 10^{-\text{pOH}} \].

Let's break down an example: given a pOH of \9.40\, the \([OH^-]\) turns out to be \([OH^-] = 10^{-9.40}\). With this, you can find \([H^+]\) using \([H^+] = \frac{K_w}{[OH^-]}\), and substituting values gives \([H^+] = \frac{1.0 \times 10^{-14}}{10^{-9.40}}\). This calculated \([H^+]\) will provide the exact acidity level of the solution.

Understanding how hydrogen ion concentration changes with pOH helps in predicting and controlling the pH level of solutions, which is vital in many scientific and industrial processes.

Hydroxide Ion Concentration

The concentration of hydroxide ions, denoted as \([OH^-]\), is integral in determining the nature of a solution, whether acidic or basic. Just like pH measures the concentration of hydrogen ions, pOH measures the concentration of hydroxide ions.

To find \([OH^-]\) given the pOH of a solution, we utilize the simple formula: \[ [OH^-] = 10^{-\text{pOH}} \]. This directly tells us the hydroxide ion concentration in given conditions. For instance, if the pOH is \9.40\, it means that \([OH^-] = 10^{-9.40}\), giving information about how basic the solution may be.

Since the hydroxide ion concentration directly influences the pH of the solution, understanding its calculation can aid in numerous chemical management processes, whether in lab settings or environmental sciences. This is particularly useful when balancing chemical reactions or adjusting the acidity/basicity for optimal reaction conditions.

Ion Product of Water (Kw)

The ion product of water, denoted as \(K_w\), is a constant at a given temperature that plays a vital role in the chemistry of aqueous solutions. \(K_w\) is defined by the product of the concentrations of the hydrogen ions (\([H^+]\)) and hydroxide ions (\([OH^-]\)) in water.

In pure water at 25°C, \(K_w\) is typically \(1.0 \times 10^{-14}\), meaning the product of \([H^+]\) and \([OH^-]\) concentrations is always this constant at that specific temperature. This constant is central to calculating either of the ions if one is known. For example, if you know \([OH^-]\), \([H^+]\) can be determined using the formula: \[ [H^+] = \frac{K_w}{[OH^-]} \].

Understanding \(K_w\) is crucial because it affects how solutions are balanced and predicts reaction outcomes. It provides insight into the behavior of solutions as they move between more acidic or basic states. Mastering \(K_w\) calculations is integral to chemistry, ensuring accurate results in both academic and professional laboratories.