Question

What is the hydroxide ion concentration in an aqueous solution when the hydronium ion concentration is \(1 \times 10^{-10}\) mole per liter?

Short answer

\(1 \times 10^{-4}\) mole per liter.

Step-by-step solution

Understanding the Relationship

In any aqueous solution at 25°C, the product of the concentrations of hydronium ions \([H_3O^+ ]\) and hydroxide ions \([OH^- ]\) is always equal to the ion product of water, which is \(1 \times 10^{-14}\). We use the formula \([H_3O^+][OH^-] = 1 \times 10^{-14}\).

Substitute the Given Value

We know that \([H_3O^+] = 1 \times 10^{-10}\). Substitute this value into the equation: \((1 \times 10^{-10})[OH^-] = 1 \times 10^{-14}\).

Solve for Hydroxide Ion Concentration

Divide both sides of the equation by \(1 \times 10^{-10}\) to solve for \([OH^-]\):\[ [OH^-] = \frac{1 \times 10^{-14}}{1 \times 10^{-10}} = 1 \times 10^{-4} \text{ mole per liter}. \]

Key concepts

Hydronium Ions

In chemistry, especially when studying solutions, hydronium ions play a crucial role. These ions are formed when an acid dissolves in water and donates a proton (H+) to a water molecule. This process effectively creates a hydronium ion, represented as \(H_3O^+\). Hydronium ions are central to understanding the concept of acidity in a solution, as they are an indicator of the solution's pH.

The concentration of hydronium ions directly affects the pH level of a solution. The pH is calculated using the formula \(pH = -\log[H_3O^+]\), where \([H_3O^+]\) is the concentration of hydronium ions.

In pure water at 25°C, the concentration of hydronium ions is usually \(1 \times 10^{-7}\) moles per liter, giving a neutral pH value of 7. When the concentration of \(H_3O^+\) is higher than this, the solution becomes acidic, and when it's lower, the solution is basic.

Hydroxide Ions

Hydroxide ions \([OH^-]\) are another crucial part of calculating a solution's pH. These ions are negatively charged and are often associated with basic or alkaline solutions. In water, hydroxide ions form typically through the dissociation of bases.

In solution chemistry at 25°C, the concentration of hydroxide ions varies as the concentration of hydronium ions shifts, maintaining constant equilibrium governed by the ion product of water. Typically, a low concentration of \(OH^-\) in a solution indicates an acidic environment, whereas a higher concentration suggests a basic one.

The concentration of hydroxide ions can be used to calculate the pOH of a solution and subsequently its pH, via the formula \(pOH = -\log[OH^-]\). Since \(pH + pOH = 14\) for solutions at 25°C, knowing the concentration of hydroxide can help determine the pH.

Ion Product of Water

The ion product of water is a fundamental concept that helps us understand the behavior of hydronium and hydroxide ions in water. At 25°C, the ion product is defined as the product of the concentrations of hydronium ions \([H_3O^+]\) and hydroxide ions \([OH^-]\), which is always equal to \(1 \times 10^{-14}\). This relationship indicates how water can self-ionize, providing a base point for calculating pH and pOH values in any aqueous solution.

Mathematically, the ion product of water can be expressed as:

• \([H_3O^+][OH^-] = 1 \times 10^{-14}\)

This constant is essential in performing calculations to find unknown concentrations of hydronium or hydroxide ions in solutions. By rearranging the equation and substituting known values, we can determine any missing concentration, such as in our example: if \([H_3O^+]\) increases, \([OH^-]\) must decrease and vice versa, to maintain the constant product of \(1 \times 10^{-14}\). This relationship is crucial for understanding how different substances change the acidity or basicity of a solution.