Question

What are the concentrations of \(\mathrm{H}_{3} \mathrm{O}^{+}\)and \(\mathrm{OH}^{-}\)in pure water (at \(25^{\circ} \mathrm{C}\) )?

Short answer

The concentrations of \(\mathrm{H}_{3} \mathrm{O}^{+}\) and \(\mathrm{OH}^{-}\) in pure water at \(25^{\circ}C\) are each \(1.0 * 10^{-7}\) M.

Step-by-step solution

Understand the Autodissociation of Water

In water, autodissociation occurs. Some water molecules donate protons to other water molecules, resulting in \(\mathrm{H}_{3} \mathrm{O}^{+}\) (hydronium) ions and \(\mathrm{OH}^{-}\) (hydroxide) ions. This occurs in such a way that the product \([H_{3}O^{+}]*[OH^{-}]\) is always equal to the ion product of water, or the Kw value.

Find the Ion Product of Water at given Temperature

The Kw value at \(25^{\circ}C\) is \(1.0 * 10^{-14}\). This equation \(Kw = [H^{+}][OH^{-}]\) eventually turns to \(1.0*10^{-14} = [H_{3}O^{+}]*[OH^{-}]\).

Determine the Concentration of Hydrogen and Hydroxide ions

In pure water, the concentrations of \(\mathrm{H}_{3} \mathrm{O}^{+}\) and \(\mathrm{OH}^{-}\) are equal. Therefore, we can set their concentrations as 'x'. So now the equation will look like: \(1.0*10^{-14} = x * x\). Solving the equation we get the value of x, which is \(1.0 * 10^{-7}\) M.

Conclusion

Since x represents the concentration of both \(\mathrm{H}_{3} \mathrm{O}^{+}\) and \(\mathrm{OH}^{-}\), we can conclude the concentration of both ions in pure water at \(25^{\circ}C\) is \(1.0 * 10^{-7}\) M.

Key concepts

Ion Product of Water

The ion product of water, designated as Kw, is a constant value that represents the equilibrium concentration of hydronium and hydroxide ions in pure water. At a standard temperature of 25 degrees Celsius, Kw is equal to approximately 1.0 x 10^-14. This constant emerges from the process called the autodissociation of water, where a water molecule (H2O) donates a proton (H+) to another water molecule, resulting in the creation of hydronium (H3O+) and hydroxide (OH-) ions.

This constant is a crucial part of understanding the concept of pH and the acidity or basicity of solutions. Knowing the ion product of water allows us to calculate the concentration of hydronium ions in a solution when we know the concentration of hydroxide ions, and vice versa, using the formula:
\[ Kw = [H_3O^+][OH^-] \].
Thus, in a neutral solution where the concentrations of hydronium and hydroxide ions are equal, each concentration can be found by taking the square root of Kw, which at room temperature gives us a value of 1.0 x 10^-7 M for both ions.

Concentration of Hydronium Ions

Hydronium ions (\( H_{3}O^{+} \)) play a significant role in determining a solution's pH. In pure water, the concentration of hydronium ions is derived from the ion product of water, Kw. The concentration of these ions in pure water at 25 degrees Celsius is 1.0 x 10^-7 M, which is reflected by the neutral pH value of 7.

When additional acids are added to water, they release more hydronium ions, increasing the concentration above 1.0 x 10^-7 M and causing the pH to drop below 7, making the solution acidic. Conversely, when bases are added, they reduce the hydronium ion concentration by combining with them to form water, thereby increasing the pH above 7 which indicates a basic solution.

Understanding the concentration of hydronium ions is essential for calculating pH and assessing the nature of a solution. It is also important for reactions that are sensitive to the pH level, such as enzyme activity in biological systems and various types of chemical reactions.

Concentration of Hydroxide Ions

Similar to hydronium ions, the concentration of hydroxide ions (\( OH^- \)) in pure water is also crucial in the study of chemistry. Like hydronium ions, the concentration of hydroxide ions at 25 degrees Celsius and in pure water is 1.0 x 10^-7 M. The relationship between hydroxide and hydronium ion concentrations is an inverse one -- as the concentration of hydroxide ions increases, the concentration of hydronium ions decreases, provided the temperature remains constant and the solution remains diluted.

In acidic solutions, the concentration of hydroxide ions is below 1.0 x 10^-7 M, while in basic solutions, it is above this value. This concentration is a key factor in determining the solution's pH. It is also pivotal in understanding neutralization reactions, where an acid reacts with a base, resulting in water and a salt, and in controlling conditions for various industrial processes that are pH-dependent. Knowing how to calculate hydroxide ion concentration using Kw and the concentration of hydronium ions allows chemists to understand and manipulate chemical reactions and solution properties more effectively.