Question

Define \(\mathrm{pOH}\). Write the equation relating \(\mathrm{pH}\) and \(\mathrm{pOH}\).

Short answer

The pOH is the negative logarithm of hydroxide ion concentration; \\( \mathrm{pH} + \mathrm{pOH} = 14 \\).

Step-by-step solution

Understanding pOH

The pOH of a solution is defined as the negative logarithm (base 10) of the hydroxide ion concentration. Mathematically it is expressed as: \[ \mathrm{pOH} = -\log[\text{OH}^-] \] where \([\text{OH}^-]\) is the concentration of hydroxide ions in the solution.

Relationship Between pH and pOH

In an aqueous solution at 25°C, the sum of the pH and pOH is always equal to 14. This is due to the properties of water's ion product constant, \( K_w \). The equation relating pH and pOH is: \[ \mathrm{pH} + \mathrm{pOH} = 14 \] This equation allows you to calculate one if the other is known.

Key concepts

Hydroxide Ion Concentration

Understanding the concept of hydroxide ion concentration is crucial for mastering pOH. Hydroxide ions, symbolized as \( \text{OH}^- \), are basic building blocks in many chemical reactions, especially in water. When you dissolve a base in water, it usually increases the concentration of these ions. To find the pOH, which represents the alkalinity of a solution, you use the formula: \[ \text{pOH} = -\log [\text{OH}^-] \]This equation uses the negative logarithm of the hydroxide ion concentration, and it's a measure of how basic a solution is.

• The higher the hydroxide concentration, the lower the pOH.
• If [\text{OH}^-] increases, the solution becomes more basic.

This means knowing the hydroxide concentration allows you to determine the pOH directly.

pH and pOH Relationship

The relationship between pH and pOH is one of the most fundamental in chemistry, especially when it involves aqueous solutions. Both pH and pOH are important because they help you understand the acidity and basicity of a solution.
The underlying principle is in the equation: \[ \text{pH} + \text{pOH} = 14 \]This equation is valid at 25°C (room temperature) and allows you to find one value if you have the other.

• If the pH of a solution is 7, the pOH must also be 7, which makes the solution neutral.
• A low pH means high acidity, so the pOH must be high to keep the sum at 14.

This balance gives insight into the nature of the solution—whether it is acidic, basic, or neutral.

Ion Product Constant for Water

The ion product constant for water, represented as \( K_w \), is a key concept that supports the relationship between pH and pOH. \( K_w \) is essentially the product of the concentrations of hydrogen ions \( [\text{H}^+] \) and hydroxide ions \([\text{OH}^-] \) in pure water.\[ K_w = [\text{H}^+] [\text{OH}^-] = 1.0 \times 10^{-14} \]This constant value remains true at 25°C and ensures the equation \( \text{pH} + \text{pOH} = 14 \) holds.

• In pure water, both \( [\text{H}^+] \) and \([\text{OH}^-] \) are equal, each being \(1.0 \times 10^{-7}\).
• Alterations in these concentrations change the pH and pOH, while \( K_w \) itself remains constant.

The constancy of \( K_w \) helps in predicting how concentrations shift in response to changes in pH or pOH.