Question

Determine the \(\mathrm{pH}\) and pOH of a \(0.0050 \mathrm{M} \mathrm{HCl}\) solution. What is the relationship between the \(\mathrm{pH}\) and pOH values?

Short answer

The pH value is 2.301 and the pOH value is 11.699. pH and pOH always add up to 14 in any aqueous solution at 25° C.

Step-by-step solution

Understanding pH and pOH

The pH of a solution is a measure of its acidity and is calculated as the negative base 10 logarithm (log10) of the concentration of H+. Formula: pH=\(-\log[H^+]\) \n Similarly, a pOH of a solution is a measure of its basicity or alkalinity and it is calculated as the negative log10 of the concentration of OH-. Formula: pOH=\(-\log[OH^-]\)

Determine pH of HCl solution

Since HCl is a strong acid, it will completely ionize in water, so [H+] is equal to the initial concentration of HCl. \n Therefore pH will be: \n pH = -log(0.0050) = 2.301

Determine pOH of the solution

The relationship between pH and pOH in any aqueous solution at 25° C (298 K) is given by the equation: \n pH + pOH = 14 \n Using the pH value determined, we can find the pOH value: \n pOH = 14 - pH = 14 - 2.301 = 11.699

Understand relationship between pH and pOH

The relationship between pH and pOH is that they always add up to 14 in any aqueous solution at 25° C. So, if one increases, the other decreases and vice versa

Key concepts

Acidity Measurement

Understanding acidity is crucial when discussing pH and pOH calculations. Acidity refers to the concentration of hydrogen ions \([H^+]\) in a solution. The pH scale, ranging from 0 to 14, helps us measure this acidity. A lower pH value means higher acidity, while a higher pH implies lower acidity. To calculate the pH of a solution, such as hydrochloric acid (HCl), we use the formula \( ext{pH} = -\log [H^+] \). Since HCl is a strong acid, it fully dissociates in water, meaning the concentration of \([H^+]\) equals the initial concentration of the acid. For example, if the concentration of HCl is \(0.0050 \text{ M}\), the pH is \(-\log(0.0050) = 2.301\). This value indicates an acidic solution.

Basicity and Alkalinity

Basicity refers to the presence of hydroxide ions \([OH^-]\) in a solution, indicating its ability to neutralize acid. Alkalinity, often used interchangeably with basicity, describes the solution's capacity to maintain a stable pH when acids are added. The pOH scale measures basicity, similar to how pH measures acidity. It uses the formula \( ext{pOH} = -\log[OH^-] \) to calculate its value. Although the solution's actual pOH can be directly determined in some cases, it's often calculated using the relationship between pH and pOH: \( \text{pH} + \text{pOH} = 14 \). Therefore, knowing either the pH or pOH allows us to find the other. For our hydrochloric acid example, with a pH of 2.301, we calculate pOH as \( 14 - 2.301 = 11.699\), reflecting a more basic or alkaline condition.

pH and pOH Relationship

The relationship between pH and pOH is fundamental in understanding chemical equilibria in aqueous solutions. At a temperature of 25°C (298 K), the sum of pH and pOH in any solution is always 14. This constant sum results from the fixed ion product of water \(K_w\), which equals \(1.0 \times 10^{-14}\) at this temperature. Hence, as the pH of a solution increases, indicating less acidity, the pOH decreases, signifying more basicity, and vice versa.Understanding this relationship helps to predict the behavior of solutions as acids or bases are added. For instance, increasing the concentration of \([H^+]\) ions in a solution decreases the pH, increasing the solution's acidity, while diminishing its pOH, thereby reducing its basicity. Conversely, raising the concentration of \([OH^-] \) ions decreases the solution's pH making it more basic.