Question

Calculate \(\left[\mathrm{OH}^{-}\right]\)for each solution. (a) \(\mathrm{pH}=1.82\) (b) \(\mathrm{pH}=13.28\) (c) \(\mathrm{pH}=8.29\) (d) \(\mathrm{pH}=2.32\)

Short answer

\(\text{(a) }\left[\mathrm{OH}^-\right] = 10^{-12.18}\), \(\text{(b) }\left[\mathrm{OH}^-\right] = 10^{-0.72}\), \(\text{(c) }\left[\mathrm{OH}^-\right] = 10^{-5.71}\), \(\text{(d) }\left[\mathrm{OH}^-\right] = 10^{-11.68}\)

Step-by-step solution

Understanding the relationship between pH, pOH, and \(\mathrm{OH}^-\) concentration

Recognize that pH and pOH are related by the equation \(pH + pOH = 14\). To find the concentration of hydroxide ions (\(\mathrm{OH}^-\)), we first need to calculate the pOH by subtracting the given pH from 14. Then use the relationship \(\mathrm{OH}^- = 10^{-pOH}\) to find the concentration of hydroxide ions.

Calculate the pOH for each pH value

Subtract the given pH value from 14 to find the pOH for each solution.\(\text{(a) pOH} = 14 - 1.82 = 12.18\)\(\text{(b) pOH} = 14 - 13.28 = 0.72\)\(\text{(c) pOH} = 14 - 8.29 = 5.71\)\(\text{(d) pOH} = 14 - 2.32 = 11.68\)

Calculate \(\mathrm{OH}^-\) concentration from the pOH

Use the relationship \(\mathrm{OH}^- = 10^{-pOH}\) to calculate the hydroxide ion concentration for each solution.\(\text{(a) }\left[\mathrm{OH}^-\right] = 10^{-12.18}\)\(\text{(b) }\left[\mathrm{OH}^-\right] = 10^{-0.72}\)\(\text{(c) }\left[\mathrm{OH}^-\right] = 10^{-5.71}\)\(\text{(d) }\left[\mathrm{OH}^-\right] = 10^{-11.68}\)

Key concepts

Hydroxide Ion Concentration

In acid-base chemistry, the hydroxide ion concentration \( \left[\mathrm{OH}^-\right] \) is a critical parameter indicating the basicity of a solution. It is measured in moles per liter (M) and represents the amount of hydroxide ions dissolved in a solution. Understanding its relationship with pH is fundamental in chemistry. When a solution is basic, or alkaline, the hydroxide ion concentration is higher, which corresponds to a lower pH value. On the other hand, acidic solutions have lower \( \left[\mathrm{OH}^-\right] \) values. The concentration is often derived from the pOH, which is the negative logarithm (base 10) of the hydroxide ion concentration, using the equation \( \left[\mathrm{OH}^-\right] = 10^{-pOH} \) as shown in the step-by-step solution above.

Understanding how to calculate this concentration helps students predict the behavior of acids and bases in various chemical reactions and real-life applications such as water treatment, pharmaceuticals, and biological systems. Accurate measurements and calculations of hydroxide ion concentration can show us how substances will interact with each other, emphasizing its relevance in the scientific and industrial fields.

pH Scale

The pH scale is used to specify the acidity or basicity of an aqueous solution. The scale ranges typically from 0 to 14, with a pH less than 7 indicating an acidic solution, a pH of 7 indicating neutrality (pure water), and a pH greater than 7 indicating a basic or alkaline solution. Each whole pH value below or above 7 is tenfold more acidic or basic than the next. This logarithmic scale is essential because it helps scientists and students quickly determine the acidity or alkalinity of a substance without dealing with very large or small concentrations of hydrogen ions. It plays a pivotal role in processes such as digestion, fermentation, and in maintaining the pH balance in environmental systems like oceans and soil.

Acid-Base Chemistry

Acid-base chemistry is a fundamental concept involving the transfer of protons between reactants. Acids are substances that release hydrogen ions \( \left[\mathrm{H}^+\right] \) when dissolved in water, whereas bases are substances that provide hydroxide ions \( \left[\mathrm{OH}^-\right] \) in solution.

Critical to understanding this concept is the Brønsted-Lowry acid-base theory, which defines acids as proton donors and bases as proton accepters. This theory helps explain the behavior of substances when they are dissolved in water and how they can change the pH of the solution. Acid-base reactions often involve the exchange of ions and are frequently used to neutralize solutions, in titrations, and to manage pH levels in various systems, hence the significance in fields like analytical chemistry, biochemistry, and environmental science.

pOH

The term pOH is related but converse to pH and represents the negative logarithm (base 10) of the hydroxide ion concentration. It is an intrinsic measure of the alkalinity of a solution. Unlike the pH scale, which has its more acidic values at the lower end, the pOH scale has more basic solutions at the lower end. The pOH can be calculated by taking the negative logarithm of the hydroxide ion concentration or, more commonly, by subtracting the pH from 14, due to the relationship \( pH + pOH = 14 \) in aqueous solutions at 25 degrees Celsius. Calculating pOH is an integral part of understanding the holistic view of a solution's acid-base properties, and it helps in determining the opposing concentration of ions to completely neutralize the solution's acidity or basicity.