Question

How are acidic, basic, and neutral solutions in water defined (a) in terms of \(\left[\mathrm{H}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\) and \((\mathbf{b})\) in terms of \(\mathrm{pH}\) and \(\mathrm{pOH}\) ?

Short answer

Acidic solutions have \(\left[\mathrm{H}^{+}\right] > \left[\mathrm{OH}^{-}\right]\) and pH < 7. Basic solutions have \(\left[\mathrm{H}^{+}\right] < \left[\mathrm{OH}^{-}\right]\) and pH > 7. Neutral solutions have \(\left[\mathrm{H}^{+}\right] = \left[\mathrm{OH}^{-}\right]\) and pH = 7.

Step-by-step solution

Understanding Acidic Solutions in Water

An acidic solution in water is defined by a higher concentration of hydrogen ions \(\left[\mathrm{H}^{+}\right]\) than hydroxide ions \(\left[\mathrm{OH}^{-}\right]\). This means that \(\left[\mathrm{H}^{+}\right] > \left[\mathrm{OH}^{-}\right]\). In terms of pH, which is the negative logarithm of the hydrogen ion concentration, an acidic solution has a pH less than 7. The pOH, which relates to the concentration of hydroxide ions, will be above 7, as pH and pOH add up to 14.

Understanding Basic Solutions in Water

A basic or alkaline solution has a lower concentration of hydrogen ions \(\left[\mathrm{H}^{+}\right]\) compared to hydroxide ions \(\left[\mathrm{OH}^{-}\right]\), or \(\left[\mathrm{H}^{+}\right] < \left[\mathrm{OH}^{-}\right]\). With regards to pH, a basic solution has a pH greater than 7. Consequently, the pOH of a basic solution will be less than 7.

Understanding Neutral Solutions in Water

A neutral solution has equal concentrations of hydrogen ions and hydroxide ions, denoted as \(\left[\mathrm{H}^{+}\right] = \left[\mathrm{OH}^{-}\right]\). In terms of pH and pOH, a neutral solution has a pH of 7, which also means a pOH of 7 because their sum equals to 14.

Key concepts

pH Scale

The pH scale is a measure of how acidic or basic a solution is. It ranges from 0 to 14, with 7 being neutral. Values below 7 indicate acidity, while values above 7 indicate basicity. The pH scale is logarithmic, meaning each whole pH value below 7 is ten times more acidic than the next higher value. Similarly, each whole pH value above 7 is ten times more basic (or less acidic) than the one below it. This scale is based on the concentration of hydrogen ions \(\left[\mathrm{H}^{+}\right]\) in a solution.

Understanding the pH scale is crucial because it helps predict the behavior and chemical properties of a solution, such as its corrosivity, ability to engage in certain reactions, and its compatibility with living organisms. For instance, human blood has a pH close to 7.4, which is slightly basic, and even minor fluctuations can be harmful. In industrial processes, the pH of a solution can affect the rate of reaction and the quality of the final product. Thus, maintaining the right pH is essential in many contexts.

Hydrogen Ion Concentration

Hydrogen ion concentration \(\left[\mathrm{H}^{+}\right]\) is a central concept in chemistry, particularly in the discussion of acid-base chemistry. It refers to the amount of hydrogen ions present in a solution. The higher the concentration of \(\left[\mathrm{H}^{+}\right]\), the more acidic the solution is. Conversely, a lower \(\left[\mathrm{H}^{+}\right]\) concentration indicates a more basic or alkaline solution. Using an equation involving the negative logarithm, we can directly relate the hydrogen ion concentration to pH; specifically, \(\mathrm{pH} = -\log\left[\mathrm{H}^{+}\right]\).

The careful measurement and calculation of hydrogen ion concentration are pivotal in many scientific and industrial processes. For example, it is essential for titration reactions in analytical chemistry, where the goal is to determine the concentration of an acid or base in a solution. It also plays a significant role in environmental science for assessing the acidity of rainwater and freshwater systems, as well as in the food industry to ensure product quality and safety.

Hydroxide Ion Concentration

Complementing the hydrogen ion concentration is the hydroxide ion concentration \(\left[\mathrm{OH}^{-}\right]\), which becomes the focus when talking about basic or alkaline solutions. In a solution, the hydroxide ions react with hydrogen ions to form water. A high concentration of \(\left[\mathrm{OH}^{-}\right]\) relative to \(\left[\mathrm{H}^{+}\right]\) means the solution is basic, whereas a lower concentration indicates an acidic solution. The relationship between hydroxide ions and pH is expressed through the pOH scale, with \(\mathrm{pOH} = -\log\left[\mathrm{OH}^{-}\right]\), and the two scales are inversely related through the equation \(\mathrm{pH} + \mathrm{pOH} = 14\) at 25°C in pure water.

Hydroxide ion concentration is crucial in various domains, such as in the treatment of wastewater, where adjusting the \(\left[\mathrm{OH}^{-}\right]\) helps to neutralize acids and precipitate heavy metals. In biology, it is significant for maintaining the pH of cellular environments, ensuring proper function and structure of the cells. Understanding \(\left[\mathrm{OH}^{-}\right]\) concentration allows chemists and engineers to control reactions and product qualities in many chemical processes.

pOH

pOH is a measure of the alkalinity of a solution, serving as the counterpart to pH. It represents the negative logarithm of hydroxide ion concentration: \(\mathrm{pOH} = -\log\left[\mathrm{OH}^{-}\right]\). The scales for pH and pOH are connected; in aqueous solutions at 25°C, \(\mathrm{pH} + \mathrm{pOH} = 14\). This relation is important as it lets us quickly convert between pH and pOH when one is known, providing a full picture of the solution's acid-base properties.

Knowing the pOH of a solution is important in several areas of chemistry and science. For example, in environmental chemistry, pOH can be used to assess the alkalinity of water bodies, which has implications for aquatic life health. In medicine, pOH levels can impact drug stability and efficacy. Additionally, in industries like dye manufacturing and leather making, maintaining the correct pH and pOH is necessary for achieving the desired product characteristics. Understanding pOH, alongside pH, hydrogen ion concentration, and hydroxide ion concentration, gives a comprehensive view of a solution's acid-base balance, informing its reactive behavior and suitability for various applications.