Question

Complete the following table.$$ \begin{array}{|c|c|c|c|c|} \hline\left[\mathrm{H}_{3} \mathrm{O}^{+}\right] & {\left[\mathrm{OH}^{-}\right]} & \mathrm{pH} & \mathrm{pOH} & \begin{array}{c} \text { Acidic } \\ \text { or Basic? } \end{array} \\ \hline & & 0.40 & & \\ \hline & 9.0 \times 10^{-10} & & & \\ \hline 1.0 \times 10^{-8} & & & & \\ \hline & & & 2.00 & \\ \hline 4.5 \times 10^{-2} & & & & \\ \hline \end{array} $$

Short answer

By using the formulas for pH and pOH, along with the pH and pOH relationship, the table would be filled out as follows: \[\begin{{array}}{{|c|c|c|c|c|}}\hline\left[\mathrm{H}_{3} \mathrm{O}^{+}\right] &{\left[\mathrm{OH}^{-}\right]} & \mathrm{pH} & \mathrm{pOH} & \begin{{array}}{{c}}\text {{ Acidic }} \\text {{ or Basic? }} \\end{{array}} \\hline 0.398 \times 10^{-1} & 2.51 \times 10^{-13} & 0.40 & 13.60 & Acidic \ \hline 1.12 \times 10^{-5} & 9.0 \times 10^{-10} & 4.95 & 9.05 & Acidic \ \hline1.0 \times 10^{-8} & 1.0 \times 10^{-6} & 8.00 & 6.00 & Basic \ \hline 2.00 \times 10^{-12} & 5.01 \times 10^{-3} & 12.00 & 2.00 & Basic \ \hline 4.5 \times 10^{-2} & 2.23 \times 10^{-13} & 1.35 & 12.65 & Acidic \ \hline \end{{array}}\]

Step-by-step solution

Calculate missing [H3O+] and [OH-] values

Use the formulas \(pH = -\log[H_3O^+]\) and \(pOH = -\log[OH^-]\) to determine the missing values. For example, for the first row where pH=0.40, calculate [H3O+] like so: \[H_3O^+ = 10^{-pH} = 10^{-0.40} = 0.398 \times 10^{-1}\]

Calculate missing pH and pOH values

Using the same formulas, but rearranged, calculate the missing pH and pOH values. For example, in the second row, pOH can be calculated as: \[pOH = -\log[OH^-] = -\log(9.0 \times 10^{-10}) = 9.05\] Then, using the formula \(pH + pOH = 14\), calculate the missing pH value as: \[pH = 14 - pOH = 14 - 9.05 = 4.95\]

Determine whether solutions are acidic or basic

Analyze the pH and pOH values. If pH < pOH, the solution is acidic. If pH > pOH, the solution is basic. For example, in the second row, the solution is acidic because pH is less than pOH (4.95 < 9.05).

Key concepts

Acid and Base Identification

Understanding whether a solution is acidic or basic is a fundamental aspect of chemistry. The pH scale, which ranges from 0 to 14, serves as a measure of the acidity or basicity of a solution. A pH value below 7 indicates an acidic solution, while a pH above 7 suggests a basic (alkaline) solution. The scale is log-based, meaning each whole pH value represents a tenfold difference in hydrogen ion concentration.

The pOH scale works in tandem with the pH scale. A pOH below 7 indicates a basic solution, while values above 7 suggest acidity. It's important to remember that pH and pOH always add up to 14 in any aqueous solution at 25°C. This relationship is pivotal for acid-base identification, as it allows us to determine the nature of the solution when either pH or pOH is known. By using the pH value, we can infer acid-base character, aiding in predictions about chemical behaviour and potential reactions.

Hydrogen Ion Concentration

The hydrogen ion concentration, often represented as \[H_3O^+\] but sometimes simplified to \[H^+\], is key to understanding the pH of a solution. The concentration of hydrogen ions is inversely related to the pH; as \[H_3O^+\] concentration increases, pH decreases, and the solution becomes more acidic. Conversely, a decrease in \[H_3O^+\] concentration causes an increase in pH, indicating a more basic solution.

To calculate the \[H_3O^+\] concentration from pH, you can use the expression \[H_3O^+ = 10^{-pH}\]. This equation is derived from the definition of pH as the negative logarithm of the hydrogen ion concentration. Understanding this relationship allows us to quickly assess the relative acidity or basicity of a solution by its pH value.

Hydroxide Ion Concentration

In contrast to the hydrogen ion concentration, hydroxide ion concentration, denoted as \[OH^-\], defines the basicity of a solution. The relationship between pOH and \[OH^-\] concentration is similar to that of pH and \[H_3O^+\]: \[OH^- = 10^{-pOH}\]. When \[OH^-\] concentration is high, pOH is low, and the solution is basic; a low \[OH^-\] concentration corresponds to a high pOH, indicating an acidic solution.

The product of the \[H_3O^+\] and \[OH^-\] concentrations is always constant at a given temperature, with a typical value of \(1 \times 10^{-14}\) at 25°C. This constant product is the foundation of the well-known water equilibrium constant (\[K_w\]), and is essential for understanding the interrelatedness of \[H_3O^+\] and \[OH^-\] concentrations in any aqueous solution.