Question

The \(\mathrm{pOH}\) of a sample of baking soda dissolved in water is \(5.74\) at \(25^{\circ} \mathrm{C}\). Calculate the \(\mathrm{pH},\left[\mathrm{H}^{+}\right]\), and \(\left[\mathrm{OH}^{-}\right]\) for this sample. Is the solution acidic or basic?

Short answer

In summary, the solution has a pH of \(8.26\), a \(\mathrm{[H^{+}]}\) concentration equal to \(5.62 \times 10^{-9} \mathrm{M}\), and a \(\mathrm{[OH^{-}]}\) concentration equal to \(1.82 \times 10^{-6} \mathrm{M}\). The solution is basic.

Step-by-step solution

Find the pH from the given pOH

We know that at 25°C, the relationship between pH and pOH is: pH + pOH = 14 We're given that pOH = 5.74, so we can find the pH as follows: pH = 14 - 5.74 = 8.26

Calculate the concentration of H+ ions [H+]

Now that we have the pH, we can find the concentration of H+ ions using the definition of pH: pH = -log[H+] Rearrange the equation to find the H+ concentration: [H+] = 10^(-pH) = 10^(-8.26) = 5.62 × 10^(-9) M

Calculate the concentration of OH- ions [OH-]

We can find the concentration of OH- ions using the definition of pOH: pOH = -log[OH-] Rearrange the equation to find the OH- concentration: [OH-] = 10^(-pOH) = 10^(-5.74) = 1.82 × 10^(-6) M

Determine if the solution is acidic or basic

We can classify the solution as acidic, neutral, or basic based on its pH value: - If pH < 7, the solution is acidic - If pH = 7, the solution is neutral - If pH > 7, the solution is basic In our case, pH = 8.26, which is greater than 7. Therefore, the solution is basic. In summary, the solution has a pH of 8.26, a [H+] concentration equal to 5.62 × 10^(-9) M, and a [OH-] concentration equal to 1.82 × 10^(-6) M. The solution is basic.

Key concepts

Understanding pH Calculation

The concept of pH is essential in understanding how acidic or basic a solution is. It's a measure of the hydrogen ion concentration \(\left[\text{H}^+\right]\) in a solution. The pH scale typically ranges from 0 to 14, where:

• pH < 7 indicates an acidic solution.
• pH = 7 indicates a neutral solution.
• pH > 7 indicates a basic, or alkaline, solution.

To determine the pH, the formula involves the negative logarithm of the hydrogen ion concentration:\(\text{pH} = -\log[\text{H}^+]\). If you know the pOH of a solution, the pH can be easily calculated using the relationship at \(25^{\circ} \,\text{C}\): \[\text{pH} + \text{pOH} = 14\].This equation allows for converting between pH and pOH values, providing insight into the nature of the solution.

Exploring pOH

While pH looks at the concentration of hydrogen ions, pOH measures the concentration of hydroxide ions \(\left[\text{OH}^-\right]\). The pOH scale also ranges from 0 to 14:

• pOH < 7 suggests a basic solution.
• pOH = 7 is a neutral solution.
• pOH > 7 indicates an acidic solution.

Similar to pH, pOH is calculated using the hydroxide ion concentration: \(\text{pOH} = -\log[\text{OH}^-]\). When given a pOH value, you can determine the pH with the formula \(\text{pH} + \text{pOH} = 14\). This means that if the pOH is low, the pH will be high and vice-versa, indicating the solution’s acidic or basic nature.

Role of Concentration in Acid-Base Chemistry

Concentration is a fundamental concept in acid-base chemistry. It refers to the amount of a solute present in a given volume of solution, commonly expressed in moles per liter (M). This concentration is crucial when determining pH or pOH, as it directly impacts these values. A higher concentration of hydrogen ions \(\left[\text{H}^+\right]\) results in a lower pH, making the solution more acidic. Conversely, a higher concentration of hydroxide ions \(\left[\text{OH}^-\right]\) leads to a lower pOH, making the solution more basic.
Concentration connects the macroscopic observations of a solution’s pH or pOH to the microscopic scale where ions interact. Understanding concentration helps us predict the behavior of solutions in various chemical reactions and processes.

Classifying Acidic and Basic Solutions

Determining whether a solution is acidic or basic is based on its pH value. This classification is critical in various scientific applications, from biology to environmental science.If a solution has a pH below 7, it is considered acidic, which means there's a higher concentration of hydrogen ions \(\left[\text{H}^+\right]\) compared to hydroxide ions. Acidic solutions have the ability to donate protons in reactions and can affect other substances in interesting ways.
Conversely, basic solutions have a pH above 7, indicating more hydroxide ions \(\left[\text{OH}^-\right]\) than hydrogen ions. These solutions are good at accepting protons and often feel slippery to the touch.This distinction is important for predicting how substances will interact in a given environment, which is why knowing the pH is so essential in chemistry and beyond.