Question

If a solution has a pH of 0.77 , what is its \(\mathrm{pOH}\), \(\left[\mathrm{H}^{+}\right]\), and \(\left[\mathrm{OH}^{-}\right]\) ?

Short answer

pOH = 13.23, \([H^+] \approx 0.1698 \text{ M}\), \([OH^-] \approx 5.88 \times 10^{-14} \text{ M}\).

Step-by-step solution

Calculate pOH

We know that \ \[ \text{pH} + \text{pOH} = 14 \]. Given that the solution has a pH of 0.77, we can rearrange the equation to solve for pOH: \ \[ \text{pOH} = 14 - \text{pH} = 14 - 0.77 = 13.23 \].

Calculate \( [H^+] \)

The concentration of hydrogen ions, \( [H^+] \), is found using the formula: \ \[ [H^+] = 10^{-\text{pH}} \]. Given that the pH is 0.77, \ \[ [H^+] = 10^{-0.77} \approx 0.1698 \text{ M} \].

Calculate \( [OH^-] \)

The concentration of hydroxide ions, \( [OH^-] \), is related to pOH by the formula: \ \[ [OH^-] = 10^{-\text{pOH}} \]. Since we have found that the pOH is 13.23, \ \[ [OH^-] = 10^{-13.23} \approx 5.88 \times 10^{-14} \text{ M} \].

Key concepts

Calculating pOH from pH

The pOH of a solution is a measure of the concentration of hydroxide ions present in it. To find the pOH when the pH is known, we can use a straightforward formula:

• The sum of pH and pOH is always equal to 14, which is an important property of water at 25°C.
• This means that if one of these values is determined, the other can be easily calculated.

To calculate the pOH from the given pH of 0.77, we use the equation: \[ \text{pOH} = 14 - \text{pH} \]Substituting the given pH value:\[ \text{pOH} = 14 - 0.77 = 13.23 \]This relationship helps us understand how acidic or basic a solution is. A low pH indicates a high hydrogen ion concentration, making the solution acidic, which naturally results in a high pOH when the solution is very acidic like in this case.

Understanding Hydrogen Ion Concentration

Hydrogen ion concentration, often written as \([H^+]\), is a critical concept for understanding the acidity of a solution. It tells us how many hydrogen ions are present, which impact the solution's properties.

• The concentration is closely tied to pH, as it determines the chemical reactions that can occur.
• By the formula \( [H^+] = 10^{-\text{pH}} \), we can calculate the concentration directly from the pH value.

Given a pH of 0.77 in our exercise:\[ [H^+] = 10^{-0.77} \approx 0.1698 \text{ M} \]This result shows a relatively high concentration of hydrogen ions, which confirms the acidic nature of the solution. The higher the concentration of \([H^+]\), the stronger the acid.

Hydroxide Ion Concentration

Hydroxide ion concentration, denoted as \([OH^-]\), is another key element in understanding a solution's properties. Like \([H^+]\), hydroxide ions influence whether a solution is acidic or basic.

• Because \([OH^-]\) is directly linked to the pOH of the solution, it can be calculated using the formula \([OH^-] = 10^{-\text{pOH}}\).
• In strongly acidic solutions, the \([OH^-]\) value is typically very low.

In our calculation, the pOH was found to be 13.23, leading to:\[ [OH^-] = 10^{-13.23} \approx 5.88 \times 10^{-14} \text{ M} \]This extremely low concentration of hydroxide ions aligns with our observation of the solution's acidic nature. The lower the hydroxide ion concentration, the more acidic the solution tends to be.