Question

Calculate the hydrogen ion concentration, in moles per liter, for solutions with each of the following \(\mathrm{pH}\) or pOH values. a. \(\mathrm{pOH}=0.90\) b. \(\mathrm{pH}=0.90\) c. \(\mathrm{pOH}=10.3\) d. \(\mathrm{pH}=5.33\)

Short answer

a. \([\mathrm{H^{+}}] = 7.94\times10^{-14} \, \mathrm{mol \, L^{-1}}\) b. \([\mathrm{H^{+}}] = 1.26\times10^{-1} \, \mathrm{mol \, L^{-1}}\) c. \([\mathrm{H^{+}}] = 1.99\times10^{-4} \, \mathrm{mol \, L^{-1}}\) d. \([\mathrm{H^{+}}] = 4.68\times10^{-6} \, \mathrm{mol \, L^{-1}}\)

Step-by-step solution

Part a: Calculate hydrogen ion concentration for \(\mathrm{pOH}=0.90\)

1. Identify the given value: \(\mathrm{pOH}=0.90\) 2. Calculate the \(\mathrm{pH}\): \(\mathrm{pH} = 14 - \mathrm{pOH} = 14 - 0.90 = 13.1\) 3. Calculate the hydrogen ion concentration: \([\mathrm{H^{+}}] = 10^{-\mathrm{pH}} = 10^{-13.1} = 7.94\times10^{-14} \, \mathrm{mol \, L^{-1}}\)

Part b: Calculate hydrogen ion concentration for \(\mathrm{pH}=0.90\)

1. Identify the given value: \(\mathrm{pH}=0.90\) 2. No need to calculate the \(\mathrm{pOH}\) as we already have the \(\mathrm{pH}\) value. 3. Calculate the hydrogen ion concentration: \([\mathrm{H^{+}}] = 10^{-\mathrm{pH}} = 10^{-0.90} = 1.26\times10^{-1} \, \mathrm{mol \, L^{-1}}\)

Part c: Calculate hydrogen ion concentration for \(\mathrm{pOH}=10.3\)

1. Identify the given value: \(\mathrm{pOH}=10.3\) 2. Calculate the \(\mathrm{pH}\): \(\mathrm{pH} = 14 - \mathrm{pOH} = 14 - 10.3 = 3.7\) 3. Calculate the hydrogen ion concentration: \([\mathrm{H^{+}}] = 10^{-\mathrm{pH}} = 10^{-3.7} = 1.99\times10^{-4} \, \mathrm{mol \, L^{-1}}\)

Part d: Calculate hydrogen ion concentration for \(\mathrm{pH}=5.33\)

1. Identify the given value: \(\mathrm{pH}=5.33\) 2. No need to calculate the \(\mathrm{pOH}\) as we already have the \(\mathrm{pH}\) value. 3. Calculate the hydrogen ion concentration: \([\mathrm{H^{+}}] = 10^{-\mathrm{pH}} = 10^{-5.33} = 4.68\times10^{-6} \, \mathrm{mol \, L^{-1}}\)

Key concepts

Hydrogen Ion Concentration

Hydrogen ion concentration is a crucial concept in understanding the acidity of a solution. It's a measure of the amount of hydrogen ions (H\(^+\)) present in a solution, reflected in its molarity, or moles per liter. The more hydrogen ions there are, the more acidic the solution is.
To calculate the hydrogen ion concentration from the pH, you can use the formula:

• \([\text{H}^+] = 10^{-\text{pH}}\)

With this formula, determining how acidic or basic a solution is becomes simpler.
This relationship also means that a lower pH indicates a higher concentration of hydrogen ions.
For instance, when the pH is 0.90, as given in one of our examples, the concentration is calculated as \(10^{-0.90} = 1.26 \times 10^{-1}\) mol L\(^{-1}\).
This represents a molar concentration of hydrogen ions that is quite high, confirming the acidity of the solution.

pH Scale

The pH scale is an essential component of acid-base chemistry, providing a quantitative measure of acidity or basicity in a solution.
The scale ranges from 0 to 14, where:

• pH < 7 indicates an acidic solution
• pH = 7 is neutral (pure water)
• pH > 7 indicates a basic or alkaline solution

The relationship between pH and hydrogen ion concentration is logarithmic, which allows us to express a wide range of concentrations in a simple form. The pH value is calculated as:

• \(\text{pH} = -\log[\text{H}^+]\)

Understanding this scale helps us determine how strong an acid or base is in a particular solution.
For example, a pH of 5.33 indicates a slightly acidic solution compared to a neutral pH of 7.

Acid-Base Chemistry

Acid-base chemistry is all about the interaction between acids and bases and their properties in solution. Acids are substances that increase the concentration of hydrogen ions (H\(^+\)) when dissolved, whereas bases decrease the concentration of hydrogen ions by either donating hydroxide ions (OH\(^-\)) or by absorbing protons.
This area of chemistry uses two related scales, pH and pOH, to describe the acidity and basicity, respectively. The relationship between them is straightforward since:

• \(\text{pH} + \text{pOH} = 14\)

This equation allows us to calculate the pH from pOH and vice versa.
Understanding this concept helps us simplify complex biochemical processes by identifying the nature of different solutions. For instance, if pOH is 0.90, then pH can be found as 13.1, indicating a highly basic solution.

Molarity Calculations

Molarity is a way of expressing the concentration of a solute in a solution, given in moles of solute per liter of solution (mol/L). This is particularly useful when discussing solutions in acid-base chemistry, such as those involving hydrogen or hydroxide ions.
Calculating molarity requires knowledge of the quantity of the solute and the volume of the solution. This makes it easy to determine the concentration of ions in a reaction, helping predict the behavior of acids and bases in a solution.
For example, if you have the pH, you can easily calculate the hydrogen ion concentration - or molarity - using the formula \([\text{H}^+] = 10^{-\text{pH}}\).
This makes molarity a cornerstone of chemical calculations, as also shown in exercises where, from a given pH or pOH, the molarity of hydrogen ions can be calculated accurately.