Question

Calculate the concentration of \(\mathrm{HNO}_{3}\) in a solution at \(25^{\circ} \mathrm{C}\) that has a \(\mathrm{pH}\) of \((\mathrm{a}) 4.21,(\mathrm{~b}) 3.55,\) and \((\mathrm{c}) 0.98\)

Short answer

(a) \(6.166 \times 10^{-5} \, \text{mol/L}\), (b) \(2.818 \times 10^{-4} \, \text{mol/L}\), (c) \(1.048 \times 10^{-1} \, \text{mol/L}\).

Step-by-step solution

Understanding pH and Concentration

The pH of a solution is defined as the negative logarithm (base 10) of the hydrogen ion concentration: \[\text{pH} = -\log[\text{H}^+]\] In other words, to find the concentration of hydrogen ions \([\text{H}^+]\), we use the inverse operation, the antilogarithm: \[[\text{H}^+] = 10^{-\text{pH}}\] Since \(\mathrm{HNO}_3\) is a strong acid, it completely dissociates in water, which means the concentration of \(\text{H}^+\) is equal to the concentration of \(\mathrm{HNO}_3\).

Calculating for Case (a)

Given \(\text{pH} = 4.21\), calculate the concentration of hydrogen ions using the formula:\[[\text{H}^+] = 10^{-4.21}\]Using a calculator, find:\[[\text{H}^+] = 6.166 \times 10^{-5} \, \text{mol/L}\] Thus, the concentration of \(\mathrm{HNO}_3\) is \(6.166 \times 10^{-5} \, \text{mol/L}\).

Calculating for Case (b)

Given \(\text{pH} = 3.55\), calculate the concentration of hydrogen ions:\[[\text{H}^+] = 10^{-3.55}\]Using a calculator, find:\[[\text{H}^+] = 2.818 \times 10^{-4} \, \text{mol/L}\]So, the concentration of \(\mathrm{HNO}_3\) is \(2.818 \times 10^{-4} \, \text{mol/L}\).

Calculating for Case (c)

Given \(\text{pH} = 0.98\), calculate the concentration of hydrogen ions:\[[\text{H}^+] = 10^{-0.98}\]Using a calculator, find:\[[\text{H}^+] = 1.048 \times 10^{-1} \, \text{mol/L}\]Hence, the concentration of \(\mathrm{HNO}_3\) is \(1.048 \times 10^{-1} \, \text{mol/L}\).

Key concepts

Hydrogen Ion Concentration

When dealing with acid solutions, understanding hydrogen ion concentration is key. Hydrogen ions \(\text{H}^+\) determine the acidity level in a solution. More hydrogen ions mean a more acidic solution.

The concentration of hydrogen ions in any solution is measured in moles per liter (mol/L). This measurement tells how many moles of hydrogen ions are there in one liter of the solution.

To find the hydrogen ion concentration from pH, we rely on the formula: \[ \text{H}^+ = 10^{-\text{pH}} \]Using this formula, you can easily calculate the hydrogen ion concentration once you know the pH. This is the antilogarithm of the negative pH value, representing the concentration of hydrogen ions in the solution.

• High \(\text{H}^+\) concentration = low pH = highly acidic.
• Low \(\text{H}^+\) concentration = high pH = less acidic.

Strong Acids

Strong acids are a group of acids that dissociate completely in water. This means they separate entirely into hydrogen ions and other ions.

Examples of strong acids include hydrochloric acid (HCl), sulfuric acid (H\(_2\)SO\(_4\)), and nitric acid (HNO\(_3\)). For any strong acid like HNO\(_3\), the concentration of the acid is equal to the concentration of hydrogen ions resulting in the solution.

For instance, if you have 1 mol/L of HNO\(_3\) in the solution, it will produce 1 mol/L of \(\text{H}^+\) ions because it dissociates fully. This makes calculations straightforward since the \(\text{H}^+\) concentration directly reflects the acid concentration.

HNO3 Concentration

Nitric acid, represented as HNO\(_3\), is a commonly used strong acid in chemistry. Its chemical behavior is crucial in many calculations, especially when dealing with pH-related problems.

As a strong acid, HNO\(_3\) fully dissociates in water. This property ensures that the concentration of HNO\(_3\) initially present is the same as the hydrogen ion concentration in the solution.

Understanding HNO\(_3\) concentration allows for straightforward pH calculations. The concentration of HNO\(_3\) can be directly obtained from the pH by applying the formula: \[ \text{Concentration of HNO}_3 = 10^{-\text{pH}} \]In practical situations, accurate pH measurements can offer reliable insights into how much HNO\(_3\) is present in a solution.

• Measure the pH of the solution.
• Apply the antilog formula to find the concentration.
• Know that the calculated H\(_3\)O\(^+\) concentration equals the HNO\(_3\) concentration.

Logarithmic Functions

Logarithmic functions play a vital role in chemistry, especially when calculating pH values. The pH is a logarithmic scale, meaning it compresses the wide range of hydrogen ion concentrations into a more manageable format.

This scaling is achieved by using the negative logarithm. The operation is essential for transforming the hydrogen ion concentration into a simpler number that represents the acidity of the solution.

Understanding logarithms involves getting familiar with two key concepts: logarithm (log) and antilogarithm (antilog). The logarithm represents the pH:\[ \text{pH} = -\log[\text{H}^+] \]The antilogarithm is used to reverse the process:\[ [\text{H}^+] = 10^{-\text{pH}} \]These functions are invaluable tools for chemists, helping them manipulate and understand acid concentrations easily.

• Logarithms convert large ranges into smaller scopes.
• Antilogarithms revert that process to calculate concentrations.
• Main tools used for pH and acidity related calculations.