Problem 186 - Introductory Chemistry Atoms First

Question

If \(100 \mathrm{~mL}\) of an aqueous solution of nitric acid contains \(0.030\) mole of \(\mathrm{HNO}_{3}\), what is the \(\mathrm{pH}\) of the solution?

Step-by-Step Solution

Answer

The pH of the aqueous solution of nitric acid containing 0.030 moles of HNO3 in 100 mL of solution is approximately 0.52.

Step 1: Calculate the concentration of HNO3 in the solution

Given that the aqueous solution has a volume of 100 mL and contains 0.030 moles of HNO3, we can calculate the molarity (concentration in moles per liter) of HNO3 in the solution using the formula: Molarity (M) = moles of solute / liters of solution First, convert the volume to liters: 100 mL = 0.100 L Now, plug the values into the molarity formula: Molarity (M) = 0.030 moles / 0.100 L Molarity (M) = 0.30 M

Step 2: Calculate the concentration of hydrogen ions (H+) in the solution

Since nitric acid (HNO3) is a strong acid and it completely dissociates in water, the concentration of H+ ions is equal to the concentration of HNO3 in the solution. Therefore, the concentration of H+ ions in the solution is 0.30 M.

Step 3: Calculate the pH of the solution

Now that we have the concentration of hydrogen ions (H+), we can find the pH using the formula: pH = -log10[H+] Where [H+] is the concentration of hydrogen ions in the solution. Plug the [H+] value into the pH formula: pH = -log10(0.30) pH ≈ 0.52 So, the pH of the aqueous solution of nitric acid containing 0.030 moles of HNO3 in 100 mL of solution is approximately 0.52.

Key Concepts

Molarity in Solution Chemistry

Molarity is an important concept in solution chemistry because it tells us the concentration of a solute in a solution. Specifically, it measures how many moles of a solute are present in one liter of solution.
To find molarity, use the formula:

• Molarity (M) = moles of solute / liters of solution

In our exercise, we have 0.030 moles of nitric acid ( HNO₃ ) in 100 mL of solution. First, we convert the volume from milliliters to liters:

• 100 mL = 0.100 L

Now we can calculate:

• Molarity (M) = 0.030 moles / 0.100 L = 0.30 M

This means the solution has a molarity of 0.30 M.

Understanding Strong Acid Dissociation

Strong acids, like nitric acid ( HNO₃ ), dissociate completely in water. This means all nitric acid molecules break apart into hydrogen ions ( H⁺ ) and nitrate ions ( NO₃⁻ ).
Because the dissociation is complete:

• The concentration of hydrogen ions is equal to the concentration of the acid.

In our example, since HNO₃ is a strong acid, the concentration of H⁺ ions is the same as HNO₃ , which is 0.30 M. This makes calculating the hydrogen ion concentration straightforward.

Calculating Hydrogen Ion Concentration

When dealing with strong acids like HNO₃ , calculating the hydrogen ion concentration is simple. You don't need additional steps to find H⁺ ions if the acid dissociates completely.
In our case:

• The molarity of H⁺ ions is directly taken from the molarity of HNO₃ .
• This results in a hydrogen ion concentration of 0.30 M.

Understanding this relationship helps in quickly determining pH, an essential property of solutions.

Exploring Acid-Base Chemistry and pH

Acid-base chemistry is all about understanding the balance and strength of hydrogen ions (H⁺) and hydroxide ions (OH⁻) in solutions. The pH scale measures how acidic or basic a solution is. It's calculated using:

• \(\text{pH} = -\log_{10} [\text{H}^+]\)

This means that for our solution:

• \([\text{H}^+] = 0.30\) M, so \(\text{pH} = -\log_{10} (0.30)\)

Performing this calculation gives a pH of approximately 0.52.
This low pH indicates a very acidic solution, typical of strong acids like nitric acid. Understanding pH helps in predicting chemical behavior and reactions.