Question

For each of the following cases, decide whether the \(\mathrm{pH}\) is less than \(7\) , equal to \(7\) , or greater than \(7\). (a) 25 mL of \(0.45 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) is mixed with \(25 \mathrm{mL}\) of 0.90 \(\mathrm{M} \mathrm{NaOH}\). (b) 15 mL of 0.050 M formic acid, \(\mathrm{HCO}_{2} \mathrm{H}\), is mixed with \(15 \mathrm{mL}\) of \(0.050 \mathrm{M} \mathrm{NaOH}\). (c) \(25 \mathrm{mL}\) of \(0.15 \mathrm{M} \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) (oxalic acid) is mixed with \(25 \mathrm{mL}\) of \(0.30 \mathrm{M} \mathrm{NaOH} .\) (Both \(\mathrm{H}^{+}\) ions of oxalic acid are removed with NaOH.)

Short answer

(a) pH = 7, (b) pH > 7, (c) pH = 7.

Step-by-step solution

Calculate Moles of H2SO4 and NaOH for Case (a)

We need to determine the total moles of acid and base to assess their reaction. For H2SO4, calculate moles using the formula: \( \text{moles} = \text{volume} \times \text{concentration} \). Given 25 mL of 0.45 M, we convert this to liters (0.025 L) and calculate: \( \text{moles of } \text{H}_2\text{SO}_4 = 0.025 \times 0.45 = 0.01125 \text{ moles} \).Since \( \text{H}_2\text{SO}_4 \) provides 2 \( \text{H}^+ \) ions per molecule, the moles of \( \text{H}^+ \) ions = 2 \times 0.01125 = 0.0225 For NaOH, \( \text{moles of NaOH} = 0.025 \times 0.90 = 0.0225 \text{ moles} \).

Determine pH for Case (a)

The moles of \( \text{H}^+ \) from \( \text{H}_2\text{SO}_4 \) and \( \text{OH}^- \) from \( \text{NaOH} \) are equal (both are 0.0225 moles). This means all \( \text{H}^+ \) ions neutralize the \( \text{OH}^- \) ions. Thus, the resulting pH is 7, indicating a neutral solution.

Calculate Moles of HCO2H and NaOH for Case (b)

Formic acid \((\text{HCO}_2\text{H})\) is a weak acid, and \( \text{NaOH} \) is a strong base. Calculate moles for each: For formic acid: \( \text{moles} = 0.015 \times 0.050 = 0.00075 \text{ moles} \).For \( \text{NaOH} \): \( \text{moles} = 0.015 \times 0.050 = 0.00075 \text{ moles} \).

Determine pH for Case (b)

Since the moles of formic acid and \( \text{NaOH} \) are equal, they completely neutralize each other. However, because formic acid is a weak acid and NaOH is a strong base, the resulting solution will be slightly basic, giving a pH greater than 7.

Calculate Moles of H2C2O4 and NaOH for Case (c)

Determine the moles for oxalic acid \((\text{H}_2\text{C}_2\text{O}_4)\) and \( \text{NaOH} \):For oxalic acid: \( \text{moles} = 0.025 \times 0.15 = 0.00375 \text{ moles} \).Since each molecule of \( \text{H}_2\text{C}_2\text{O}_4 \) can donate 2 \( \text{H}^+ \) ions, total \( \text{H}^+ \) is \( 2 \times 0.00375 = 0.0075 \) moles.For \( \text{NaOH} \): \( \text{moles} = 0.025 \times 0.30 = 0.0075 \text{ moles} \).

Determine pH for Case (c)

In this case, the moles of \( \text{H}^+ \) from oxalic acid and \( \text{OH}^- \) from \( \text{NaOH} \) are equal (0.0075 moles each). They neutralize each other, resulting in a neutral solution with a pH of 7.

Key concepts

Understanding Acid-Base Neutralization

Whenever an acid and a base are mixed together, a chemical reaction known as neutralization occurs. This reaction typically results in the formation of water and a salt. The key idea is that the hydrogen ions equally balanced with hydroxide ions leads to water, which has a neutral pH of 7.

In the context of pH determination, it's important to determine:

• Which substance is in excess.
• If this excess leads to a surplus of hydrogen ions (H⁺) or hydroxide ions (OH^-).

Greater concentrations of H⁺ ions will lead to a lower pH, indicating an acidic solution. On the other hand, an excess of OH^- ions will result in a higher pH, indicating a basic solution. Neutralization can either perfectly balance both sides, resulting in a pH of 7, or leave some ions un neutralized, causing the pH to deviate from neutral.

Performing Molarity Calculations

Molarity is a measure of the concentration of a solute in a solution, expressed in moles per liter (M). This calculation is crucial for understanding the quantity of reactive entities during a neutralization process.

To calculate molarity, you must first determine the number of moles of the reactants. Given volume (in liters) and concentration (in molarity), the calculation is straightforward:
The formula is:\[ \text{moles} = \text{volume} \times \text{concentration} \]For example, if you have a 25 mL solution of 0.45 M H₂SO₄, first convert the volume into liters (0.025 L), then multiply by the molarity to find the number of moles. This process allows you to determine how many hydrogen ions are available to react with hydroxide ions in a base.

Once you know the moles of each reactant, you can compare them to determine the extent of the reaction and whether any reactant is left over. This helps decide if the pH will be acidic, neutral, or basic.

Differences Between Strong and Weak Acids

Understanding the distinction between strong and weak acids is vital in pH determination because it affects how completely an acid dissociates into hydrogen ions.

Strong Acids: These acids fully dissociate in water, releasing all of their hydrogen ions.

• An example is sulfuric acid ( H₂SO₄), which releases two hydrogen ions per molecule.
• This complete dissociation makes the amount of hydrogen ions predictable for neutralization reactions.

Weak Acids: In contrast, weak acids only partially dissociate in water.

• For instance, formic acid ( HCO₂H) does not release all its hydrogen ions, meaning fewer ions are available for reactions.
• This partial dissociation results in more complicated pH calculations, since equilibrium considerations come into play.

In pH determination exercises, knowing whether you are dealing with a strong or weak acid lets you predict and understand the behavior of the solution and the resulting pH more accurately.