Problem 64 - Chemistry and Chemical Reactivity

Question

For each of the following cases, decide whether the pH is less than 7 , equal to 7 , or greater than 7 . (a) \(25 \mathrm{mL}\) 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.)

Step-by-Step Solution

Answer

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

Step 1: Calculate moles of each reactant in case (a)

First, find the moles of sulfuric acid \( \text{H}_2\text{SO}_4 \) in 25 mL using the formula: \( \text{moles} = \text{volume (L)} \times \text{molarity} \).\[\text{Moles of } \text{H}_2\text{SO}_4 = 0.025 \times 0.45 = 0.01125 \text{ mol} \]Since sulfuric acid is diprotic, it provides 0.0225 mol of \( \text{H}^+ \) ions.Next, calculate the moles of \( \text{NaOH} \) in 25 mL:\[\text{Moles of } \text{NaOH} = 0.025 \times 0.90 = 0.0225 \text{ mol} \]

Step 2: Compare moles of H+ and OH- in case (a)

In this case, \( \text{H}_2\text{SO}_4 \) produces 0.0225 mol of \( \text{H}^+ \) ions, and there are 0.0225 mol of \( \text{OH}^- \) ions from \( \text{NaOH} \).Since the moles of \( \text{H}^+ \) and \( \text{OH}^- \) are equal, the solution is neutral, and the pH is equal to 7.

Step 3: Calculate moles for case (b)

Find the moles of formic acid, \( \text{HCO}_2\text{H} \), in 15 mL:\[\text{Moles of } \text{HCO}_2\text{H} = 0.015 \times 0.050 = 0.00075 \text{ mol} \]Then, calculate the moles of \( \text{NaOH} \) in 15 mL:\[\text{Moles of } \text{NaOH} = 0.015 \times 0.050 = 0.00075 \text{ mol} \]

Step 4: Determine pH for case (b)

Since the moles of \( \text{HCO}_2\text{H} \) and \( \text{NaOH} \) are equal, all the acid reacts with the base to produce water and formate ion.This results in a neutral solution and the pH is equal to 7.

Step 5: Calculate moles for case (c)

Calculate the moles of oxalic acid, \( \text{H}_2\text{C}_2\text{O}_4 \), in 25 mL:\[\text{Moles of } \text{H}_2\text{C}_2\text{O}_4 = 0.025 \times 0.15 = 0.00375 \text{ mol} \]Oxalic acid is diprotic, providing twice as many moles of \( \text{H}^+ \), so 0.0075 mol.Calculate the moles of \( \text{NaOH} \) in 25 mL:\[\text{Moles of } \text{NaOH} = 0.025 \times 0.30 = 0.0075 \text{ mol} \]

Step 6: Determine pH for case (c)

In this case, the moles of \( \text{H}^+ \) from oxalic acid are exactly neutralized by the moles of \( \text{OH}^- \) from \( \text{NaOH} \).Therefore, the reaction results in a completely neutral solution, and the pH is equal to 7.

Key Concepts

acid-base reaction

An acid-base reaction is a chemical process that involves the transfer of protons, or hydrogen ions (\(\text{H}^+\)), between an acid and a base. In simple terms, an acid is a proton donor, and a base is a proton acceptor.
For instance, when sulfuric acid (\(\text{H}_2\text{SO}_4\)) reacts with sodium hydroxide (\(\text{NaOH}\)), it donates protons to the base. This leads to the formation of water and a salt.

• An acid-base reaction often results in changes in the pH of the solution.
• This type of reaction is characterized by the formation of water and a salt.

It's important to determine the number of moles of each reactant to predict the outcome of the reaction. This forms the basis of more complex analysis, such as neutralization reactions.

neutralization reaction

Neutralization is a specific kind of acid-base reaction where an acid and a base react to form water and a salt. This reaction generally results in a neutral solution with a pH of 7.
In the cases provided, each solution ended up with a pH of 7 because the moles of hydrogen ions equaled the moles of hydroxyl ions.
Consider the examples:

• Formic acid and \(\text{NaOH}\) react to form water and sodium formate.
• Diprotic acids like sulfuric and oxalic acid also undergo neutralization, requiring two hydroxyl ions for full neutralization.

Since the moles of acid and base exactly matched in these reactions, they resulted in complete neutralization producing a neutral solution.

molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. This is a key factor in acid-base reactions because it dictates how much of a reactant can participate in a reaction.
To calculate molarity:

• Use the formula \(\text{Molarity} = \frac{\text{moles of solute}}{\text{volume of solution in Liters}}\).
• It's vital for understanding how many moles of a substance are present in a given volume of liquid.

In the exercise given, molarity was used to determine how many moles of \(\text{H}^+\) and \(\text{OH}^-\) ions were present in the solutions, which is crucial for balancing the equations and predicting pH changes.

stoichiometry

Stoichiometry is the aspect of chemistry that deals with the quantities of substances that participate in chemical reactions. It's like a recipe that tells how much of each ingredient you need.
In acid-base reactions, stoichiometry helps in balancing equations and calculating how much acid is needed to neutralize a base (or vice versa).
For instance: when sulfuric acid (\(\text{H}_2\text{SO}_4\)) reacts with \(\text{NaOH}\), it creates 0.0225 moles of \(\text{H}^+\) ions for every mole of acid. Therefore, two moles of \(\text{NaOH}\) are needed for each mole of \(\text{H}_2\text{SO}_4\).

• This balanced approach ensures that no excess of reactants is left over.
• Stoichiometry also allows chemists to accurately predict product formation and resultant pH.

Accurate stoichiometric calculations facilitate understanding of chemical processes like neutralization, ensuring better predictions of the outcomes and pH.