Problem 76 - 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) Equal volumes of \(0.10 \mathrm{M}\) acetic acid, \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H},\) and \(0.10 \mathrm{M} \mathrm{KOH}\) are mixed. (b) \(25 \mathrm{mL}\) of \(0.015 \mathrm{M} \mathrm{NH}_{3}\) is mixed with \(12 \mathrm{mL}\) of \(0.015 \mathrm{M} \mathrm{HCl}\) (c) \(150 \mathrm{mL}\) of \(0.20 \mathrm{M} \mathrm{HNO}_{3}\) is mixed with \(75 \mathrm{mL}\) of \(0.40 \mathrm{M} \mathrm{NaOH}\) (d) \(25 \mathrm{mL}\) of \(0.45 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) is mixed with \(25 \mathrm{mL}\) of \(0.90 \mathrm{M} \mathrm{NaOH}\)

Step-by-Step Solution

Answer

(a) Greater than 7; (b) Greater than 7; (c) Equal to 7; (d) Equal to 7.

Step 1: Analyze Reaction for (a)

In this step, we analyze the reaction between acetic acid \((\mathrm{CH}_3\mathrm{CO}_2\mathrm{H})\) and potassium hydroxide \((\mathrm{KOH})\). Both are equal in concentration and volume (0.10 M, equal volumes), therefore they neutralize each other, forming a solution of sodium acetate (a salt of a weak base and weak acid). This results in a slightly basic solution.

Step 2: Analyze Reaction for (b)

Here we mix ammonia \((\mathrm{NH}_3)\), a weak base, with hydrochloric acid \((\mathrm{HCl})\), a strong acid. Calculate moles: \(0.025 \times 0.015 = 0.000375\) moles \(\mathrm{NH}_3\) and \(0.012 \times 0.015 = 0.00018\) moles \(\mathrm{HCl}\). Since \(\mathrm{NH}_3\) provides more moles, it slightly neutralizes \(\mathrm{HCl}\) leaving an excess of \(\mathrm{NH}_3\), making the solution slightly basic.

Step 3: Analyze Reaction for (c)

For \(\mathrm{HNO}_3\) (a strong acid) and \(\mathrm{NaOH}\) (a strong base), calculate moles: \(0.150 \times 0.20 = 0.030\) moles \(\mathrm{HNO}_3\) and \(0.075 \times 0.40 = 0.030\) moles \(\mathrm{NaOH}\). Both react completely, forming a neutral solution. Therefore, the pH will be equal to 7.

Step 4: Analyze Reaction for (d)

\(\mathrm{H}_2\mathrm{SO}_4\), a strong diprotic acid, mixed with \(\mathrm{NaOH}\), calculate moles available: \(0.025 \times 0.45 = 0.01125\) moles \(\mathrm{H}_2\mathrm{SO}_4\) provides \(0.0225\) equivalents of H+ (because it's diprotic) and \(0.025 \times 0.90 = 0.0225\) moles \(\mathrm{NaOH}\). Equal equivalents ensure neutralization, resulting in a neutral solution with pH equal to 7.

Key Concepts

Acid-Base Reactions

Acid-base reactions are fundamental in chemistry, involving the transfer of protons between reactants. When an acid and a base are combined, they can neutralize each other, forming water and a salt. This process is reversible and can reach a state of equilibrium.
For example, in the reaction between acetic acid (\( \text{CH}_3\text{CO}_2\text{H} \)) and potassium hydroxide (\(\text{KOH}\)), the acid donates a proton (\(\text{H}^+\)) to the base, resulting in the formation of water and potassium acetate (\(\text{CH}_3\text{CO}_2\text{K}\)).
The solution's pH depends on the strength of the acids and bases involved. A weak acid with a strong base can lead to a basic solution, as seen in this example.

Neutralization

Neutralization occurs when an acid and a base completely react to form water and a salt. This reaction typically moves the solution towards a neutral pH of 7. However, the final pH can vary depending on the strength of the acid and base.
In the case of ammonia (\(\text{NH}_3\)) neutralizing hydrochloric acid (\(\text{HCl}\)), we need to consider the stoichiometry. Ammonia, as a weak base, partially neutralizes the strong \(\text{HCl}\), resulting in a slightly basic solution.
Understanding the mole ratios is essential to determine the extent of neutralization and predict pH changes.

Molarity

Molarity measures the concentration of a solution, expressed in moles of solute per liter of solution (\( \text{mol/L} \)). It's crucial for calculating the number of moles in a given volume, which helps predict the behavior of acid-base reactions.
For instance, knowing the molarity of nitric acid (\(\text{HNO}_3\)) and sodium hydroxide (\(\text{NaOH}\)), you can calculate moles by multiplying molarity by volume.
\[ \text{Moles} = \text{Volume (L)} \times \text{Molarity (mol/L)} \] In neutral reactions, equal moles of acid and base result in a neutral pH of 7.

Chemical Equilibrium

Chemical equilibrium occurs when the forward and reverse reactions proceed at the same rate, resulting in constant concentrations of reactants and products.
In acid-base reactions, equilibrium can determine the final pH of a solution. With sulfuric acid (\(\text{H}_2\text{SO}_4\)), a strong diprotic acid, its neutralization with sodium hydroxide (\(\text{NaOH}\)) means complete reaction occurs with available equivalents.

• For diprotic acids like \(\text{H}_2\text{SO}_4\), each molecule can donate two protons, affecting the equilibrium equation and stoichiometry.

When equilibrium is reached, the pH is determined by the balance between remaining ions, often leading to a neutral pH when equivalents match.