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 \(25 \mathrm{mL}\) of \(0.015 \mathrm{M}\) HCI (c) \(150 \mathrm{mL}\) of \(0.20 \mathrm{M} \mathrm{HNO}_{3}\) is mixed with \(75 \mathrm{mL}\) of \(0.40 \mathrm{M} \mathrm{NaOH}\)

Short answer

(a) pH > 7; (b) pH < 7; (c) pH = 7.

Step-by-step solution

Determine Moles of each Reactant (a)

For acetic acid and KOH, both at a concentration of 0.10 M with equal volume, we have:Number of moles of acetic acid and KOH = \(V \times C = 0.10 \times V\).Since their volumes are equal, they will completely neutralize each other, producing water and acetate ions. The resulting solution is a basic buffer due to acetate ions.

pH of the Solution (a)

The product (acetate ion) when acetic acid is neutralized is a conjugate base and gives a basic pH (>7).

Determine Moles of each Reactant (b)

For NH3 and HCl, both at a concentration of 0.015 M and an equal volume of 25 mL,we have:Number of moles of NH3 and HCl = \(0.015 \times 0.025 = 0.000375\). Since they completely neutralize each other, the pH is driven by the product, ammonium chloride, which is slightly acidic.

pH of the Solution (b)

The presence of ammonium ions will make the solution slightly acidic, thus the pH is less than 7.

Determine Moles of each Reactant (c)

For HNO3 and NaOH:- Moles of HNO3 = \(0.20 \times 0.150 = 0.030 \) moles- Moles of NaOH = \(0.40 \times 0.075 = 0.030 \) molesThese reactants are in equal molar amounts, thus they will completely neutralize each other, resulting in a neutral pH.

pH of the Solution (c)

The resulting solution after complete neutralization of an equal molar amount of strong acid and base is neutral, so the pH is equal to 7.

Key concepts

Neutralization Reaction

A neutralization reaction occurs when an acid and a base react to form water and a salt. These reactions are central to understanding how pH levels change when substances are mixed. In the given problems, we focus on mixing an acid and a base and determining the resulting pH.
- **For acetic acid and KOH**: Equal moles mean each molecule of acetic acid neutralizes with a molecule of KOH. The reaction produces water and acetate ions, which makes the solution slightly basic. This is typical for weak acid and strong base reactions.
- **For HCl and NH3**: Here, the strong acid (HCl) neutralizes with the weak base (NH3), forming ammonium chloride. This reaction results in a slightly acidic solution due to excess hydrogen ions.
- **For HNO3 and NaOH**: Both reactants are strong, with equal moles present, resulting in complete neutralization, forming water and a salt (sodium nitrate), making the solution neutral (pH = 7).

Acid-Base Chemistry

Acid-base chemistry explores the nature of acids and bases, dealing with their strength, reactions, and the concept of pH.
- **Acids** are substances that donate protons (H⁺ ions) in a solution. Strong acids, like HCl and HNO3, completely dissociate in water, making them key players in reactions. Weak acids, like acetic acid, partially dissociate, creating equilibrium and different pH effects.
- **Bases** accept protons. Strong bases, such as KOH and NaOH, dissociate fully, providing OH⁻ ions to neutralize acids effectively.
- The **pH scale** ranges from 0 to 14, with acids having pH less than 7, bases greater than 7, and neutral solutions at 7.
Understanding these principles is crucial in predicting the behavior of a solution after mixing.

Buffer Solutions

Buffer solutions are special mixtures that resist changes in pH, even when small amounts of acid or base are added. They are crucial in maintaining stable conditions in biological and chemical systems.
- A **buffer** is typically made from a weak acid and its conjugate base or a weak base and its conjugate acid.
- In our exercise, the mixture of acetic acid and KOH forms a buffer. The acetate ions formed can react with added acids or bases to stabilize pH levels.
- Buffers work by absorbing excess H⁺ or OH⁻, preventing drastic changes in pH.
This makes them indispensable in environments that require pH stability, such as blood in human bodies or industrial processes.