Theme: Physical Chemistry - pH and Dilution
The pH scale is logarithmic, meaning each unit change in pH represents a 10-fold change in the concentration of hydrogen ions ($\text{H}^{+}$).
- $\text{pH} = -log_{10}[\text{H}^{+}]$.
- $[\text{H}^{+}] = 10^{-\text{pH}}$.
To change the pH from 2 to 4, the concentration of $\text{H}^{+}$ must decrease by two orders of magnitude (from $10^{-2}$ to $10^{-4}$), which is a 100-fold dilution. In a strong acid solution, we assume complete dissociation, so the dilution of the acid is directly proportional to the change in ion concentration.
1. Find Initial Concentration ($M_1$):
- $\text{pH} = 2 \Rightarrow [\text{H}^{+}] = 10^{-2} \text{ M}$.
2. Find Final Concentration ($M_2$):
- $\text{pH} = 4 \Rightarrow [\text{H}^{+}] = 10^{-4} \text{ M}$.
3. Calculate the Dilution Factor:
- $\text{Factor} = M_1 / M_2 = 10^{-2} / 10^{-4} = 10^2 = 100$.
- The solution must be diluted 100 times.
4. Determine Final Volume ($V_2$):
- $V_1 = 1 \text{ mL}$.
- $V_2 = V_1 \times \text{Factor} = 1 \text{ mL} \times 100 = 100 \text{ mL}$.
The Brønsted-Lowry theory defines an acid as a proton ($\text{H}^{+}$) donor and a base as a proton acceptor. Every acid-base reaction involves the transfer of a proton from the acid to the base, resulting in a "conjugate" pair.
- When an acid loses a proton, it becomes its Conjugate Base.
- When a base gains a proton, it becomes its Conjugate Acid.
The strength of an acid is inversely related to the strength of its conjugate base. A strong acid is one that has an extremely high tendency to donate its proton. This means the resulting conjugate base has a negligible tendency to "take it back." Therefore, strong acids always form very weak (stable) conjugate bases.
1. Analyze the Reaction: $ ext{Acid} + ext{H}_2 ext{O} leftrightarrow ext{Conjugate Base} + ext{H}_3 ext{O}^+$.
2. Define a Strong Acid: The equilibrium lies almost entirely to the right (the acid is "desperate" to lose the proton).
3. Deduce Conjugate Behavior: If the equilibrium is far to the right, it means the reverse reaction (the conjugate base taking a proton back) is highly unlikely.
4. Apply Definitions: A species that does not want to accept a proton is a weak base.
5. Match with options:
- A) Forms a weak conjugate base. (Correct).
- B) Strong conjugate base. (Incorrect; this is true for weak acids).
- C) Poor proton donor. (Incorrect; this is the definition of a weak acid).
- D) Good proton acceptor. (Incorrect; this is the definition of a base).
- E) Must be in aqueous solution. (Incorrect; this is a limitation of the Arrhenius theory, not Brønsted-Lowry).
Common confusion: "If the acid is strong, shouldn't its base also be strong?" No, acidity and basicity are like a see-saw. If one end is up (strong), the other must be down (weak). Strategy: Remember the classic example: $\text{H}\text{Cl}$ (extremely strong acid) $
ightarrow \text{Cl}^{-}$ (extremely weak base, it doesn't even affect the pH).
This relationship is the basis of Buffer Systems in the body, such as the Bicarbonate buffer. Carbonic acid is a weak acid, meaning its conjugate base (Bicarbonate, $\text{H}\text{C}\text{O}_{3}^{-}$) is relatively strong. This strength allows Bicarbonate to effectively "soak up" excess protons in the blood, maintaining a constant pH of 7.4. If we had only strong acids in our blood, we would have no ability to buffer changes in acidity.
Answer: $
ightarrow$ A) forms a weak conjugate base.