Given the following acid with Ka values

Given the following acid with Ka values.

• HClO4 1×10⁷
• HOAc 1.76×10^-5
• HCN 4.93×10^-10
• HF 3.53×10^-4

What is the order of increasing base strength?

Can someone explain how they solved this problem?

The correct answer and explanation is :

To determine the order of increasing base strength based on the provided (K_a) values, we first need to understand the relationship between the acid strength and base strength.

Key Concept:

• The acid dissociation constant (Ka) measures how strong an acid is. The higher the (K_a), the stronger the acid.
• The base dissociation constant (Kb) measures the strength of the conjugate base of an acid. It is related to the acid dissociation constant by the equation:
  [
  K_b = \frac{K_w}{K_a}
  ]
  where (K_w) is the ionization constant for water, (K_w = 1 \times 10^{-14}) at 25°C.
• The stronger the acid, the weaker the conjugate base. This means that acids with higher (K_a) values will have weaker conjugate bases (lower (K_b) values), and vice versa.

Step-by-step Explanation:

We are given the following acids and their respective (K_a) values:

1. Perchloric acid (HClO4): (K_a = 1 \times 10^7)
2. Acetic acid (HOAc): (K_a = 1.76 \times 10^{-5})
3. Hydrocyanic acid (HCN): (K_a = 4.93 \times 10^{-10})
4. Hydrofluoric acid (HF): (K_a = 3.53 \times 10^{-4})

To find the order of increasing base strength, we calculate (K_b) for each conjugate base using the formula (K_b = \frac{K_w}{K_a}):

1. For HClO4:
   [
   K_b = \frac{1 \times 10^{-14}}{1 \times 10^7} = 1 \times 10^{-21}
   ]
2. For HOAc:
   [
   K_b = \frac{1 \times 10^{-14}}{1.76 \times 10^{-5}} \approx 5.68 \times 10^{-10}
   ]
3. For HCN:
   [
   K_b = \frac{1 \times 10^{-14}}{4.93 \times 10^{-10}} \approx 2.03 \times 10^{-5}
   ]
4. For HF:
   [
   K_b = \frac{1 \times 10^{-14}}{3.53 \times 10^{-4}} \approx 2.83 \times 10^{-11}
   ]

Now, we arrange the (K_b) values in order of increasing size (because higher (K_b) values correspond to stronger bases):

• (K_b) for HClO4 = (1 \times 10^{-21}) (weakest base)
• (K_b) for HF = (2.83 \times 10^{-11})
• (K_b) for HOAc = (5.68 \times 10^{-10})
• (K_b) for HCN = (2.03 \times 10^{-5}) (strongest base)

Final Answer:

The order of increasing base strength is:
HClO4 < HF < HOAc < HCN

Explanation:

• HClO4 is the strongest acid (highest (K_a)), so its conjugate base is the weakest.
• HCN is the weakest acid (lowest (K_a)), so its conjugate base is the strongest.
• The base strength increases as the (K_a) value decreases, following the inverse relationship between acid strength and base strength.