The solubility product of three sparingly soluble salts are given below:
`{:("No","Formula","Solubility product"),(1,PQ,4.0 xx 10^(-20),(2,PQ_(2),3.2 xx 10^(-14)),(3,PQ_(3), 2.7 xx 10^(-35)):}`
The correct order of decreasing molar solubility is

Options

A. `1 gt 2 gt 3`
B. `2 gt 1 gt 3`
C. `3 gt 2 gt 1`
D. `2 gt 3 gt 1`

Answer

To determine the correct order of decreasing molar solubility for the salts PQ, PQ2, and PQ3 based on their solubility products (Ksp), we will follow these steps:

### Step 1: Write down the Ksp values
The given solubility products for the salts are:
- For PQ: Ksp = 4.0 x 10^(-20)
- For PQ2: Ksp = 3.2 x 10^(-14)
- For PQ3: Ksp = 2.7 x 10^(-35)

### Step 2: Determine the dissociation of each salt
1. **For PQ**:
- Dissociation: PQ ⇌ P⁺ + Q⁻
- If the solubility is 's', then Ksp = s².

2. **For PQ2**:
- Dissociation: PQ2 ⇌ P²⁺ + 2Q⁻
- If the solubility is 's', then Ksp = (s)(2s)² = 4s³.

3. **For PQ3**:
- Dissociation: PQ3 ⇌ P³⁺ + 3Q⁻
- If the solubility is 's', then Ksp = (s)(3s)³ = 27s⁴.

### Step 3: Calculate the molar solubility for each salt
1. **For PQ**:
\[ Ksp = s² \implies s = \sqrt{Ksp} = \sqrt{4.0 \times 10^{-20}} = 2.0 \times 10^{-10} \]

2. **For PQ2**:
\[ Ksp = 4s³ \implies s = \left(\frac{Ksp}{4}\right)^{1/3} = \left(\frac{3.2 \times 10^{-14}}{4}\right)^{1/3} = \left(0.8 \times 10^{-14}\right)^{1/3} = 2.0 \times 10^{-5} \]

3. **For PQ3**:
\[ Ksp = 27s⁴ \implies s = \left(\frac{Ksp}{27}\right)^{1/4} = \left(\frac{2.7 \times 10^{-35}}{27}\right)^{1/4} = \left(1.0 \times 10^{-36}\right)^{1/4} = 10^{-9} \]

### Step 4: Compare the molar solubility values
- Molar solubility of PQ = \(2.0 \times 10^{-10}\)
- Molar solubility of PQ2 = \(2.0 \times 10^{-5}\)
- Molar solubility of PQ3 = \(10^{-9}\)

### Step 5: Order the solubility values
Now we can arrange the molar solubility values in decreasing order:
1. PQ2: \(2.0 \times 10^{-5}\)
2. PQ: \(2.0 \times 10^{-10}\)
3. PQ3: \(10^{-9}\)

### Final Order of Decreasing Molar Solubility
The correct order of decreasing molar solubility is:
**PQ2 > PQ > PQ3**