The solubility of product `(K_(sp))` of the following compounds are given at `25^(@)C`
`{:("Compound",K_(sp),"Compound",K_(sp),),(AgCl,1.1 xx 10^(-10),PbCrO_(4),4.0 xx 10^(-4),),(AgI,1.0 xx 10^(-16),Ag_(2)XO_(3),8.0 xx 10^(-12),):}`
The most soluble and least soluble compounds are respectively

Options

A. AgCl and `PbCrO_4`
B. AgI and `Ag_(2)CO_(3)`
C. AgCl and `Ag_(2)CO_(3)`
D. `Ag_(2)CO_(3)` and `PbCrO_(4)`

Explanation

To determine the most soluble and least soluble compounds from the given solubility products (Ksp) at 25°C, we can follow these steps:

### Step 1: List the given compounds and their Ksp values
We have the following compounds and their corresponding Ksp values:
- AgCl: \( K_{sp} = 1.1 \times 10^{-10} \)
- AgI: \( K_{sp} = 1.0 \times 10^{-16} \)
- PbCrO4: \( K_{sp} = 4.0 \times 10^{-4} \)
- Ag2XO3: \( K_{sp} = 8.0 \times 10^{-12} \)

### Step 2: Understand the relationship between solubility and Ksp
The solubility product (Ksp) indicates the extent to which a compound can dissolve in water. A higher Ksp value means that the compound is more soluble, while a lower Ksp value indicates lower solubility.

### Step 3: Compare the Ksp values
Now, we will compare the Ksp values of the compounds:
- AgCl: \( 1.1 \times 10^{-10} \)
- AgI: \( 1.0 \times 10^{-16} \)
- PbCrO4: \( 4.0 \times 10^{-4} \)
- Ag2XO3: \( 8.0 \times 10^{-12} \)

### Step 4: Identify the most soluble compound
The compound with the highest Ksp value is PbCrO4, which has a Ksp of \( 4.0 \times 10^{-4} \). Therefore, PbCrO4 is the most soluble compound.

### Step 5: Identify the least soluble compound
The compound with the lowest Ksp value is AgI, which has a Ksp of \( 1.0 \times 10^{-16} \). Therefore, AgI is the least soluble compound.

### Conclusion
The most soluble compound is **PbCrO4** and the least soluble compound is **AgI**.

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