The solubility product `(K_(sp))` of the following compounds are given at `25^(@)C`
`{:("Compound",,"K"_(sp)),("AgCl",,1.1xx10^(-10)),(Agl,,1.0xx10^(-16)),(PbCrO_(4),,4.0xx10^(-14)),(Ag_(2)CO_(3),,8.0xx10^(-12)):}`
The most soluble and least soluble compound are respectively

Options

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

Answer

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

### Step 1: List the given compounds and their Ksp values
We have the following compounds and their respective Ksp values:

1. AgCl: \( K_{sp} = 1.1 \times 10^{-10} \)
2. AgI: \( K_{sp} = 1.0 \times 10^{-16} \)
3. PbCrO₄: \( K_{sp} = 4.0 \times 10^{-14} \)
4. Ag₂CO₃: \( K_{sp} = 8.0 \times 10^{-12} \)

### Step 2: Understand the relationship between Ksp and solubility
The solubility product constant (Ksp) is a measure of the solubility of a compound in a saturated solution. A higher Ksp value indicates greater solubility, while a lower Ksp value indicates lower solubility.

### Step 3: Compare the Ksp values
Now, we will compare the Ksp values to determine which compound is the most soluble and which is the least soluble:

- AgCl: \( K_{sp} = 1.1 \times 10^{-10} \)
- AgI: \( K_{sp} = 1.0 \times 10^{-16} \)
- PbCrO₄: \( K_{sp} = 4.0 \times 10^{-14} \)
- Ag₂CO₃: \( K_{sp} = 8.0 \times 10^{-12} \)

### Step 4: Identify the highest and lowest Ksp values
- The highest Ksp value is \( 1.1 \times 10^{-10} \) for AgCl.
- The lowest Ksp value is \( 1.0 \times 10^{-16} \) for AgI.

### Step 5: Conclusion
From the comparison:
- The most soluble compound is **AgCl** (highest Ksp).
- The least soluble compound is **AgI** (lowest Ksp).

### Final Answer
The most soluble and least soluble compounds are respectively **AgCl** and **AgI**.

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