In which of the following compounds does the ratio of anion to cation size have the lowest value?

Options

A. NaCl
B. KCl
C. `MgCl_2`
D. NaBr

Answer

To solve the question regarding which compound has the lowest ratio of anion to cation size, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Question**: We need to find the compound with the lowest ratio of anion size to cation size. This means we want the size of the anion to be as small as possible and the size of the cation to be as large as possible.

2. **Identify the Compounds**: The compounds given are NaCl, KCl, MgCl2, and NaBr. We need to analyze the cations and anions in each compound:
- **NaCl**: Cation = Na⁺, Anion = Cl⁻
- **KCl**: Cation = K⁺, Anion = Cl⁻
- **MgCl2**: Cation = Mg²⁺, Anion = Cl⁻
- **NaBr**: Cation = Na⁺, Anion = Br⁻

3. **Determine the Sizes of Cations and Anions**:
- **Cations**:
- Na⁺ (Sodium) - relatively small
- K⁺ (Potassium) - larger than Na⁺
- Mg²⁺ (Magnesium) - smaller than K⁺ but larger than Na⁺
- **Anions**:
- Cl⁻ (Chloride) - standard size
- Br⁻ (Bromide) - larger than Cl⁻

4. **Analyze the Ratios**:
- For **NaCl**: Ratio = size of Cl⁻ / size of Na⁺
- For **KCl**: Ratio = size of Cl⁻ / size of K⁺
- For **MgCl2**: Ratio = size of Cl⁻ / size of Mg²⁺
- For **NaBr**: Ratio = size of Br⁻ / size of Na⁺

5. **Compare the Ratios**:
- Since we want the lowest ratio, we need to maximize the size of the cation and minimize the size of the anion.
- K⁺ is the largest cation among the options, and Cl⁻ is the smallest anion in KCl.
- In MgCl2, although Mg²⁺ is a cation, it is smaller than K⁺. Thus, the ratio of Cl⁻ to Mg²⁺ will be higher compared to KCl.
- Na⁺ is smaller than K⁺, and since Br⁻ is larger than Cl⁻, NaBr will also have a higher ratio compared to KCl.

6. **Conclusion**: The compound with the lowest ratio of anion to cation size is **KCl**.

### Final Answer:
The compound with the lowest ratio of anion to cation size is **KCl**.