Based on the following reactions, arrange the metals in increasing order of their reduction potentials.
`Cu+2Ag^(+)toCu^(2+)+2Ah`
`Mg+Zn^(2+)toMg^(2+)+Zn`
`Zn+Cu^(2+)toZn^(2+)+Cu`

Options

A. `Mg gt Zn gt Cu gt Ag`
B. `Mg lt Zn lt Cu lt Ag`
C. `Zn gt Cu gt Ag gt Mg`
D. `Mg gt Cu gt Zn gt Ag`

Explanation

To arrange the metals in increasing order of their reduction potentials based on the provided reactions, we will analyze each reaction step by step.

### Step 1: Analyze the first reaction
The first reaction is:
\[ \text{Cu} + 2\text{Ag}^+ \rightarrow \text{Cu}^{2+} + 2\text{Ag} \]

In this reaction, silver ions (\( \text{Ag}^+ \)) are being reduced to silver metal (\( \text{Ag} \)), while copper (\( \text{Cu} \)) is being oxidized to copper ions (\( \text{Cu}^{2+} \)). This indicates that silver has a higher reduction potential than copper because it is gaining electrons.

**Hint for Step 1:** Identify which species is being reduced and which is being oxidized to determine their relative reduction potentials.

### Step 2: Analyze the second reaction
The second reaction is:
\[ \text{Mg} + \text{Zn}^{2+} \rightarrow \text{Mg}^{2+} + \text{Zn} \]

In this reaction, zinc ions (\( \text{Zn}^{2+} \)) are being reduced to zinc metal (\( \text{Zn} \)), while magnesium (\( \text{Mg} \)) is being oxidized to magnesium ions (\( \text{Mg}^{2+} \)). This indicates that zinc has a higher reduction potential than magnesium.

**Hint for Step 2:** Look for the species that is reduced to determine which metal has a higher reduction potential.

### Step 3: Analyze the third reaction
The third reaction is:
\[ \text{Zn} + \text{Cu}^{2+} \rightarrow \text{Zn}^{2+} + \text{Cu} \]

In this reaction, copper ions (\( \text{Cu}^{2+} \)) are being reduced to copper metal (\( \text{Cu} \)), while zinc (\( \text{Zn} \)) is being oxidized to zinc ions (\( \text{Zn}^{2+} \)). This indicates that copper has a higher reduction potential than zinc.

**Hint for Step 3:** Determine which metal is reduced and which is oxidized to compare their reduction potentials.

### Step 4: Summarize the findings
From the analysis of the three reactions, we can summarize the relationships:
1. \( \text{Ag}^+ > \text{Cu} \) (from Step 1)
2. \( \text{Zn}^{2+} > \text{Mg} \) (from Step 2)
3. \( \text{Cu}^{2+} > \text{Zn} \) (from Step 3)

### Step 5: Arrange the metals in increasing order of reduction potentials
From the above relationships, we can deduce the following order of reduction potentials:
- Magnesium (\( \text{Mg} \)) has the lowest reduction potential.
- Zinc (\( \text{Zn} \)) has a higher reduction potential than magnesium.
- Copper (\( \text{Cu} \)) has a higher reduction potential than zinc.
- Silver (\( \text{Ag} \)) has the highest reduction potential.

Thus, the increasing order of reduction potentials is:
\[ \text{Mg} < \text{Zn} < \text{Cu} < \text{Ag} \]

**Final Answer:** \( \text{Mg} < \text{Zn} < \text{Cu} < \text{Ag} \)