`H_(2)` can displace the metal from its aqueous solution.

Options

A. `Li^(+)`
B. `Sr^(2+)`
C. `A1^(3+)`
D. `Ag^(+)`

Explanation

To determine whether \( H_2 \) can displace a metal from its aqueous solution, we need to analyze the standard electrode potentials (\( E^\circ \)) of the metals in question compared to that of hydrogen. Here’s a step-by-step solution:

### Step 1: Understand the concept of displacement
A metal can be displaced from its solution by another element if the element has a higher reduction potential than the metal ion in solution. In this case, \( H_2 \) can displace metal ions if the reduction potential of \( H^+ \) (from \( H_2 \)) is higher than that of the metal ions.

### Step 2: Identify the standard electrode potential of hydrogen
The standard electrode potential for the half-reaction \( H^+ + e^- \rightarrow H_2 \) is defined as:
\[ E^\circ = 0 \, \text{V} \]
This means that \( H_2 \) can act as a reducing agent.

### Step 3: Compare with other metals
Now, we need to compare the standard electrode potentials of the metals mentioned:
- Lithium (\( Li^+ \)): \( E^\circ \approx -3.04 \, \text{V} \)
- Strontium (\( Sr^{2+} \)): \( E^\circ \approx -2.89 \, \text{V} \)
- Aluminum (\( Al^{3+} \)): \( E^\circ \approx -1.66 \, \text{V} \)
- Silver (\( Ag^+ \)): \( E^\circ \approx +0.80 \, \text{V} \)

### Step 4: Analyze the potentials
From the values:
- \( Li^+, Sr^{2+}, \) and \( Al^{3+} \) have negative potentials, indicating they are stronger reducing agents than \( H_2 \).
- \( Ag^+ \) has a positive potential, indicating it is a stronger oxidizing agent than \( H_2 \).

### Step 5: Conclusion
Since \( H_2 \) can only displace metals with lower reduction potentials than itself, it can displace \( Ag^+ \) from its solution but cannot displace \( Li^+, Sr^{2+}, \) or \( Al^{3+} \).

Thus, the answer is that \( H_2 \) can displace \( Ag^+ \) from its aqueous solution.

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