How many gm of silver will be displaced from a solution of `AgNO_(3)` by 4gm of magnesium?

Options

A. 18 gm
B. 4 gm
C. 4 gm
D. 2 gm

Explanation

To determine how many grams of silver (Ag) will be displaced from a solution of silver nitrate (AgNO₃) by 4 grams of magnesium (Mg), we can follow these steps:

### Step 1: Write the balanced chemical equation
The reaction between magnesium and silver nitrate can be written as:
\[ \text{Mg} + 2 \text{AgNO}_3 \rightarrow \text{Mg(NO}_3\text{)}_2 + 2 \text{Ag} \]
This equation shows that 1 mole of magnesium displaces 2 moles of silver.

### Step 2: Calculate the molar mass of magnesium and silver
- The molar mass of magnesium (Mg) is approximately 24 g/mol.
- The molar mass of silver (Ag) is approximately 108 g/mol.

### Step 3: Determine the moles of magnesium used
Using the mass of magnesium provided:
\[ \text{Moles of Mg} = \frac{\text{mass}}{\text{molar mass}} = \frac{4 \text{ g}}{24 \text{ g/mol}} = \frac{1}{6} \text{ mol} \]

### Step 4: Use the stoichiometry of the reaction
From the balanced equation, we see that 1 mole of magnesium displaces 2 moles of silver. Therefore, the moles of silver displaced can be calculated as:
\[ \text{Moles of Ag displaced} = 2 \times \text{Moles of Mg} = 2 \times \frac{1}{6} = \frac{1}{3} \text{ mol} \]

### Step 5: Convert moles of silver to grams
Now, we convert the moles of silver displaced to grams:
\[ \text{Mass of Ag} = \text{Moles of Ag} \times \text{Molar mass of Ag} = \frac{1}{3} \text{ mol} \times 108 \text{ g/mol} = 36 \text{ g} \]

### Final Answer
Thus, 4 grams of magnesium will displace **36 grams of silver** from the solution of AgNO₃.

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