Silver is removed from the solutions of its salts with metallic zinc, according to the reaction
`Zn + 2 Ag^(o+) rarr Zn^(2+) + 2Ag`.
A `65.4 g` piece of `Zn` is put into a `100 L` vat containing `3.24 g` `Ag^(o+)` per litre. How amny moles of reactant remained unreacted?

Explanation

To solve the problem, we will follow these steps:

### Step 1: Calculate the total mass of Ag⁺ in the solution
The concentration of Ag⁺ is given as 3.24 g/L and the volume of the solution is 100 L.

\[ \text{Total mass of Ag}^+ = \text{Concentration} \times \text{Volume} = 3.24 \, \text{g/L} \times 100 \, \text{L} = 324 \, \text{g} \]

### Step 2: Calculate the number of moles of Ag⁺
To find the number of moles of Ag⁺, we use the formula:

\[ \text{Moles of Ag}^+ = \frac{\text{Mass}}{\text{Molar mass}} \]

The molar mass of Ag is approximately 108 g/mol.

\[ \text{Moles of Ag}^+ = \frac{324 \, \text{g}}{108 \, \text{g/mol}} = 3 \, \text{moles} \]

### Step 3: Calculate the number of moles of Zn
The mass of Zn provided is 65.4 g, and the molar mass of Zn is also 65.4 g/mol.

\[ \text{Moles of Zn} = \frac{65.4 \, \text{g}}{65.4 \, \text{g/mol}} = 1 \, \text{mole} \]

### Step 4: Determine the stoichiometry of the reaction
From the balanced chemical equation:

\[ \text{Zn} + 2 \text{Ag}^+ \rightarrow \text{Zn}^{2+} + 2 \text{Ag} \]

1 mole of Zn reacts with 2 moles of Ag⁺. Therefore, 1 mole of Zn will require 2 moles of Ag⁺ to react completely.

### Step 5: Determine the limiting reactant
We have 1 mole of Zn, which can react with 2 moles of Ag⁺. Since we have 3 moles of Ag⁺ available, Zn is the limiting reactant.

### Step 6: Calculate the moles of Ag⁺ consumed
Since 1 mole of Zn reacts with 2 moles of Ag⁺:

\[ \text{Moles of Ag}^+ \text{ consumed} = 2 \, \text{moles} \]

### Step 7: Calculate the moles of Ag⁺ remaining
Now we can find the moles of Ag⁺ that remain unreacted:

\[ \text{Moles of Ag}^+ \text{ remaining} = \text{Initial moles of Ag}^+ - \text{Moles of Ag}^+ \text{ consumed} \]

\[ \text{Moles of Ag}^+ \text{ remaining} = 3 \, \text{moles} - 2 \, \text{moles} = 1 \, \text{mole} \]

### Final Answer
Thus, the number of moles of reactant (Ag⁺) that remain unreacted is **1 mole**.

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