The chief are of Zn is the sulphide , ZnS. The Ore is concentrated by froth floation process and then heated in air to convert Zns to Zno.
`2ZnS+30_(2)overset(80%)to 2ZnO+ 2SO_(2)`
`ZnO+H_(2)SO_(4)overset(100%)to ZnSO_(4)+ H_(2)`
`2ZnSO_(4)+2H_(2)Ooverset(80%)to 2Zn+ 2H_(2)SO_(4)+O_(2)`
The number of moles of ZnS required for producing 2 moles of Zn will be:

Options

A. `3.125`
B. `2`
C. `2.125`
D. `4`

Answer

To solve the problem of how many moles of ZnS are required to produce 2 moles of Zn, we will follow the stoichiometric relationships in the given chemical reactions step by step.

### Step 1: Analyze the Reactions
The reactions provided are:
1. \( 2 \text{ZnS} + 3 \text{O}_2 \xrightarrow{80\%} 2 \text{ZnO} + 2 \text{SO}_2 \)
2. \( \text{ZnO} + \text{H}_2\text{SO}_4 \xrightarrow{100\%} \text{ZnSO}_4 + \text{H}_2 \)
3. \( 2 \text{ZnSO}_4 + 2 \text{H}_2\text{O} \xrightarrow{80\%} 2 \text{Zn} + 2 \text{H}_2\text{SO}_4 + \text{O}_2 \)

### Step 2: Determine Moles of Zn Produced
We want to produce 2 moles of Zn. From the third reaction, we can see that to produce 2 moles of Zn, we need 2 moles of ZnSO4 (since the stoichiometry is 2:2).

### Step 3: Calculate Moles of ZnSO4 Required
From the second reaction, we see that 1 mole of ZnO produces 1 mole of ZnSO4. Therefore, to produce 2 moles of ZnSO4, we need 2 moles of ZnO.

### Step 4: Determine Moles of ZnO Required
From the first reaction, we see that 2 moles of ZnS produce 2 moles of ZnO. Therefore, to produce 2 moles of ZnO, we need 2 moles of ZnS.

### Step 5: Adjust for Reaction Yields
However, we need to take into account the yields of the reactions. The first reaction has an 80% yield, meaning that only 80% of the ZnS will convert to ZnO. Therefore, if we need 2 moles of ZnO, we must calculate how much ZnS we need to start with.

Let \( x \) be the moles of ZnS we need to start with. The amount of ZnO produced from \( x \) moles of ZnS is given by:
\[ 0.8 \times \frac{x}{2} = 2 \quad \text{(since 2 moles of ZnS produce 2 moles of ZnO)} \]

### Step 6: Solve for x
Rearranging the equation:
\[ 0.8 \times \frac{x}{2} = 2 \]
\[ 0.4x = 2 \]
\[ x = \frac{2}{0.4} = 5 \]

### Conclusion
Thus, the number of moles of ZnS required to produce 2 moles of Zn is **5 moles**.

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