`50 g` of ZnS are strongly heated in air to effect partial oxidation and the resultant mass weighed `44 g`. What is the ratio of ZnO to ZnS in the resultant mixture :

Options

A. `13.5 : 30.5`
B. `27 : 12.58`
C. `27 : 15.31`
D. `30.52 : 13.48`

Answer

To solve the problem, we need to determine the ratio of zinc oxide (ZnO) to zinc sulfide (ZnS) in the resultant mixture after the partial oxidation of ZnS. Here’s a step-by-step solution:

### Step 1: Identify the Molar Masses
First, we need to know the molar masses of ZnS and ZnO:
- Molar mass of ZnS = 97.4 g/mol
- Molar mass of ZnO = 81.4 g/mol

### Step 2: Set Up the Problem
Let \( x \) grams of ZnS react during the heating process. Then, the remaining unreacted ZnS would be:
\[ 50 - x \text{ grams} \]

### Step 3: Calculate the Mass of ZnO Formed
The mass of ZnO formed from \( x \) grams of ZnS can be calculated using the stoichiometric relationship:
\[ \text{Mass of ZnO} = \left( \frac{81.4}{97.4} \right) x \]

### Step 4: Write the Total Mass Equation
According to the problem, the total mass after the reaction is 44 grams. Therefore, we can set up the following equation:
\[ (50 - x) + \left( \frac{81.4}{97.4} \right) x = 44 \]

### Step 5: Solve for \( x \)
Rearranging the equation gives us:
\[ 50 - x + \left( \frac{81.4}{97.4} \right) x = 44 \]
\[ 50 - 44 = x - \left( \frac{81.4}{97.4} \right) x \]
\[ 6 = x \left( 1 - \frac{81.4}{97.4} \right) \]

Calculating the fraction:
\[ 1 - \frac{81.4}{97.4} = \frac{97.4 - 81.4}{97.4} = \frac{16}{97.4} \]

Thus, we have:
\[ 6 = x \left( \frac{16}{97.4} \right) \]
\[ x = 6 \cdot \frac{97.4}{16} \]
\[ x = 36.48 \text{ grams} \]

### Step 6: Calculate the Mass of Unreacted ZnS
Now, we can find the mass of unreacted ZnS:
\[ \text{Mass of unreacted ZnS} = 50 - x = 50 - 36.48 = 13.52 \text{ grams} \]

### Step 7: Calculate the Mass of ZnO Formed
Next, we can find the mass of ZnO formed:
\[ \text{Mass of ZnO} = 44 - \text{Mass of unreacted ZnS} = 44 - 13.52 = 30.48 \text{ grams} \]

### Step 8: Calculate the Ratio of ZnO to ZnS
Finally, we can find the ratio of ZnO to ZnS:
\[ \text{Ratio of ZnO to ZnS} = \frac{\text{Mass of ZnO}}{\text{Mass of unreacted ZnS}} = \frac{30.48}{13.52} \]

### Step 9: Simplify the Ratio
Calculating the ratio:
\[ \text{Ratio} = \frac{30.48}{13.52} \approx 2.25 \]

### Final Answer
The ratio of ZnO to ZnS in the resultant mixture is approximately 2.25:1.

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