Zinc metal reacts with yellow crystals of sulfur in a fiery reaction to produce a white powder of zinc sulfide. A chemist determines that 65.4 g of zinc reacts with 32.1 g of sulfur. How many grams of zinc sulfide could be produced from 36.9 g of zinc metal?

To solve this problem, we need to use the concept of stoichiometry, which is based on the law of conservation of mass and the balanced chemical equation for the reaction between zinc (Zn) and sulfur (S) to form zinc sulfide (ZnS).

### Step 1: Write the Balanced Chemical Equation
The balanced chemical equation for the reaction is:

\[
\text{Zn} + \text{S} \rightarrow \text{ZnS}
\]

This equation shows that 1 mole of zinc reacts with 1 mole of sulfur to produce 1 mole of zinc sulfide.

### Step 2: Calculate Molar Masses
- **Molar mass of zinc (Zn):** \( 65.4 \, \text{g/mol} \)
- **Molar mass of sulfur (S):** \( 32.1 \, \text{g/mol} \)
- **Molar mass of zinc sulfide (ZnS):** \( 65.4 \, \text{g/mol} + 32.1 \, \text{g/mol} = 97.5 \, \text{g/mol} \)

### Step 3: Use Given Data to Determine the Mass Ratio
From the problem, we know that 65.4 g of zinc reacts with 32.1 g of sulfur to produce zinc sulfide. Since the molar masses of zinc and sulfur match the given masses (1:1 molar ratio), the entire mass of zinc and sulfur is converted into zinc sulfide.

\[
\text{Mass of ZnS produced} = 65.4 \, \text{g} + 32.1 \, \text{g} = 97.5 \, \text{g}
\]

### Step 4: Determine How Much ZnS Can Be Produced from 36.9 g of Zinc
Since the reaction produces 97.5 g of ZnS from 65.4 g of Zn, we can set up a proportion to find the mass of ZnS produced from 36.9 g of Zn.

\[
\frac{97.5 \, \text{g ZnS}}{65.4 \, \text{g Zn}} = \frac{x \, \text{g ZnS}}{36.9 \, \text{g Zn}}
\]

Now solve for \( x \):

\[
x = \frac{97.5 \times 36.9}{65.4} \, \text{g ZnS}
\]

\[
x \approx 55.0 \, \text{g ZnS}
\]

### Answer:
Therefore, **55.0 grams of zinc sulfide** can be produced from 36.9 grams of zinc metal.

Would you like further details or have any questions?

Here are some related questions you might explore:
1. What would happen if you used less sulfur than required?
2. How would you determine the limiting reactant in this reaction?
3. How can you calculate the percent yield if only 50 g of ZnS were produced?
4. What mass of sulfur would you need to react completely with 36.9 g of zinc?
5. How does the law of conservation of mass apply to this reaction?

**Tip:** Always verify that your chemical equations are balanced before proceeding with stoichiometric calculations to ensure accurate results.

Discover how to calculate the amount of zinc sulfide produced from the reaction between zinc metal and sulfur using stoichiometry principles. This problem demonstrates key concepts such as mass conservation, molar mass calculations, and proportional reasoning, making it suitable for students in Grades 10-12.

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