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4. There are several stages to the production of sulfuric acid in the industry.

(a) Sulfur dioxide is required for the production of sulfuric acid. Sulfur dioxide can be obtained by heating copper sulfide, [tex]$Cu_2S$[/tex], in excess air.

[tex]\[ Cu_2S + O_2 \rightarrow 2 Cu + SO_2 \][/tex]

Calculate the atom economy for the production of sulfur dioxide, [tex]$SO_2$[/tex], in this reaction.

Relative atomic masses:
[tex]\[ Cu = 63.5 \][/tex]

Relative formula masses:
[tex]\[ O_2 = 32.0, \quad Cu_2S = 159.0, \quad SO_2 = 64.0 \][/tex]

Give your answer to two significant figures.



Answer :

GinnyAnswer
To calculate the atom economy for the production of sulfur dioxide ([tex]$SO_2$[/tex]) from the reaction of copper sulfide ([tex]$Cu_2S$[/tex]) with oxygen ([tex]$O_2$[/tex]), you can follow these steps:

1. Write down the balanced chemical equation:
[tex]\[ Cu_2S + O_2 \rightarrow 2Cu + SO_2 \][/tex]

2. Identify the molar masses (relative formula masses) of the reactants and products:
- [tex]$Cu_2S$[/tex] has a molar mass of 159.0 g/mol
- [tex]$O_2$[/tex] has a molar mass of 32.0 g/mol
- [tex]$SO_2$[/tex] has a molar mass of 64.0 g/mol

3. Calculate the total molar mass of the desired product ([tex]$SO_2$[/tex]) produced:
In this reaction, 1 mole of [tex]$Cu_2S$[/tex] produces 1 mole of [tex]$SO_2$[/tex].
- Molar mass of [tex]$SO_2$[/tex]: 64.0 g/mol

4. Calculate the atom economy using the formula:
[tex]\[ \text{Atom Economy} = \left( \frac{\text{Molar mass of desired product}}{\text{Molar mass of all reactants}} \right) \times 100 \][/tex]
Here, we only need to consider the mass of [tex]$Cu_2S$[/tex] as it is the compound from which [tex]$SO_2$[/tex] is derived directly.
[tex]\[ \text{Atom Economy} = \left( \frac{64.0}{159.0} \right) \times 100 \][/tex]

5. Perform the division and multiplication to find the atom economy:
[tex]\[ \text{Atom Economy} = \left( \frac{64.0}{159.0} \right) \times 100 \approx 40.25\% \][/tex]

6. Round the answer to two significant figures:
The atom economy for producing sulfur dioxide is approximately 40%.

Thus, the atom economy for the production of sulfur dioxide ([tex]$SO_2$[/tex]) in this reaction is 40.25%, and when rounded to two significant figures, it is 40%.