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%.
