The law of conservation of mass states that matter is neither created nor destroyed in a chemical reaction. Therefore, the total mass of the reactants must equal the total mass of the products.
In your example, you have:
- Start with 12.7 g of Cu (copper)
- Start with 3.2 g of S (sulfur)
The total mass of the reactants is:
\[ 12.7 , \text{g} + 3.2 , \text{g} = 15.9 , \text{g} \]
If Cu\(_2\)S (copper(I) sulfide) is the only product formed, the mass of Cu\(_2\)S produced must also be 15.9 g, in accordance with the law of conservation of mass.
To verify the calculation and stoichiometry, we can calculate the molar masses and see if the amount of reactants given can indeed form Cu\(_2\)S:
- The molar mass of Cu is approximately 63.55 g/mol.
- The molar mass of S is approximately 32.07 g/mol.
- The molar mass of Cu\(_2\)S can be calculated as follows:
\[ \text{Molar mass of Cu}_2\text{S} = 2 \times 63.55 , \text{g/mol} + 32.07 , \text{g/mol} = 159.17 , \text{g/mol} \]
Next, we can calculate the moles of Cu and S:
- Moles of Cu:
\[ \text{Moles of Cu} = \frac{12.7 , \text{g}}{63.55 , \text{g/mol}} \approx 0.199 , \text{mol} \]
- Moles of S:
\[ \text{Moles of S} = \frac{3.2 , \text{g}}{32.07 , \text{g/mol}} \approx 0.100 , \text{mol} \]
The balanced chemical equation for the formation of Cu\(_2\)S is:
\[ 2 , \text{Cu} + \text{S} \rightarrow \text{Cu}_2\text{S} \]
From this balanced equation, we can see that 2 moles of Cu are required for every 1 mole of S. Given that you have approximately 0.199 moles of Cu and 0.100 moles of S, the limiting reagent will be sulfur (S), as it provides fewer moles relative to the balanced equation ratio.
Thus, using 0.100 moles of S will require:
\[ 2 \times 0.100 , \text{mol} , \text{Cu} = 0.200 , \text{mol} , \text{Cu} \]
However, you only have approximately 0.199 moles of Cu available. This confirms that S limits the reaction.
When the reaction goes to completion, you will produce:
\[ 0.100 , \text{mol} , \text{Cu}_2\text{S} \]
Converting moles of Cu\(_2\)S back to grams gives:
\[ 0.100 , \text{mol} \times 159.17 , \text{g/mol} = 15.92 , \text{g} \]
Thus, the total mass of the products, which is approximately 15.9 g, aligns with the initial mass of reactants with a minor variation due to rounding.
In conclusion, the total mass of the product (Cu\(_2\)S) produced is indeed consistent with the total mass of the reactants, confirming the conservation of mass in this reaction.
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