Question: Tennantite is an ore of copper with the formula $\mathrm{Cu}_{12}\mathrm{As}_{4}\mathrm{S}_{13}$. How many moles of copper are present in a sample of tennantite with a mass of $2730$ grams? Enter answer: moles Cu
1. **State the problem:** We want to find how many moles of copper (Cu) are in $2730$ grams of tennantite, which has the formula $\mathrm{Cu}_{12}\mathrm{As}_{4}\mathrm{S}_{13}$.
2. **Find the molar mass of tennantite:** Calculate the molar mass by summing the atomic masses of all atoms in the formula. Atomic masses (approximate):
- Cu: $63.55$ g/mol
- As: $74.92$ g/mol
- S: $32.06$ g/mol
3. Calculate molar mass:
$$M = 12 \times 63.55 + 4 \times 74.92 + 13 \times 32.06$$
$$M = 762.6 + 299.68 + 416.78 = 1479.06 \text{ g/mol}$$
4. **Calculate moles of tennantite in $2730$ g:**
$$\text{moles tennantite} = \frac{2730}{1479.06}$$
$$= 1.845 \text{ moles}$$
5. **Calculate moles of copper:** Each mole of tennantite contains $12$ moles of Cu atoms, so
$$\text{moles Cu} = 12 \times 1.845 = 22.14 \text{ moles}$$
**Final answer:** There are approximately $22.14$ moles of copper in $2730$ grams of tennantite.