To determine how many moles of [tex]\( \text{SnO}_2 \)[/tex] are needed to produce 500.0 grams of Sn, we will follow these steps:
1. Calculate the molar mass of tin (Sn):
The molar mass of Sn is approximately 118.71 g/mol.
2. Determine the number of moles of tin (Sn) we have:
Given that we have 500.0 grams of tin, we can use the formula for the number of moles:
[tex]\[
\text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}}
\][/tex]
Plugging in the values:
[tex]\[
\text{Number of moles of Sn} = \frac{500.0 \text{ grams}}{118.71 \text{ g/mol}}
\][/tex]
3. Perform the division to find the number of moles of Sn:
[tex]\[
\text{Number of moles of Sn} \approx 4.211945
\][/tex]
4. Relate the moles of Sn produced to the moles of [tex]\( \text{SnO}_2 \)[/tex] used:
According to the balanced chemical equation:
[tex]\[
\text{SnO}_2 + 2\text{H}_2 \rightarrow \text{Sn} + 2\text{H}_2\text{O}
\][/tex]
It shows that 1 mole of [tex]\( \text{SnO}_2 \)[/tex] produces 1 mole of Sn.
5. Therefore, the moles of [tex]\( \text{SnO}_2 \)[/tex] needed:
Since the moles of [tex]\( \text{SnO}_2 \)[/tex] required are the same as the moles of Sn produced, we have:
[tex]\[
\text{Number of moles of } \text{SnO}_2 = 4.211945
\][/tex]
From the calculations and the chemical reaction, we can conclude that the number of moles of [tex]\( \text{SnO}_2 \)[/tex] needed to produce 500.0 grams of Sn is approximately [tex]\( 4.211945 \)[/tex].
Thus, the correct answer is:
B. [tex]\( 4.21 \)[/tex]
