Select the correct answer.

Given:
[tex]\[ \text{SnO}_2 + 2 \text{H}_2 \rightarrow \text{Sn} + 2 \text{H}_2\text{O} \][/tex]

Tin oxide reacts with hydrogen to produce tin and water. How many moles of \(\text{SnO}_2\) are needed to produce 500.0 grams of \(\text{Sn}\)?

A. \(1.57\)

B. \(4.21\)

C. \(634.8\)

D. [tex]\(59,350\)[/tex]



Answer :

To determine how many moles of SnO₂ are needed to produce 500.0 grams of tin (Sn), we can follow a structured approach involving stoichiometry and molar mass relationships.

1. Identify the chemical reaction and relevant molar masses:

The provided chemical reaction is:
[tex]\[ SnO_2 + 2 H_2 \rightarrow Sn + 2 H_2O \][/tex]
The relevant molar masses are:
- Molar mass of \(Sn\) (Tin): 118.71 g/mol
- Molar mass of \(SnO_2\) (Tin(IV) oxide): 150.71 g/mol

2. Calculate the number of moles of Tin (Sn):

We are given 500.0 grams of Tin (Sn). To find the moles of Sn, we use the formula:
[tex]\[ \text{moles of Sn} = \frac{\text{mass of Sn}}{\text{molar mass of Sn}} \][/tex]
Substituting the given values:
[tex]\[ \text{moles of Sn} = \frac{500.0 \text{ g}}{118.71 \text{ g/mol}} \approx 4.21 \text{ moles} \][/tex]

3. Relate moles of Sn to moles of SnO₂:

From the balanced chemical equation, we see that 1 mole of Sn is produced from 1 mole of SnO₂ (the stoichiometric coefficients are 1:1 for SnO₂ to Sn):
[tex]\[ 1 \text{ mole of SnO}_2 \rightarrow 1 \text{ mole of Sn} \][/tex]
Therefore, the moles of SnO₂ needed to produce 4.21 moles of Sn are the same as the moles of Sn:
[tex]\[ \text{moles of SnO}_2 = 4.21 \text{ moles} \][/tex]

So, the number of moles of \( SnO_2 \) needed to produce 500.0 grams of \( Sn \) is \( 4.21 \). The correct answer is:
[tex]\[ \boxed{4.21} \][/tex]