Sure! To determine the number of moles of [tex]\(\text{CO}_2\)[/tex] formed when 22.4 liters of [tex]\(\text{CO}\)[/tex] react with oxygen at standard temperature and pressure (STP), let's follow these steps:
1. Understanding Standard Temperature and Pressure (STP):
- At STP, 1 mole of any ideal gas occupies 22.4 liters.
2. Given Data:
- Volume of [tex]\(\text{CO}\)[/tex]: 22.4 liters.
- The balanced chemical equation: [tex]\(2 \text{CO} (g) + \text{O}_2 (g) \rightarrow 2 \text{CO}_2 (g)\)[/tex].
3. Calculating Moles of CO:
- Since 1 mole of gas occupies 22.4 liters at STP, the moles of [tex]\(\text{CO}\)[/tex] can be calculated as:
[tex]\[
\frac{\text{Volume of CO}}{\text{Molar volume of gas at STP}} = \frac{22.4 \text{ L}}{22.4 \text{ L/mol}} = 1.0 \text{ mol of CO}
\][/tex]
4. Using the Stoichiometric Ratios:
- According to the balanced equation, the molar ratio of [tex]\(\text{CO}\)[/tex] to [tex]\(\text{CO}_2\)[/tex] is 1:1.
- This means 1 mole of [tex]\(\text{CO}\)[/tex] produces 1 mole of [tex]\(\text{CO}_2\)[/tex].
5. Calculating Moles of CO[tex]\(_2\)[/tex]:
- Since we have 1 mole of [tex]\(\text{CO}\)[/tex]:
[tex]\[
\text{Moles of } \text{CO}_2 = 1.0 \text{ mol of CO} \times \frac{1 \text{ mol of CO}_2}{1 \text{ mol of CO}} = 1.0 \text{ mol of CO}_2
\][/tex]
Hence, when 22.4 liters of [tex]\(\text{CO}\)[/tex] react with oxygen at STP, 1.0 mole of [tex]\(\text{CO}_2\)[/tex] is formed.
