To solve the question of how many moles of [tex]\( CO_2 \)[/tex] form when 22.4 liters of [tex]\( CO \)[/tex] react with oxygen at STP, we need to take several steps. Let's go through this process in detail:
1. Understand the balanced chemical equation:
[tex]\[ 2 CO (g) + O_2 (g) \rightarrow 2 CO_2 (g) \][/tex]
This equation tells us that 2 moles of [tex]\( CO \)[/tex] react with 1 mole of [tex]\( O_2 \)[/tex] to produce 2 moles of [tex]\( CO_2 \)[/tex].
2. Determine the volume occupied by 1 mole of gas at STP:
At STP (Standard Temperature and Pressure), 1 mole of any ideal gas occupies 22.4 liters.
3. Calculate the number of moles of [tex]\( CO \)[/tex]:
We are given that 22.4 liters of [tex]\( CO \)[/tex] are available. Since 22.4 liters is the volume occupied by 1 mole of a gas at STP, we can calculate the moles of [tex]\( CO \)[/tex] as follows:
[tex]\[
\text{Number of moles of } CO = \frac{\text{Volume of } CO}{22.4 \, \text{liters/mole}}
\][/tex]
Substituting the given volume:
[tex]\[
\text{Number of moles of } CO = \frac{22.4 \, \text{liters}}{22.4 \, \text{liters/mole}} = 1.0 \, \text{moles}
\][/tex]
4. Use the stoichiometric relationship from the balanced equation:
According to the balanced equation, 2 moles of [tex]\( CO \)[/tex] produce 2 moles of [tex]\( CO_2 \)[/tex]. This means the molar ratio of [tex]\( CO \)[/tex] to [tex]\( CO_2 \)[/tex] is 1:1. Therefore, 1 mole of [tex]\( CO \)[/tex] will produce 1 mole of [tex]\( CO_2 \)[/tex].
5. Calculate the number of moles of [tex]\( CO_2 \)[/tex] formed:
Since we have 1.0 mole of [tex]\( CO \)[/tex], and the ratio is 1:1, the moles of [tex]\( CO_2 \)[/tex] produced will also be:
[tex]\[
\text{Number of moles of } CO_2 = \text{Number of moles of } CO = 1.0 \, \text{moles}
\][/tex]
So, when 22.4 liters of [tex]\( CO \)[/tex] react with oxygen at STP, 1.0 mole of [tex]\( CO_2 \)[/tex] is formed.
