Question
Consider the combustion of carbon monoxide (CO) in oxygen gas:
2CO (g) + O2 (g) = 2CO2(g)
In this reaction, 10.8 moles of carbon dioxide (CO2) were produced. Calculate the number of moles of carbon dioxide (CO2) and oxygen (O2) used in this reaction to produce such number of moles of carbon dioxide.
2CO (g) + O2 (g) = 2CO2(g)
In this reaction, 10.8 moles of carbon dioxide (CO2) were produced. Calculate the number of moles of carbon dioxide (CO2) and oxygen (O2) used in this reaction to produce such number of moles of carbon dioxide.
Answers
GPT-4o mini
To solve this problem, we can use the stoichiometry of the balanced chemical equation for the combustion of carbon monoxide (CO):
\[
2 CO (g) + O_2 (g) \rightarrow 2 CO_2 (g)
\]
### Step 1: Determine Moles of CO2 Produced
From the balanced equation, we see that 2 moles of carbon monoxide (CO) produce 2 moles of carbon dioxide (CO2). This establishes a 1:1 ratio between CO and CO2. Therefore, if we have produced 10.8 moles of CO2:
\[
\text{Moles of CO} = \text{Moles of CO2} = 10.8 \text{ moles}
\]
### Step 2: Calculate Moles of O2 Used
According to the balanced chemical equation, for every 2 moles of CO that react, 1 mole of O2 is consumed. Thus, the ratio between CO and O2 is 2:1.
Since we have determined that 10.8 moles of CO were used to produce 10.8 moles of CO2, we can find the moles of O2 consumed using the following:
\[
\text{Moles of O2} = \frac{\text{Moles of CO}}{2}
\]
Substituting the value of moles of CO into the equation:
\[
\text{Moles of O2} = \frac{10.8}{2} = 5.4 \text{ moles}
\]
### Summary of Results
- Moles of CO produced: **10.8 moles**
- Moles of O2 used: **5.4 moles**
Thus, to produce 10.8 moles of carbon dioxide (CO2), **10.8 moles of carbon monoxide (CO)** and **5.4 moles of oxygen (O2)** were used in the reaction.
\[
2 CO (g) + O_2 (g) \rightarrow 2 CO_2 (g)
\]
### Step 1: Determine Moles of CO2 Produced
From the balanced equation, we see that 2 moles of carbon monoxide (CO) produce 2 moles of carbon dioxide (CO2). This establishes a 1:1 ratio between CO and CO2. Therefore, if we have produced 10.8 moles of CO2:
\[
\text{Moles of CO} = \text{Moles of CO2} = 10.8 \text{ moles}
\]
### Step 2: Calculate Moles of O2 Used
According to the balanced chemical equation, for every 2 moles of CO that react, 1 mole of O2 is consumed. Thus, the ratio between CO and O2 is 2:1.
Since we have determined that 10.8 moles of CO were used to produce 10.8 moles of CO2, we can find the moles of O2 consumed using the following:
\[
\text{Moles of O2} = \frac{\text{Moles of CO}}{2}
\]
Substituting the value of moles of CO into the equation:
\[
\text{Moles of O2} = \frac{10.8}{2} = 5.4 \text{ moles}
\]
### Summary of Results
- Moles of CO produced: **10.8 moles**
- Moles of O2 used: **5.4 moles**
Thus, to produce 10.8 moles of carbon dioxide (CO2), **10.8 moles of carbon monoxide (CO)** and **5.4 moles of oxygen (O2)** were used in the reaction.