Question
chemistry problem calculating mass of carbon dioxide from methane reaction
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GPT-4o mini
To calculate the mass of carbon dioxide produced from the reaction of methane, we can use the balanced chemical equation for the combustion of methane. The balanced equation is:
\[ \text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(g) \]
From this equation, we can see that 1 mole of methane (CH₄) produces 1 mole of carbon dioxide (CO₂) when it reacts completely with oxygen (O₂).
### Step 1: Determine the moles of CH₄ used
If you know the mass of methane you have, you can convert that mass to moles using its molar mass. The molar mass of methane (CH₄) is approximately 16.04 g/mol.
\[ \text{Moles of CH}_4 = \frac{\text{Mass of CH}_4}{\text{Molar mass of CH}_4} = \frac{\text{Mass of CH}_4}{16.04 \, \text{g/mol}} \]
### Step 2: Calculate the moles of CO₂ produced
From the balanced equation, we see that 1 mole of CH₄ produces 1 mole of CO₂. Thus, the moles of CO₂ produced will be equal to the moles of CH₄ reacted.
### Step 3: Convert moles of CO₂ to mass
Next, convert moles of CO₂ to mass using its molar mass. The molar mass of carbon dioxide (CO₂) is approximately 44.01 g/mol.
\[ \text{Mass of CO}_2 = \text{Moles of CO}_2 \times \text{Molar mass of CO}_2 = \text{Moles of CO}_2 \times 44.01 \, \text{g/mol} \]
### Example Calculation
Let’s say you start with 32.08 g of methane (which is 2 moles of CH₄).
1. Calculate moles of CH₄:
\[
\text{Moles of CH}_4 = \frac{32.08 \, \text{g}}{16.04 \, \text{g/mol}} \approx 2 \, \text{mol}
\]
2. Moles of CO₂ produced (equal to moles of CH₄ reacted):
\[
\text{Moles of CO}_2 = 2 \, \text{mol}
\]
3. Convert moles of CO₂ to mass:
\[
\text{Mass of CO}_2 = 2 \, \text{mol} \times 44.01 \, \text{g/mol} \approx 88.02 \, \text{g}
\]
### Conclusion
Thus, if you react 32.08 g of methane, you will produce approximately **88.02 g of carbon dioxide**. You can replace the mass of methane in the calculation with any starting mass you have to find the corresponding mass of carbon dioxide produced.
\[ \text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(g) \]
From this equation, we can see that 1 mole of methane (CH₄) produces 1 mole of carbon dioxide (CO₂) when it reacts completely with oxygen (O₂).
### Step 1: Determine the moles of CH₄ used
If you know the mass of methane you have, you can convert that mass to moles using its molar mass. The molar mass of methane (CH₄) is approximately 16.04 g/mol.
\[ \text{Moles of CH}_4 = \frac{\text{Mass of CH}_4}{\text{Molar mass of CH}_4} = \frac{\text{Mass of CH}_4}{16.04 \, \text{g/mol}} \]
### Step 2: Calculate the moles of CO₂ produced
From the balanced equation, we see that 1 mole of CH₄ produces 1 mole of CO₂. Thus, the moles of CO₂ produced will be equal to the moles of CH₄ reacted.
### Step 3: Convert moles of CO₂ to mass
Next, convert moles of CO₂ to mass using its molar mass. The molar mass of carbon dioxide (CO₂) is approximately 44.01 g/mol.
\[ \text{Mass of CO}_2 = \text{Moles of CO}_2 \times \text{Molar mass of CO}_2 = \text{Moles of CO}_2 \times 44.01 \, \text{g/mol} \]
### Example Calculation
Let’s say you start with 32.08 g of methane (which is 2 moles of CH₄).
1. Calculate moles of CH₄:
\[
\text{Moles of CH}_4 = \frac{32.08 \, \text{g}}{16.04 \, \text{g/mol}} \approx 2 \, \text{mol}
\]
2. Moles of CO₂ produced (equal to moles of CH₄ reacted):
\[
\text{Moles of CO}_2 = 2 \, \text{mol}
\]
3. Convert moles of CO₂ to mass:
\[
\text{Mass of CO}_2 = 2 \, \text{mol} \times 44.01 \, \text{g/mol} \approx 88.02 \, \text{g}
\]
### Conclusion
Thus, if you react 32.08 g of methane, you will produce approximately **88.02 g of carbon dioxide**. You can replace the mass of methane in the calculation with any starting mass you have to find the corresponding mass of carbon dioxide produced.
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