How Many Grams Of Sodium Hydrogen Carbonate Decompose To Give 25.0 ML Of Carbon Dioxide Gas At STP? 2NaHCO3(s)Na2CO3(s)+H2O(l)+CO2(g)
Understanding the relationship between chemical reactions and the amount of gases produced is fundamental in chemistry. Specifically, determining how many grams of sodium hydrogen carbonate (commonly known as baking soda) decompose to produce a specific volume of carbon dioxide (CO₂) at standard temperature and pressure (STP) is a common problem that demonstrates stoichiometry in action. In this article, we'll explore this question step-by-step, providing a comprehensive guide to calculating the mass of sodium hydrogen carbonate required to generate 25.0 mL of CO₂ at STP, based on the balanced chemical equation:
2NaHCO₃(s) → Na₂CO₃(s) + H₂O(l) + CO₂(g)
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Understanding the Chemical Reaction
Before diving into calculations, it’s essential to understand the reaction involved and the significance of each component.
The Balanced Equation
The chemical equation for the decomposition of sodium hydrogen carbonate is:
2NaHCO₃(s) → Na₂CO₃(s) + H₂O(l) + CO₂(g)
This indicates that:
- 2 moles of sodium hydrogen carbonate decompose to produce
- 1 mole of sodium carbonate,
- 1 mole of water,
- 1 mole of carbon dioxide gas.
Implications for Stoichiometry
From the balanced equation, we see that:
- 2 moles of NaHCO₃ produce 1 mole of CO₂.
- Therefore, the molar ratio of NaHCO₃ to CO₂ is 2:1.
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Calculating the Moles of CO₂ at STP
The first step involves converting the given volume of CO₂ to the number of moles.
Volume of CO₂ at STP
Standard Temperature and Pressure (STP) conditions are:
- Temperature: 0°C (273.15 K)
- Pressure: 1 atm
At STP, 1 mole of any ideal gas occupies 22.4 liters (L).
Given:
- Volume of CO₂ = 25.0 mL
Convert this volume to liters:
25.0 mL × (1 L / 1000 mL) = 0.025 L
Calculate moles of CO₂:
Number of moles = Volume / Molar volume at STP = 0.025 L / 22.4 L/mol ≈ 0.00111607 mol
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Relating Moles of CO₂ to Moles of Sodium Hydrogen Carbonate
Using the molar ratio from the balanced equation:
- 2 mol NaHCO₃ produce 1 mol CO₂.
Therefore:
Number of moles of NaHCO₃ = 2 × (moles of CO₂) = 2 × 0.00111607 mol ≈ 0.00223214 mol
This is the amount of sodium hydrogen carbonate required to produce 25.0 mL of CO₂ at STP.
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Calculating the Mass of Sodium Hydrogen Carbonate Needed
Next, determine how many grams of NaHCO₃ correspond to this number of moles.
Molar Mass of Sodium Hydrogen Carbonate
Calculate the molar mass:
- Sodium (Na): 22.99 g/mol
- Hydrogen (H): 1.008 g/mol
- Carbon (C): 12.01 g/mol
- Oxygen (O): 16.00 g/mol
Sum:
Molar mass of NaHCO₃ = 22.99 + 1.008 + 12.01 + (3 × 16.00)
= 22.99 + 1.008 + 12.01 + 48.00
= 84.008 g/mol
Mass Calculation
Multiply moles by molar mass:
Mass = moles × molar mass ≈ 0.00223214 mol × 84.008 g/mol ≈ 0.1874 g
Therefore, approximately 0.187 grams of sodium hydrogen carbonate decompose to produce 25.0 mL of CO₂ at STP.
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Summary of the Calculation
| Step | Description | Result |
|---------|----------------|---------|
| 1 | Convert volume of CO₂ to moles at STP | 0.001116 mol |
| 2 | Use molar ratio from balanced equation | 0.002232 mol NaHCO₃ |
| 3 | Calculate mass of NaHCO₃ | ≈ 0.187 g |
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Additional Considerations
While the calculation above provides an accurate estimate under ideal conditions, real-world factors such as impurities, reaction completeness, and measurement precision can influence the actual amount needed.
Practical Applications
This calculation is useful in various contexts:
- Baking: understanding how much baking soda to use for a specific leavening effect.
- Laboratory experiments: designing reactions that produce controlled amounts of CO₂.
- Environmental studies: estimating gas emissions from decomposition processes.
Common Mistakes to Avoid
- Forgetting to convert volume to moles at STP.
- Using incorrect molar volume (some resources cite 22.4 L/mol, but at non-STP conditions, volume changes).
- Mixing units or neglecting significant figures.
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Conclusion
In summary, to produce 25.0 mL of carbon dioxide gas at STP via the decomposition of sodium hydrogen carbonate, approximately 0.187 grams of NaHCO₃ are required. This calculation hinges on understanding the balanced chemical equation, converting gas volume to moles, applying stoichiometry, and then translating moles back to mass using molar mass. Mastery of these steps empowers chemists and students alike to predict reaction outcomes accurately, optimize laboratory procedures, and deepen their understanding of chemical principles.
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Final Note
Always remember to verify conditions and units in your calculations, and consider practical factors that may influence real-world reactions. With this methodology, you can confidently determine the amount of sodium hydrogen carbonate needed for various gas production scenarios, making your chemistry experiments more precise and effective.
