How Many Grams Of Sodium Hydrogen Carbonate Decompose To Give 28.7 ML Of Carbon Dioxide Gas At STP? 2NaHCO₃(s) → Na₂CO₃(s) + H₂O(l) + CO₂(g) Explained
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Introduction
Understanding chemical reactions and their quantitative aspects is fundamental in chemistry, especially when dealing with gases produced during reactions. One common reaction involves sodium hydrogen carbonate, also known as baking soda, decomposing to produce carbon dioxide gas. This reaction is not only significant in culinary and industrial applications but also serves as a classic example in stoichiometry calculations.
In this article, we will explore the question: How many grams of sodium hydrogen carbonate (NaHCO₃) decompose to give 28.7 mL of carbon dioxide gas at Standard Temperature and Pressure (STP)? We will walk through the step-by-step process of calculating the required mass, based on the principles of gas laws, molar relationships, and stoichiometry.
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Understanding the Reaction
Let's first review the chemical equation involved:
2NaHCO₃(s) → Na₂CO₃(s) + H₂O(l) + CO₂(g)
This balanced reaction indicates that:
- 2 moles of sodium hydrogen carbonate decompose to produce
- 1 mole of carbon dioxide gas (CO₂),
- along with sodium carbonate (Na₂CO₃) and water (H₂O).
This molar ratio (2:1) is key to determining how much NaHCO₃ is needed to produce a given volume of CO₂ gas.
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Understanding the Volume of Gas at STP
Standard Temperature and Pressure (STP):
- Temperature: 0°C (273.15 K)
- Pressure: 1 atm
At STP, one mole of any ideal gas occupies 22.4 liters (L).
This value allows us to convert between volume and moles of gas:
\[ 1\, \text{mol} \, \text{gas} = 22.4\, \text{L} \]
In our problem, the volume of CO₂ produced is 28.7 milliliters (mL). To work with molar quantities, convert this volume to liters:
\[ 28.7\, \text{mL} = 0.0287\, \text{L} \]
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Calculating Moles of CO₂ Gas Produced
Using the molar volume at STP, the number of moles of CO₂ gas produced is:
\[ \text{Moles of CO}2 = \frac{\text{Volume of CO}2\, (\text{L})}{22.4\, \text{L/mol}} \]
Plugging in the values:
\[ \text{Moles of CO}_2 = \frac{0.0287\, \text{L}}{22.4\, \text{L/mol}} \approx 0.00128\, \text{mol} \]
This is the quantity of CO₂ generated from the decomposition of sodium hydrogen carbonate.
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Relating Moles of NaHCO₃ to CO₂ Produced
From the balanced chemical equation:
\[ 2\, \text{mol NaHCO}3 \rightarrow 1\, \text{mol CO}2 \]
The molar ratio between NaHCO₃ and CO₂ is 2:1. Therefore, the number of moles of NaHCO₃ needed to produce 0.00128 mol of CO₂ is:
\[ \text{Moles of NaHCO}3 = 2 \times \text{Moles of CO}2 = 2 \times 0.00128 = 0.00256\, \text{mol} \]
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Calculating the Mass of Sodium Hydrogen Carbonate
The molar mass of NaHCO₃ is calculated as:
- Sodium (Na): 23.0 g/mol
- Hydrogen (H): 1.0 g/mol
- Carbon (C): 12.0 g/mol
- Oxygen (O): 16.0 g/mol × 3 = 48.0 g/mol
Adding these:
\[ \text{Molar mass of NaHCO}_3 = 23.0 + 1.0 + 12.0 + 48.0 = 84.0\, \text{g/mol} \]
Now, the mass of NaHCO₃ required:
\[ \text{Mass} = \text{Moles} \times \text{Molar mass} = 0.00256 \times 84.0\, \text{g} \approx 0.215\, \text{g} \]
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Final Answer
Approximately 0.215 grams of sodium hydrogen carbonate decompose to produce 28.7 mL of carbon dioxide gas at STP.
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Additional Considerations and Practical Applications
- Significance in Laboratory and Industry
- This calculation is fundamental in laboratory settings where precise gas volumes are required for experiments.
- In industries like baking, understanding the amount of baking soda needed to produce the desired leavening effect involves similar principles.
- Limitations and Assumptions
- The calculations assume ideal gas behavior, which is accurate at STP.
- Real gases may deviate slightly from ideal behavior, but for most practical purposes, the approximation holds.
- The reaction is assumed to go to completion with no side reactions.
- How to Use This Method
- Convert the gas volume to moles using molar volume at STP.
- Use the molar ratio from the balanced equation to find the amount of reactant.
- Convert moles to grams using molar mass.
Summary
In summary, to determine how many grams of sodium hydrogen carbonate decompose to produce a specific volume of carbon dioxide gas at STP, you must:
- Convert the volume to liters.
- Calculate the moles of CO₂ using the molar volume.
- Use the molar ratio from the balanced chemical equation to find moles of NaHCO₃.
- Convert moles of NaHCO₃ to grams using its molar mass.
For the given problem, approximately 0.215 grams of NaHCO₃ are required to produce 28.7 mL of CO₂ gas at STP.
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By mastering these calculations, students and professionals can accurately predict gas volumes and required reactant amounts, vital for laboratory experiments, industrial processes, and understanding chemical reactions involving gases.
