To solve the problem, we need to identify the limiting reactant and calculate the amount of carbon dioxide ($CO_2$) produced. Let’s go step by step:

Step 1: Write the balanced chemical equation

The reaction between sodium carbonate ($Na_2CO_3$) and hydrochloric acid ($HCl$) is:

$Na_2CO_3 + 2HCl \rightarrow 2NaCl + H_2O + CO_2$

From the equation, 1 mole of sodium carbonate reacts with 2 moles of hydrochloric acid to produce 1 mole of $CO_2$.

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Step 2: Calculate moles of sodium carbonate

The mass of sodium carbonate is $3.471 \, \text{g}$, and its molar mass is $105.99 \, \text{g/mol}$. Using the formula:

$\text{Moles of } Na_2CO_3 = \frac{\text{Mass}}{\text{Molar mass}}$

$\text{Moles of } Na_2CO_3 = \frac{3.471}{105.99} \approx 0.0327 \, \text{moles}$

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Step 3: Calculate moles of hydrochloric acid

The volume of hydrochloric acid is $16.90 \, \text{mL}$ or $0.01690 \, \text{L}$, and its molarity is $0.55 \, \text{M}$. Using the formula:

$\text{Moles of } HCl = \text{Molarity} \times \text{Volume (L)}$

$\text{Moles of } HCl = 0.55 \times 0.01690 \approx 0.00930 \, \text{moles}$

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Step 4: Determine the limiting reactant

From the balanced equation:

• 1 mole of $Na_2CO_3$ reacts with 2 moles of $HCl$.
• Therefore, $0.0327 \, \text{moles of } Na_2CO_3$ requires $2 \times 0.0327 = 0.0654 \, \text{moles of } HCl$.

However, we only have $0.00930 \, \text{moles of } HCl$. Hence, hydrochloric acid is the limiting reactant.

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Step 5: Calculate moles of $CO_2$ produced

From the balanced equation, 2 moles of $HCl$ produce 1 mole of $CO_2$. Therefore:

$\text{Moles of } CO_2 = \frac{\text{Moles of } HCl}{2}$

$\text{Moles of } CO_2 = \frac{0.00930}{2} \approx 0.00465 \, \text{moles}$

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Step 6: Calculate the mass of $CO_2$ produced

The molar mass of $CO_2$ is $44.01 \, \text{g/mol}$. Using the formula:

$\text{Mass of } CO_2 = \text{Moles of } CO_2 \times \text{Molar mass}$

$\text{Mass of } CO_2 = 0.00465 \times 44.01 \approx 0.2046 \, \text{g}$

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Final Answer:

• Limiting reactant: Hydrochloric acid
• Mass of $CO_2$: $0.2046 \, \text{g}$

Would you like a detailed explanation of any step or additional examples?

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Related Questions:

1. How would the results change if more hydrochloric acid were added?
2. What is the theoretical yield of sodium chloride ($NaCl$) in this reaction?
3. How does the reaction progress if hydrochloric acid concentration is reduced?
4. What volume of $CO_2$ gas is produced at STP?
5. Can a different acid be used to achieve the same reaction?

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Tip:

Always confirm the limiting reactant before calculating the product yield to avoid over