Problem 74 - General Chemistry: Principles and Modern Applications

Question

Show that, in principle, \(\mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{aq})\) can be converted almost completely to NaOH(aq) by the reaction \(\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{s})+\mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{aq}) \longrightarrow\) $$ \mathrm{CaCO}_{3}(\mathrm{s})+2 \mathrm{NaOH}(\mathrm{aq}) $$

Step-by-Step Solution

Answer

Yes, in theory and ideally, Na2CO3 can be converted almost entirely into NaOH using the reaction \(\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{s}) + \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{aq}) \longrightarrow \mathrm{CaCO}_{3}(\mathrm{s}) + 2 \mathrm{NaOH}(\mathrm{aq})\), assuming there's sufficient Ca(OH)2 available.

Step 1: Recognize the Reaction Type

This is a double replacement (also known as metathesis) chemical reaction where two compounds exchange ions or bonds to form different compounds. Specifically, Na2CO3 is reacting with Ca(OH)2 to form CaCO3 and NaOH.

Step 2: Analyze the Stoichiometry

Looking at the balanced chemical equation, it can be seen that 1 mole of Na2CO3 reacts with 1 mole of Ca(OH)2 to produce 1 mole of CaCO3 and 2 moles of NaOH. Here, we must note that Na2CO3 is converted almost completely to NaOH, which means Na2CO3 is the limiting reagent in this reaction.

Step 3: Understand the Reaction Conditions

Assuming we have enough Ca(OH)2, then every Na2CO3 molecule will react and will form two NaOH molecules for every one Na2CO3 molecule.

Step 4: Result

Therefore, in principle, Na2CO3(aq) can be converted almost completely to NaOH(aq) by the reaction with Ca(OH)2(s). The Na2CO3 will all be used up, resulting in 2 times as many moles of NaOH, which is the final product of the reaction.

Key Concepts

Stoichiometry

Stoichiometry is a foundational concept in chemistry that deals with the calculation of reactants and products in a chemical reaction. It's all about the numbers and ratios. In the chemical equation provided, \( \mathrm{Ca} (\mathrm{OH})_{2}(\mathrm{s}) + \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{aq}) \rightarrow \mathrm{CaCO}_{3}(\mathrm{s}) + 2 \mathrm{NaOH}(\mathrm{aq}) \), we observe that:

• 1 mole of \( \mathrm{Ca} (\mathrm{OH})_{2} \) reacts with 1 mole of \( \mathrm{Na}_{2} \mathrm{CO}_{3} \).
• This results in the formation of 1 mole of \( \mathrm{CaCO}_{3} \) and 2 moles of \( \mathrm{NaOH} \).

Stoichiometry allows us to determine how much of each substance is consumed and produced. By understanding these proportions, we predict the amount of products formed from given amounts of reactants. This balance is critical in both laboratory settings and industrial chemical manufacturing.
Therefore, it's essential to balance the chemical equations as this provides the correct stoichiometric coefficients, ensuring the law of conservation of mass is upheld.

Limiting Reagent

The concept of the limiting reagent is crucial in chemical reactions. The limiting reagent is the reactant that gets completely consumed first, stopping the reaction from continuing. In our example, \( \mathrm{Na}_{2} \mathrm{CO}_{3} \) is the limiting reagent. This means that its quantity determines the maximum amount of product that can be formed.
To identify the limiting reagent:

• Calculate the moles of each reactant based on the initial conditions.
• Compare their stoichiometric ratios.
• The reactant that produces the least amount of product is the limiting reagent.

In the given reaction, if we have an excess of \( \mathrm{Ca} (\mathrm{OH})_{2} \), it ensures that all the \( \mathrm{Na}_{2} \mathrm{CO}_{3} \) can react, supporting the conclusion that \( \mathrm{Na}_{2} \mathrm{CO}_{3} \) is used up entirely, thus confirming it as the limiting reagent. Understanding which reactant limits the reaction is essential in yield prediction and optimizing reaction conditions.

Metathesis Reaction

A metathesis reaction, also known as a double replacement reaction, occurs when two compounds exchange partners to form two new compounds. These reactions are often seen in ionic compounds in aqueous solutions.
In our example, \( \mathrm{Ca} (\mathrm{OH})_{2}(\mathrm{s}) + \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{aq}) \rightarrow \mathrm{CaCO}_{3}(\mathrm{s}) + 2 \mathrm{NaOH}(\mathrm{aq}) \), each compound swaps its partners:

• \( \mathrm{Na}_{2} \mathrm{CO}_{3} \) donates its carbonate ion \( \mathrm{CO}_{3}^{2-} \) to calcium, forming \( \mathrm{CaCO}_{3} \).
• \( \mathrm{Ca} (\mathrm{OH})_{2} \) supplies hydroxide ions \( \mathrm{OH}^{-} \) to sodium, resulting in \( \mathrm{NaOH} \).

Metathesis reactions are common in many applications, like water softening and chemical synthesis. They are primarily driven by the formation of a stable product, such as a solid precipitate (\( \mathrm{CaCO}_{3} \) in this case), which removes certain ions from the solution, facilitating the reaction's progress.