Question

Sodium bicarbonate on heating decomposes to form sodium carbonate, \(\mathrm{CO}_{2}\) and water. If \(0.2\) moles of sodium bicarbonate is completely decomposed, how many moles of sodium carbonate is formed? (a) \(0.1\) (b) \(0.2\) (c) \(0.05\) (d) \(0.025\)

Short answer

0.1 moles of sodium carbonate is formed. Option (a).

Step-by-step solution

Understand the Chemical Reaction

The decomposition reaction of sodium bicarbonate (NaHCO₃) is: \[ \text{2 NaHCO}_3(s) \rightarrow \text{Na}_2\text{CO}_3(s) + \text{CO}_2(g) + \text{H}_2\text{O}(g) \] This tells us that 2 moles of sodium bicarbonate decomposes to form 1 mole of sodium carbonate.

Set Up the Mole Ratio

From the balanced equation, the mole ratio of sodium bicarbonate (NaHCO₃) to sodium carbonate (Na₂CO₃) is 2:1. This means 2 moles of NaHCO₃ are needed to produce 1 mole of Na₂CO₃.

Calculate the Moles of Sodium Carbonate Formed

Given that 0.2 moles of sodium bicarbonate is completely decomposed, we can find the moles of sodium carbonate produced. Using the 2:1 ratio: \( \text{Moles of Na}_2\text{CO}_3 = \frac{0.2\ moles\ of\ NaHCO_3}{2} = 0.1\ moles \).

Verify the Solution

Verify that the calculated moles of sodium carbonate matches one of the given options. We calculated 0.1 moles of sodium carbonate, which matches option (a).

Key concepts

Mole Ratio

In chemistry, the concept of mole ratio is key to understanding how substances interact in a chemical reaction. A mole ratio is derived from the coefficients of a balanced chemical equation, showing us the proportional relationship between reactants and products.
For the decomposition of sodium bicarbonate, the balanced chemical equation is:

• \( 2 \ \text{NaHCO}_3 (s) \rightarrow \text{Na}_2\text{CO}_3 (s) + \text{CO}_2 (g) + \text{H}_2\text{O} (g) \)

This equation tells us that two moles of sodium bicarbonate decompose to form one mole of sodium carbonate. Hence, the mole ratio of sodium bicarbonate to sodium carbonate in this reaction is 2:1.
Understanding this ratio is crucial because it helps us calculate the number of moles of products formed when given a certain amount of reactants. In our example, if you begin with 0.2 moles of sodium bicarbonate, a 2:1 mole ratio means that half of 0.2 moles will form as sodium carbonate, resulting in 0.1 moles of sodium carbonate.

Sodium Bicarbonate Decomposition

When sodium bicarbonate, commonly known as baking soda, undergoes decomposition, it breaks down into three distinct products: sodium carbonate, carbon dioxide, and water. This type of reaction is known as a decomposition reaction because a single compound divides into multiple, simpler substances.
In chemical terms, the decomposition of sodium bicarbonate can be represented by the following equation:

• \( 2 \ \text{NaHCO}_3 (s) \rightarrow \text{Na}_2\text{CO}_3 (s) + \text{CO}_2 (g) + \text{H}_2\text{O} (g) \)

Upon heating, the sodium bicarbonate loses carbon dioxide and water, transforming into sodium carbonate. This process is not only fascinating in the context of chemistry but also has practical applications, such as in baking where the release of gas causes dough to rise.
The decomposition process is efficient, as the balanced chemical equation demonstrates the precise exchange between reactants and products. This efficiency is what makes understanding the mole ratio so important.

Sodium Carbonate Formation

The end product of the sodium bicarbonate decomposition reaction includes sodium carbonate, which is a vital industrial chemical widely used in various applications such as glass manufacturing and as a cleaning agent. The conversion from sodium bicarbonate to sodium carbonate can be effectively tracked using a balanced chemical equation.
As per our reaction equation for sodium bicarbonate decomposition:

• \( 2 \ \text{NaHCO}_3 (s) \rightarrow \text{Na}_2\text{CO}_3 (s) + \text{CO}_2 (g) + \text{H}_2\text{O} (g) \)

The formation of sodium carbonate arises directly from the breakdown of sodium bicarbonate. In this reaction, two moles of sodium bicarbonate yield one mole of sodium carbonate, effectively reducing the oxides and hydrogens present.
This transformation not only produces sodium carbonate but also contributes to the release of carbon dioxide and water vapor, which may be observed as effervescence or bubbling during the reaction. Understanding the formation of sodium carbonate further emphasizes the importance of balancing chemical equations and relying on mole ratios to predict and calculate the results of reactions.