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

(a) 0.1 moles of sodium carbonate is formed.

Step-by-step solution

Write the Chemical Equation

The decomposition reaction of sodium bicarbonate (NaHCO₃) is: \[ 2\mathrm{NaHCO}_{3} \rightarrow \mathrm{Na}_{2}\mathrm{CO}_{3} + \mathrm{CO}_{2} + \mathrm{H}_{2}\mathrm{O} \] This equation shows that 2 moles of sodium bicarbonate decompose to produce 1 mole of sodium carbonate.

Analyze the Mole Ratio

From the balanced chemical equation, the mole ratio of sodium bicarbonate (NaHCO₃) to sodium carbonate (Na₂CO₃) is 2:1. This means for every 2 moles of sodium bicarbonate decomposed, 1 mole of sodium carbonate is formed.

Calculate Moles of Sodium Carbonate

Given 0.2 moles of sodium bicarbonate, use the mole ratio from Step 2 to calculate sodium carbonate produced: \[ \text{Moles of } \mathrm{Na}_{2}\mathrm{CO}_{3} = \frac{0.2 \text{ moles of } \mathrm{NaHCO}_{3}}{2} = 0.1 \text{ moles} \] This means 0.1 moles of sodium carbonate is formed from the complete decomposition of 0.2 moles of sodium bicarbonate.

Key concepts

Stoichiometry

Stoichiometry is like a recipe for chemical reactions. When cooking a meal, you need certain amounts of ingredients to make the perfect dish. Similarly, in chemistry, stoichiometry helps us understand the quantitative relationship between reactants and products. It tells us how much of each substance is consumed or produced in a chemical reaction.
In our exercise, stoichiometry allows us to calculate how many moles of sodium carbonate are formed when sodium bicarbonate decomposes. It's about using the balanced chemical equation to predict the outcome precisely. This concept ensures we're not just randomly mixing chemicals but are following a calculated plan to achieve the desired products.

Mole Ratio

The mole ratio is a crucial concept that emerges from the balanced chemical equation. It's essentially a guide that shows the proportion of reactants needed and the amount of products formed.
In the decomposition of sodium bicarbonate, the balanced chemical equation reveals a mole ratio of 2:1 between sodium bicarbonate and sodium carbonate. This means that for every 2 moles of sodium bicarbonate that break down, 1 mole of sodium carbonate is produced.

• This ratio is used to convert moles of one substance into moles of another in a chemical reaction.
• Mole ratios ensure that the law of conservation of mass is adhered to, as they represent the exact number of molecules involved.

Understanding mole ratios is essential because it helps achieve precise results in chemical calculations, like determining the moles of sodium carbonate from given moles of sodium bicarbonate.

Balanced Chemical Equation

A balanced chemical equation is fundamental in stoichiometry. This equation illustrates the relationship between reactants and products in a chemical reaction. For a chemical equation to be balanced, it must reflect the law of conservation of mass, meaning the number of atoms of each element is the same on both sides of the equation.
In our exercise, the balanced equation for the decomposition of sodium bicarbonate is:\[ 2\mathrm{NaHCO}_{3} \rightarrow \mathrm{Na}_{2}\mathrm{CO}_{3} + \mathrm{CO}_{2} + \mathrm{H}_{2}\mathrm{O} \]
This shows that two molecules of sodium bicarbonate decompose to form one molecule of sodium carbonate, one molecule of carbon dioxide, and one molecule of water. The balanced equation:

• Ensures the conservation of atoms.
• Provides the mole ratio for the reactants and products.
• Acts as a tool for predicting the quantities of different substances in a reaction.

Balanced chemical equations are the groundwork for accurate chemical calculations and are indispensable in predicting reaction outcomes.