Question

How many moles of potassium chlorate should be decomposed completely to obtain \(67.2\) litres of oxygen at STP? (a) 1 (b) 2 (c) 3 (d) 4

Short answer

2 moles of potassium chlorate are needed.

Step-by-step solution

Understanding the Reaction

The chemical decomposition of potassium chlorate \((KClO_3)\) produces potassium chloride \((KCl)\) and oxygen gas \((O_2)\). The balanced equation for this reaction is:\[2KClO_3(s) \rightarrow 2KCl(s) + 3O_2(g)\]This shows that 2 moles of potassium chlorate produce 3 moles of oxygen gas.

Volume-Mole Conversion

At Standard Temperature and Pressure (STP), 1 mole of any gas occupies \(22.4 \text{ liters}\). To find the moles of oxygen, divide the given volume by the molar volume: \[\text{moles of } O_2 = \frac{67.2 \text{ liters}}{22.4 \text{ liters/mole}} = 3 \text{ moles of } O_2\]

Stoichiometric Calculations

Using the balanced chemical equation, 3 moles of \(O_2\) are produced from 2 moles of \(KClO_3\). Since we have 3 moles of oxygen, the number of moles of \(KClO_3\) required is:\[ \text{moles of } KClO_3 = \frac{2 \text{ moles } KClO_3}{3 \text{ moles } O_2} \times 3 \text{ moles } O_2 = 2 \text{ moles } KClO_3\]

Key concepts

Chemical Reactions

Chemical reactions are processes in which substances, known as reactants, are transformed into new substances called products. This transformation involves the breaking and forming of chemical bonds. The decomposition reaction of potassium chlorate \(KClO_3\) into potassium chloride \(KCl\) and oxygen gas \(O_2\), is an example of a chemical reaction. A balanced chemical equation provides crucial information about the reaction.

• In the equation \[2KClO_3 \rightarrow 2KCl + 3O_2\], each term represents a distinct chemical compound.
• The coefficients in front of each compound indicate the mole ratio, which is the proportion in which the reactants and products participate in the reaction.
• Here, the equation tells us that 2 moles of \(KClO_3\) produce 3 moles of \(O_2\).

This ratio is essential for making stoichiometric calculations.

Moles and Molecules

The concept of "moles" is central to stoichiometry and chemistry as a whole. A mole is a unit of measurement that represents a specific quantity of chemical entities such as atoms, molecules, or ions. One mole is equivalent to Avogadro's number, which is approximately \(6.022 \times 10^{23}\) entities. This allows chemists to count extremely large numbers of small particles in a practical way.

• "Molar mass" refers to the mass of one mole of a given substance and is usually expressed in grams per mole (g/mol).
  
• In the given problem, moles of oxygen are converted using its molar volume at STP.
• For gases, 1 mole typically occupies \(22.4\) liters, providing a convenient conversion factor between volume and moles.

Understanding these principles is essential for calculating the amount of reactants/products in a reaction.

Gas Laws

Gas laws describe the behavior of gases and help in converting between various units like pressure, volume, and temperature. At Standard Temperature and Pressure (STP), gases have defined properties that simplify stoichiometric calculations.

• STP is defined as a temperature of 0°C (273.15 K) and a pressure of 1 atmosphere (atm).
• Under these conditions, 1 mole of any gas occupies \(22.4\) liters of volume. This universal volume simplifies the conversion between volume and moles in gases.
• In this exercise, the gas law concept is used to convert the given volume of oxygen (\(67.2\) liters) to moles.

This understanding is crucial for solving real-world problems involving gas reactions.