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A balanced chemical equation is a fundamental aspect of stoichiometry. It shows the exact numbers of atoms and molecules involved in a chemical reaction. For the decomposition of potassium chlorate (KClO_3) into potassium chloride (KCl) and oxygen gas (O_2), the balanced chemical equation is:

• \[ 2KClO_3 (s) \rightarrow 2KCl (s) + 3O_2 (g) \]

In this equation, the numbers before each chemical formula are the coefficients. They indicate the moles of each substance consumed or produced. Notice that the number of each type of atom remains the same on both sides of the equation, adhering to the law of conservation of mass.
Understanding how to balance equations is crucial for determining the mole ratios needed for stoichiometric calculations, which we use to solve the problem in the exercise. Here, 2 moles of KClO_3 break down to produce 3 moles of O_2.

The Ideal Gas Law helps relate the amount of a gas to its volume, pressure, and temperature. Though not directly calculated here, the concept is central to why gases behave predictably. The law is expressed as follows:

• \[ PV = nRT \]

where:

• \( P \) is the pressure of the gas,
• \( V \) is the volume,
• \( n \) is the number of moles,
• \( R \) is the ideal gas constant, and
• \( T \) is the temperature in Kelvin.

At Standard Temperature and Pressure (STP), the pressure and temperature are set constants: 1 atm for pressure and 273 K for temperature. This standardization lets us use a simplified relationship instead of the full Ideal Gas Law, which provides that 1 mole of any gas at STP occupies 22.4 liters.
This knowledge simplifies our calculations for the number of moles in specific gas volumes.

The mole concept is a cornerstone of chemistry, allowing us to convert between atoms, molecules, and grams, and is central to the exercise's solution. One mole equals Avogadro's number \(6.02 \times 10^{23}\) of molecules. This number lets us transform between microscopic quantities the number of molecules to macroscopic measurable amounts, i.e., grams.
For gases at STP, one mole occupies a fixed volume of 22.4 liters. In the exercise, understanding the relation between moles and volume allows us to determine how much KClO_3 is required to decomposed into a specific volume of O_2. Given that 67.2 liters of oxygen would contain 3 moles (since \( \frac{67.2}{22.4} = 3 \)), we use the mole ratio from the balanced equation to find that 2 moles of KClO_3 are necessary.

Standard Temperature and Pressure (STP) is a reference point used in chemistry to make calculations involving gases easier and more consistent. STP is defined as a temperature of 273 Kelvin (0°C) and a pressure of 1 atmosphere.

• Temperature: 273 K (0°C),
• Pressure: 1 atm

At STP, 1 mole of any ideal gas occupies 22.4 liters. This constant allows us to infer the behavior and quantity of gases without complex calculations. In this particular problem, knowing the volume of O_2 produced at STP enabled us to calculate the moles of gas and then relate that to the moles of KClO_3 required.
These fixed standards simplify calculations as they provide a consistent frame of reference for stoichiometric calculations, making it easier to handle varying gas quantities and reactions.