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A balanced chemical equation is crucial in understanding chemical reactions because it shows how reactants transform into products while conserving matter. Each side of the equation has the same number of atoms for every element, ensuring mass conservation.
For the reaction under consideration, sulfur dioxide ( \( \text{SO}_2 \) ) reacts with oxygen ( \( \text{O}_2 \) ) to form sulfur trioxide ( \( \text{SO}_3 \) ). The balanced equation for this is: \[ 2 \text{SO}_2(g) + \text{O}_2(g) \rightarrow 2 \text{SO}_3(g) \]
This equation tells us that 2 moles of \( \text{SO}_2 \) react with 1 mole of \( \text{O}_2 \) to produce 2 moles of \( \text{SO}_3 \).

• The subscripts next to the chemical formulas indicate the number of moles for each substance.
• The coefficients ensure that the number of atoms for each element is equal on both sides of the equation. For instance, there are 2 sulfur atoms and 6 oxygen atoms on each side.

Understanding balanced equations helps predict how much product will form and what quantities of reactants are required.

Gas laws, such as the ideal gas law, can help in relating the volumes, pressures, and temperatures of gases in chemical reactions. At constant temperature and pressure, the volume of a gas is directly proportional to the number of moles ( \( V \propto n \) ). This relationship simplifies comparing volumes of gas before and after a reaction, as in this problem.
By understanding that volume changes are due to changes in the number of moles, we can derive valuable insights. The combined gas law helps us state that: \[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \]
In this equation:

• P stands for pressure
• V stands for volume
• T stands for temperature

When temperature and pressure are constant, we find that \( V_1/V_2 = n_1/n_2 \) , meaning the volume ratio equals the mole ratio. This knowledge simplifies predicting how gas mixtures change in reactions, like the formation of sulfur trioxide.

In chemical reactions, the term 'reaction completion' indicates that the reaction proceeds until one of the reactants is entirely consumed, and no further reaction occurs. This is vital to know how the moles of substances change during a reaction.
In the reaction between \( \text{SO}_2 \) and \( \text{O}_2 \) , we're assuming it goes to completion, meaning all of one reactant is used up. For this reaction:

• All initial moles of \( \text{SO}_2 \) are totally consumed.
• Half the initial moles of \( \text{O}_2 \) are consumed.
• The reaction produces moles of \( \text{SO}_3 \) according to the stoichiometry.

By understanding the concept of completion, we see how moles and thus volumes change, affecting calculations for volume ratios. Reaction completion allows us to analyze changes effectively and predict the quantities of remaining substances.

The mole ratio in a balanced chemical equation tells us the proportions of reactants and products involved in the reaction. It forms a fundamental part of stoichiometry, which ensures that chemical equations are balanced.
In the balanced equation: \( 2 \text{SO}_2(g) + \text{O}_2(g) \rightarrow 2 \text{SO}_3(g) \), the mole ratio between \( \text{SO}_2, \text{O}_2, \text{and}\, \text{SO}_3 \) are 2 : 1 : 2 respectively.
This means:

• 2 moles of sulfur dioxide react with 1 mole of oxygen.
• This ratio dictates how much \( \text{SO}_3 \) is formed from specific amounts of \( \text{SO}_2 \) and \( \text{O}_2 \).

By using the mole ratio, we can calculate the exact amounts of products formed or reactants required. This also helps derive the initial and final volume ratios in the exercise, as the mole ratio directly affects these calculations, determining how reactions proceed.