Problem 51 - Chemistry Matter and Change

Question

Air Pollution The pollutant \(\mathrm{SO}_{2}\) is removed from the air by in a reaction that also involves calcium carbonate and oxygen. The products of this reaction are calcium sulfate and carbon dioxide. Determine the mole ratio you would use to convert moles of \(\mathrm{SO}_{2}\) to moles of \(\mathrm{CaSO}_{4}\)

Step-by-Step Solution

Answer

The mole ratio to convert moles of SO2 to moles of CaSO4 in the balanced chemical equation 2 SO2 + CaCO3 + O2 → CaSO4 + 2 CO2 is 2:1, meaning 2 moles of SO2 react to produce 1 mole of CaSO4.

Step 1: Write the unbalanced chemical equation

First, let's write the unbalanced chemical equation for the reaction: SO2 + CaCO3 + O2 → CaSO4 + CO2

Step 2: Balance the chemical equation

Next, we need to balance the chemical equation, ensuring that the number of atoms for each element is equal on both sides of the equation: 2 SO2 + CaCO3 + O2 → CaSO4 + 2 CO2 To check, let's count the atoms for each element on both sides of the equation: Left side: Right side: 2 S 1 S 4 O (from SO2) 4 O (from CaSO4) 3 O (from CaCO3) 4 O (from 2 CO2) 1 Ca 1 Ca 1 C (from CaCO3) 1 C (from 2 CO2) The equation is now balanced.

Step 3: Determine the mole ratio

Now, we can determine the mole ratio of the reactant SO2 to the product CaSO4 from the balanced chemical equation. The coefficients in the balanced chemical equation will provide the mole ratio. In this case, the mole ratio of SO2 to CaSO4 is: \( \frac{2 \text{ moles of SO}_2}{1 \text{ mole of CaSO}_4} \) So, the mole ratio to convert moles of SO2 to moles of CaSO4 is 2:1, meaning 2 moles of SO2 react to produce 1 mole of CaSO4.

Key Concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It involves calculations that rely on the mole ratio, which defines how many moles of one substance react with or are produced from a certain number of moles of another substance. The mole, a fundamental unit in chemistry, represents Avogadro's number, approximately 6.022 x 1023 particles, and is used to convert between particles and mass since it's impractical to count out individual atoms or molecules.

For a reaction to occur, reactants must come together in the correct proportion. Understanding stoichiometry is essential for predicting how much product can be made from a given amount of reactants, which has practical applications in everything from laboratory experiments to industrial production. Furthermore, stoichiometry is not limited to mass calculations; it can also involve volumes (in the case of gases) or concentrations when dealing with solutions.

In the given exercise, learning about stoichiometry helps predict how much calcium sulfate would be formed from a certain amount of sulfur dioxide and calcium carbonate in the process of air purification.

Chemical Equation Balancing

Why Balance Chemical Equations?

Balancing chemical equations is a vital process because it reflects the law of conservation of mass, stating that matter cannot be created or destroyed in a chemical reaction. Therefore, we need an equal number of each type of atom on both sides of the equation. Achieving this balance ensures that the chemical equation represents what actually happens during the reaction.

How to Balance Equations

The process involves adjusting coefficients, the numbers before reactants and products, to get the same number of each element on both sides. In our air pollution exercise, for example, the pollutants and reactants were effectively balanced to display equal numbers of sulfur, oxygen, carbon, and calcium atoms. Properly balanced equations constitute the first and essential step in performing stoichiometric calculations, as they provide the exact mole ratios needed for these computations.

Common Pitfalls

One common mistake is altering subscripts of compounds, which changes their identities. Remember, only the coefficients should be modified to balance equations. Another tip is to start with the most complex molecule or the element that appears in fewer substances and proceed to the simpler ones.

Reaction Yield

The concept of reaction yield is critical when considering the efficiency and practicality of a chemical process. There are two types of yields: theoretical and actual. Theoretical yield is the amount of product that would result from a perfect chemical reaction based on stoichiometry, assuming 100% efficiency and no side reactions. In contrast, actual yield is the amount of product actually obtained from the reaction, which is almost always lower due to various factors such as incomplete reactions, side reactions, or loss of product during processing.

In the context of air pollution and removal of sulfur dioxide, comprehending reaction yield is crucial for evaluating the effectiveness of the pollution control measures. If the actual yield is significantly lower than the theoretical yield, this can indicate that the process may need to be improved to increase efficiency. Such insights can lead to the optimization of the chemical process, ensuring that pollutants like SO2 are removed more effectively from the air, contributing to better environmental health and safety.