Problem 90 - Introductory Chemistry Atoms First

Question

When \(5 \mathrm{~g}\) of compound \(\mathrm{A}\) reacts with an unlimited amount of compound \(\mathrm{B}, 7 \mathrm{~g}\) of compound \(\mathrm{C}\) is formed. How many grams of compound B must have reacted, and what law allows you to answer the question?

Step-by-Step Solution

Answer

2 grams of compound B reacted in the reaction, and the Law of Conservation of Mass allowed us to determine this value.

Step 1: 1. Identify the given information and the unknowns

(We are given the mass of compound A before the reaction, the mass of compound C after the reaction, and we need to find the mass of compound B that reacts.)

Step 2: 2. Apply the Law of Conservation of Mass

(According to the Law of Conservation of Mass, the total mass of the reactants must be equal to the total mass of the products. So, Mass of A + Mass of B = Mass of C)

Step 3: 3. Write down the equation in terms of the unknown mass of B

(We are given the mass of A and the mass of C, so we can write the equation as: Mass of B = Mass of C - Mass of A)

Step 4: 4. Substitute the given values into the equation and solve for the mass of B

(We know that 5 g of A reacts with B and 7 g of C is formed, so we can plug these values into the equation: Mass of B = 7 g - 5 g)

Step 5: 5. Calculate the mass of compound B

(By subtracting the mass of A from the mass of C, we find that Mass of B = 2 g. So, 2 grams of compound B must have reacted with 5 grams of compound A.) Answer: 2 grams of compound B reacted in the reaction, and the Law of Conservation of Mass allowed us to determine this value.

Key Concepts

Reaction Stoichiometry

Reaction stoichiometry is the branch of chemistry that deals with the quantitative relationships between the substances involved in chemical reactions. It allows us to predict the amount of products formed from given reactants or vice versa. In our exercise, we focused on how much compound B reacts based on known quantities of compound A and the product, compound C.
To properly apply stoichiometry, it's essential to have a balanced chemical equation. This equation helps in maintaining the correct ratio of reactants to products. In a balanced equation, the coefficients denote these ratios, allowing for the conversion between moles of different substances.

• For example, if the balanced equation states that 1 mole of A reacts with 1 mole of B to form 1 mole of C, the direct stoichiometric relationship makes calculations straightforward.
• However, if the ratios are different, stoichiometric coefficients become necessary to calculate how much of each substance is needed or produced in a reaction.

In our case, although we don't have a balanced equation, the example provides sufficient information based on masses to infer how much compound B is involved in the reaction using stoichiometry principles.

Mass Calculation

Mass calculation in chemical reactions involves determining the mass of reactants or products involved, based on the Law of Conservation of Mass. This law states that mass is neither created nor destroyed in a chemical reaction. Instead, the total mass of the reactants must equal the total mass of the products.
For the exercise, we are given that 5 grams of compound A reacts to form 7 grams of compound C. To find the mass of compound B that reacted, we utilize the principle that:
\[ \text{Mass of A} + \text{Mass of B} = \text{Mass of C} \]
After identifying the known values:

• Mass of A = 5 g
• Mass of C = 7 g

We rearrange the equation to solve for the unknown:

• Mass of B = Mass of C - Mass of A
• Substitute to find Mass of B: Mass of B = 7 g - 5 g = 2 g

Thus, 2 grams of compound B reacted. This straightforward calculation exemplifies the direct application of the Law of Conservation of Mass in determining unknown quantities in a chemical reaction.

Chemical Equations

Chemical equations symbolize chemical reactions with reactants and products represented by their chemical formulas. They provide a concise way of conveying information about the reaction, including which substances are involved, and in what proportions they react and are produced.
In dealing with chemical equations, ensuring that they are balanced is crucial, as this reflects the Law of Conservation of Mass. A balanced chemical equation has an equal number of each type of atom on both sides of the equation.

• Balancing chemical equations involves adjusting the coefficients in front of each substance, ensuring mass conservation.
• Once balanced, a chemical equation serves as a tool for reaction stoichiometry, helping to determine amounts of reactants and products.

While our exercise involved an implicit understanding of these concepts through mass calculations, chemical equations often give explicit structures that guide these stoichiometric calculations. In real-world applications, knowing the chemical equation aids in understanding the reaction's complete profile, including intermediate steps and energy changes.