Problem 8 - Chemistry: An Atoms-Focused Approach

Question

In the reaction \(A+B \rightarrow C+D, 3.00\) grams of substance \(C\) and 3.00 grams of substance \(\mathrm{D}\) are produced as 2.00 grams of substance A are consumed. How many grams of substance B are also consumed?

Step-by-Step Solution

Answer

Question: In the balanced chemical reaction A + B → C + D, 2.00 grams of substance A is consumed and 3.00 grams each of substances C and D are produced. Calculate the mass of substance B consumed in this reaction. Answer: 2.00 grams of substance B are consumed in the reaction.

Step 1: Determine the mole ratios from the balanced equation

In the balanced chemical equation, \(A + B \rightarrow C + D\), the coefficients of all substances are 1, so the mole ratios are: \(A:B:C:D = 1:1:1:1\)

Step 2: Calculate the moles of substance A consumed

We know the mass of substance A consumed (2.00 grams), and we need to determine the moles of substance A consumed. To do this, we need the molar mass of substance A. Unfortunately, we don't have that information, so we should look for a different path to solve the problem. Let's look at the mole ratios of the other substances instead.

Step 3: Use the mole ratios of the other substances to determine the mass of substance B consumed

Since we don't know the molar masses of the substances involved, we can't directly calculate the moles consumed. However, we know the mole ratios of the substances, and we know the masses of substance \(C\) and substance \(D\). According to the balanced equation, the mole ratio of substance \(C\) and \(D\) produced is 1:1. Therefore, the mass ratio of each substance should be the same as their mole ratios (since we don't have their molar masses, we are assuming their molar masses are the same). Since substance \(C\) and substance \(D\) have the same mass (3.00 grams each) and the mole ratio for substances A, B, C, and D are equal, we can determine the mass of substance \(B\) consumed: Mass of substance B consumed = Mass of substance A consumed = 2.00 grams So, in this reaction, 2.00 grams of substance B are consumed.

Key Concepts

Mole Ratios

In the study of chemistry, understanding mole ratios is essential for analyzing and predicting the outcomes of chemical reactions. Essentially, mole ratios give us the proportion of moles of each substance involved in a chemical reaction. This ratio is determined from the coefficients in a balanced chemical equation.
For example, in the reaction equation \(A + B \rightarrow C + D\), if the equation is balanced as such, then the mole ratio is \(A:B:C:D = 1:1:1:1\).

• Mole ratios are fixed and pertain to any given chemical reaction as reflected in its balanced equation.
• These ratios are crucial for converting between moles of different substances, allowing us to predict how reactants are consumed and products formed.

When you know the mass of one or more substances in the reaction, mole ratios enable you to find the mass needed or produced for any other substance, assuming you know the substances' molar masses.

Chemical Reaction

A chemical reaction is a process where substances, known as reactants, are transformed into different substances, known as products. In our example, the reaction \(A + B \rightarrow C + D\) involves the combination of substances \(A\) and \(B\) to produce \(C\) and \(D\).

• Each chemical reaction is characterized by a balanced equation which reflects the conservation of mass. This means matter is neither created nor destroyed in a chemical reaction.
• The reaction coefficients (numbers in front of molecules in a chemical equation) indicate the relative number of moles involved in the reaction.

Understanding reactions involves not just what the reactants and products are, but how many units (or moles) of each are involved. This is where mole ratios come into play, allowing you to scale the reaction up or down based on the amounts of reactants or products you have.

Balanced Equation

In chemistry, a balanced equation is crucial because it ensures that the Law of Conservation of Mass is obeyed. This law dictates that mass in a closed system must remain constant over time. Therefore, in a balanced equation, the number of each type of atom on the reactant side must equal the number on the product side.
The chemical equation \(A + B \rightarrow C + D\) is balanced as given. Here:

• Each substance A, B, C, and D has a coefficient of 1, indicating that one mole of A reacts with one mole of B to produce one mole each of C and D.
• Balanced equations help us determine correct mole ratios and are crucial in quantitative chemical analysis since they help predict the correct amounts of reactants needed or products formed.

Whenever you encounter a chemical problem that involves calculations, the first step often involves writing or confirming a balanced equation to ensure accurate computations. This step is vital for determining how reactants convert to products accurately in terms of moles and grams.