Question

Consider a reaction represented by the following balanced equation \\[ 2 A+3 B \rightarrow C+4 D \\] You find that it requires equal masses of \(A\) and \(B\) so that there are no reactants left over. Which of the following is true? Justify your choice. a. The molar mass of A must be greater than the molar mass of B. b. The molar mass of A must be less than the molar mass of B. c. The molar mass of \(A\) must be the same as the molar mass of B.

Short answer

The correct answer is b. The molar mass of A must be less than the molar mass of B. This is because, after analyzing the balanced equation and establishing a relationship between the number of moles and molar masses of A and B, we find that M(B) = 1.5 * M(A), which implies that the molar mass of B is 1.5 times larger than the molar mass of A.

Step-by-step solution

Understanding the balanced equation

First, we should understand the balanced chemical equation. The given balanced equation is: \\[ 2 A+3 B \rightarrow C+4 D \\] This equation tells us that for 2 moles of A, we need 3 moles of B to react completely and produce one mole of C and 4 moles of D.

Calculate the number of moles using equal masses of A and B

We know that the relationship between mass (m) and the number of moles (n) is: n = m/M Where M is the molar mass of the substance It is given that equal masses of A and B are used for the reaction. Let the mass be x for both A and B: m(A) = m(B) = x Now, we can determine the number of moles for A and B using the above equation: n(A) = x/M(A) n(B) = x/M(B)

Use the balanced equation to establish a relationship between moles

From the balanced equation, we can see the stoichiometric relationship between A and B: n(A)/2 = n(B)/3 Substitute the number of moles of A and B from step 2: (x/M(A))/2 = (x/M(B))/3 Simplify the equation: 3 * (x / M(A)) = 2 * (x / M(B))

Determine the relationship between molar masses

Now, let's eliminate x from the equation and determine the relationship between M(A) and M(B): 3 / M(A) = 2 / M(B) Rearrange, and we get: M(B) / M(A) = 3 / 2

Conclusion

Comparing the M(B) and M(A), we conclude that the molar mass of B is 1.5 times larger than the molar mass of A: M(B) = 1.5 * M(A) Therefore, the molar mass of A must be less than the molar mass of B. Hence, the correct answer is: b. The molar mass of A must be less than the molar mass of B.

Key concepts

Molar Mass

Molar mass is a foundational concept in chemistry, reflecting the mass of one mole of a substance. It is expressed in grams per mole (g/mol) and helps relate the mass of a chemical substance to the amount of that substance in moles. This is critical when dealing with chemical reactions, as you often need to convert between mass and moles to understand how much of each substance is involved.

To calculate molar mass, you sum the atomic masses of all atoms in a molecular formula, using values from the periodic table. For example, water (\(H_2O\)) has a molar mass calculated by adding the mass of two hydrogen atoms and one oxygen atom.

• Atomic mass of Hydrogen = \(1.01\, g/mol\)
• Atomic mass of Oxygen = \(16.00\, g/mol\)

Thus, \(M(H_2O) = (2\times 1.01) + 16.00 = 18.02\, g/mol\).

This knowledge assists in determining how much of each reactant is needed or produced in a reaction, allowing scientists to plan experiments and manufacture substances efficiently.

Balanced Chemical Equation

A balanced chemical equation accurately represents a chemical reaction, detailing the reactants and products while ensuring that the equation obeys the law of mass conservation. This law states that matter cannot be created or destroyed in a chemical reaction, meaning the mass and number of atoms must be the same on both sides of the equation.

For a balanced equation like \(2 A + 3 B \rightarrow C + 4 D\), coefficients in front of chemical formulas indicate the relative number of moles needed to react with each other.

Balancing equations involves adjusting these coefficients to ensure that the number of atoms of each element is the same on both sides. This is essential in stoichiometry to accurately predict reactants' and products' amounts, based on mole ratios derived from the balanced equation.

Stoichiometry

Stoichiometry revolves around quantitative relationships within a chemical reaction. It's the calculation of reactants and products using a balanced equation. Through stoichiometry, you can predict how much of each reactant is needed to produce a desired amount of product, or how much product will be formed from given reactants.

In the exercise, stoichiometry involves setting up a ratio from the equation \(2 A + 3 B \rightarrow C + 4 D\). This ratio informs us that 2 moles of \(A\) react with 3 moles of \(B\).

By knowing the molar masses and having equal masses, we can use stoichiometry to derive the moles relationship: \(n(A)/2 = n(B)/3\). This leads us to understand the proportional relationships between substances in the reaction, which is crucial for chemical engineering and synthesis.

Moles and Mass Relationship

The relationship between moles and mass is fundamental in chemistry, bridging matter's microscopic and macroscopic worlds. Moles provide a means of expressing amounts of a chemical substance used in reactions, while mass is the measurable quantity.

The key formula connecting these quantities is \(n = m/M\), where \(n\) is the number of moles, \(m\) is the mass of the substance in grams, and \(M\) is the molar mass.

In our context, given equal masses of \(A\) and \(B\), the relationship \(n(A)/2 = n(B)/3\) arises, leading us to determine that the molar mass \(M(B)\) must be greater than \(M(A)\) to satisfy the conditions described. This highlights how even with equal masses, varying molar masses lead to different mole amounts, an essential factor in predicting reaction outcomes.