Question

Consider the general chemical equation \(2 \mathrm{~A}+3 \mathrm{~B} \longrightarrow 2 \mathrm{C}+\mathrm{D}\) (a) How many moles of \(\mathrm{C}\) are produced from \(2 \mathrm{~mol}\) of \(\mathrm{A} ?\) (b) How many liters of gas \(\mathrm{B}\) must react to give \(1 \mathrm{~L}\) of gas \(\mathrm{D}\)

Short answer

(a) 2 moles of C are produced from 2 moles of A. (b) 3 liters of B are needed to produce 1 liter of D.

Step-by-step solution

Identify the Reaction Stoichiometry for Part (a)

The given chemical reaction is balanced: \(2\, \mathrm{A} + 3\, \mathrm{B} \rightarrow 2\, \mathrm{C} + \mathrm{D}\). This means that 2 moles of A react to produce 2 moles of C. We have a direct 1:1 mole ratio for A to C.

Calculate Moles of C Produced

Since 2 moles of A produce 2 moles of C, if you start with 2 moles of A, you also produce 2 moles of C.

Identify the Reaction Stoichiometry for Part (b)

Again, using the balanced equation \(2\, \mathrm{A} + 3\, \mathrm{B} \rightarrow 2\, \mathrm{C} + \mathrm{D}\), we look at the stoichiometry for B and D. The ratio of B to D is 3:1.

Calculate Volume of B Needed

Remember that at the same temperature and pressure, equal volumes of gases contain equal numbers of moles (Avogadro's law). Thus, if 1 liter of D is produced, then 3 liters of B are required to react to produce it, according to the 3:1 ratio of B to D in the reaction.

Key concepts

Moles

In chemistry, the concept of "moles" is essential for quantifying substances. A mole is a unit that measures the amount of a substance and is defined as containing exactly 6.022 x 10\(^{23}\) entities, such as atoms or molecules. This number is known as Avogadro's number.
A mole allows chemists to use the atomic scale for practical laboratory work. For example, when the exercise asks how many moles of C are produced from A, the balanced equation shows that from 2 moles of A, 2 moles of C can be produced. This means that, in this particular reaction, the number of moles of A consumed is the same as the number of moles of C produced, illustrating the concept of a mole ratio.
The mole relationship is crucial because it bridges the atomic world with the macroscopic quantities that we can measure.

Balanced Chemical Equation

A balanced chemical equation is vital for understanding how reactants transform into products. It represents not only the chemicals involved but also the quantities in which they react. For a reaction to be balanced, the number of atoms of each element must be the same on both sides of the equation.
In the given exercise, the equation is: \[2 \mathrm{A} + 3 \mathrm{B} \longrightarrow 2 \mathrm{C} + \mathrm{D}\] This balanced equation tells us that for every 2 molecules of A and 3 molecules of B that react, 2 molecules of C and 1 molecule of D are produced.
The coefficients (the numbers in front of the chemical formulas) indicate the ratios in which the substances react and are produced. For part (b) of the exercise, knowing the balanced chemical equation allows you to deduce that to produce 1 liter of gas D, you will need 3 liters of gas B.

Avogadro's Law

Avogadro's Law is a principle in chemistry that states that equal volumes of gases, at the same temperature and pressure, contain the same number of molecules or moles. This concept is key in the exercise when calculating how much volume of gas B is required.
The exercise involves gases B and D, and according to Avogadro's Law, we know that their volumes can be directly compared in terms of moles. Given the balanced equation \[2 \mathrm{A} + 3 \mathrm{B} \rightarrow 2 \mathrm{C} + \mathrm{D}\], the stoichiometric ratio from B to D is 3:1. So, to produce 1 liter of D, 3 liters of B are needed.
Understanding Avogadro's Law helps in making these calculations easy by using direct volume-to-volume ratios, without requiring conversions to moles, as the conditions are already the same for both gases.