Question

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

Short answer

(a) 3 moles of C; (b) 2 liters of B.

Step-by-step solution

Analyze the Stoichiometry from A to C

In the chemical equation \(A + 2B \longrightarrow 3C + 2D\), the stoichiometry indicates that 1 mole of \(A\) produces 3 moles of \(C\). Thus, 1 mole of \(A\) results in the formation of 3 moles of \(C\).

Understand the Stoichiometric Relationship for Gases

According to the equation \(A + 2B \longrightarrow 3C + 2D\), 2 moles of \(B\) yield 2 moles of \(D\), maintaining a 1:1 volumetric ratio if measured under the same conditions of temperature and pressure (Charles's and Avogadro's laws).

Calculate Liters of Gas B for Desired Volume of D

Given the 1:1 stoichiometric ratio between \(B\) and \(D\), to obtain 2 L of gas \(D\), one must react 2 L of gas \(B\) at constant temperature and pressure, according to the equation's stoichiometry.

Key concepts

Mole Concept

The mole concept is a fundamental chemistry idea that helps to translate the micro world of atoms and molecules into the macro world we can observe. It allows us to count particles like atoms or molecules by weighing them, using the unit of moles. One mole is defined as exactly 6.022 x 10²³ particles of that substance, a number known as Avogadro's number.
This unit bridges the gap between atomic scale and practical laboratory scale. When we say there are 1 mole of chemical substances, it means there are 6.022 x 10²³ units of those substances, be they atoms, molecules, ions, or electrons.
In the chemical equation given, if we know that 1 mole of "A" reacts, we can predict that it will form 3 moles of "C" through stoichiometric calculations, highlighting the direct application of the mole concept.

Avogadro's Law

Avogadro's Law states that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules. This law is incredibly useful for chemical reactions involving gases. It teaches us that volume ratios of gases can often be equated to mole ratios.
In the equation provided, 2 moles of gas "B" produce 2 moles of gas "D", demonstrating Avogadro's Law. Due to this 1:1 mole ratio, under the same conditions, 2 liters of gas "B" would yield 2 liters of gas "D".
This concept simplifies many quantitative relationships in gas chemistry and is foundational for understanding gas volumes in reactions.

Volumetric Ratios

Volumetric ratios in chemistry allow us to relate quantities of reactants and products in their gaseous state. Because of Avogadro's Law, the volume ratio of reacting gases at constant temperature and pressure can be directly related to the mole ratio.
For the equation showed, the stoichiometry is such that the ratio of gas volumes is the same as ratio of moles. Thus, reacting 2 liters of gas "B" with the amount of "A" given would yield 2 liters of gas "D".

• A volumetric ratio of gases reflects their respective mole ratios.
• This ratio is particularly useful since measuring volume is often more practical than directly counting molecules or moles.

Understanding these relationships is crucial for accurately predicting the outcomes of reactions involving gases.

Chemical Reactions

Chemical reactions involve transforming reactants into products through the breaking and forming of chemical bonds. Every reaction has a balanced equation, indicating the proportions of reactants and products, and this is key to understanding how much of each substance is involved.
In the reaction given, "A" combines with "B" to produce "C" and "D". The reaction is balanced, with stoichiometric coefficients indicating a clear relationship:

• 1 mole of "A" reacts with 2 moles of "B".
• This reaction produces 3 moles of "C" and 2 moles of "D".

The equation reveals how many moles of each reactant are needed and how many moles of each product will form under ideal conditions. By understanding chemical reactions, we predict and control how chemicals interact in practical scenarios like labs and industry.