Question

Consider the combustion of carbon monoxide (CO) in oxygen gas: $$ 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g) $$ Starting with 3.60 moles of \(\mathrm{CO},\) calculate the number of moles of \(\mathrm{CO}_{2}\) produced if there is enough oxygen gas to react with all the CO.

Short answer

3.60 moles of CO₂ are produced.

Step-by-step solution

Write Down the Balanced Equation

The balanced chemical equation for the combustion of carbon monoxide (CO) in oxygen gas is given as:\[ 2 \mathrm{CO}(g) + \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{CO}_{2}(g) \]

Identify the Mole Ratios

From the balanced chemical equation, we see that 2 moles of CO produce 2 moles of CO\(_2\). This gives a mole ratio of \(\frac{2 \text{ moles of } \mathrm{CO}}{2 \text{ moles of } \mathrm{CO}_2}\). Simplified, the mole ratio is 1:1.

Calculate Moles of CO2 Produced

Starting with 3.60 moles of CO, and using the 1:1 mole ratio, the moles of CO\(_2\) produced can be calculated as follows:\[ \text{Moles of } \mathrm{CO}_2 = 3.60 \text{ moles of } \mathrm{CO} \times \frac{2 \text{ moles of } \mathrm{CO}_2}{2 \text{ moles of } \mathrm{CO}} = 3.60 \text{ moles of } \mathrm{CO}_2 \]

Key concepts

Stoichiometry

Stoichiometry plays a crucial role in understanding chemical reactions. It deals with the quantitative relationships between reactants and products in a chemical reaction. In this case, by mastering stoichiometry, you can predict how much product will form from a given amount of reactants.
For example, in the combustion of carbon monoxide to form carbon dioxide, stoichiometry helps us calculate the exact amount of carbon dioxide produced when starting with a certain amount of carbon monoxide.
The balanced chemical equation is at the heart of stoichiometry, acting like a "recipe" for the reaction. In the equation provided: \[2\mathrm{CO}(g) + \mathrm{O}_2(g) \rightarrow 2\mathrm{CO}_2(g)\], each molecule or mole of a compound is symbolized by coefficients that illustrate how many units of each substance are involved.
These coefficients help create mole ratios, which are essential for stoichiometric calculations, allowing you to convert moles of one substance to moles of another using simple ratio calculations. For instance, every 2 moles of CO reacts to produce 2 moles of CO₂, giving you a mole ratio that simplifies your calculations.

Combustion Reactions

Combustion reactions are a type of chemical reaction where fuel reacts with an oxidant, often oxygen, releasing energy, usually in the form of heat and light. These reactions are exothermic, which means they release energy.
The combustion of carbon monoxide (CO) is a classic example of such a reaction, where CO combines with oxygen gas (O₂) to form carbon dioxide (CO₂). This particular reaction can be represented by the balanced chemical equation: \[2\mathrm{CO}(g) + \mathrm{O}_2(g) \rightarrow 2\mathrm{CO}_2(g)\].
Understanding combustion reactions is essential for both practical applications, such as energy production and environmental protection, by ensuring the complete burning of fuels to prevent toxic emissions like CO.
Moreover, these reactions showcase the importance of oxygen in the chemical process. Without sufficient oxygen, incomplete combustion occurs, leading to the formation of harmful substances.

Mole Concept

The mole concept is a central unit in chemistry that helps in quantifying substances. It provides a bridge between the atomic world and the macro-scale quantities we can measure in a laboratory.
A mole is defined as the amount of substance that contains as many elementary entities as there are atoms in 12 grams of pure carbon-12 (\(^{12}C\)). This number is Avogadro's number, approximately \(6.022 \times 10^{23}\).
In the exercise, understanding the mole concept allows you to determine the number of moles of CO₂ produced from a known number of moles of CO. Since 3.60 moles of CO are provided, and the reaction has a 1:1 mole ratio, a straightforward calculation using the mole concept gives the same number of moles of CO₂, which is 3.60 moles.
Essentially, the mole concept enables chemists to work with the submicroscopic amount of substances, making calculations and predictions about chemical reactions more feasible.