Question

Assuming all gases are at the same temperature and pressure, how many liters of oxygen gas react with \(10.0 \mathrm{~L}\) of carbon monoxide? $$2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)$$

Short answer

5.0 liters of oxygen gas react with 10.0 liters of carbon monoxide.

Step-by-step solution

Write the Balanced Chemical Equation

The balanced chemical equation is given by \(2 \text{ CO}(g) + \text{ O}_2(g) \rightarrow 2 \text{ CO}_2(g)\). This equation shows that two volumes of carbon monoxide react with one volume of oxygen gas.

Understand the Ratio of Volumes

Since the volumes of gases at the same temperature and pressure can be directly compared to the coefficients in the chemical equation, the ratio of carbon monoxide to oxygen in the reaction is \(2:1\). This means 2 liters of carbon monoxide reacts with 1 liter of oxygen.

Calculate the Volume of Oxygen Gas Required

Given that \(10.0\) liters of carbon monoxide reacts, we use the ratio \(2 \text{ L CO} : 1 \text{ L } \text{O}_2\). Divide by the ratio: \(10.0 \text{ L CO} \times \frac{1 \text{ L } \text{O}_2}{2 \text{ L CO}} = 5.0 \text{ L } \text{O}_2\).

Key concepts

Balanced Chemical Equation

A balanced chemical equation allows us to understand the proportions in which different substances react. In a chemical reaction, the law of conservation of mass dictates that the number of atoms of each element must remain the same before and after the reaction. This means that the number of atoms for each element on the reactant side must equal the number on the product side.
To achieve this, we adjust the coefficients, or the numbers in front of the chemical formulas.

• The coefficients indicate the number of units of each substance involved in the reaction.
• For gases, these coefficients also reflect how the volumes interact under the same conditions of temperature and pressure.

In the example of the chemical equation:\[2\,\text{CO}(g) + \text{O}_2(g) \rightarrow 2\,\text{CO}_2(g)\]this equation shows that two molecules of carbon monoxide react with one molecule of oxygen to produce two molecules of carbon dioxide. Thus, the equation is balanced because there are equal numbers of each type of atom on both sides of the equation. Understanding this allows us to calculate the yields of the products and determine what amount of reactants we need for the reaction.

Volume Ratio

The volume ratio is a key concept in gas stoichiometry, particularly when the gases are measured under the same conditions of temperature and pressure. According to Avogadro's law, equal volumes of gases contain equal numbers of molecules, as long as they are at the same temperature and pressure.
This means the volume ratios of reacting gases can be directly compared to the coefficients in their balanced chemical equation.For our example,

• The coefficient ratio of carbon monoxide to oxygen gas is \(2:1\).
• This directly translates into a volume ratio, meaning 2 liters of CO will react with 1 liter of \(\text{O}_2\).

So, if you have 10 liters of \(\text{CO}\), the volume ratio tells us that only 5 liters of \(\text{O}_2\) would be needed to completely react with it. This concept is crucial in predicting the volumes of gases in reactions and optimizing the amounts of each gas used.

Reaction Coefficients

Reaction coefficients are the numerical values placed before the chemical formulas in a balanced equation to indicate the number of moles of each substance involved in the reaction. They allow us to quantify the exact proportions of reactants and products.

• These coefficients guide us in determining the exact amounts of reactants needed for a reaction, or the amounts of products formed.
• In gas reactions, they also determine the volume relationships, since equal coefficients mean equal volumes (under the same conditions).

In our chemical equation:
\[ 2\,\text{CO}(g) + \text{O}_2(g) \rightarrow 2\,\text{CO}_2(g) \]
the coefficients (2, 1, and 2) tell us that two moles (or volumes, in terms of gases) of carbon monoxide react with one mole (or volume) of oxygen, producing two moles (or volumes) of carbon dioxide.
Understanding reaction coefficients is essential, as they help in predicting the amounts and yields in both chemistry problems and real-world chemical production.