Question

If $70.0\mathrm{mL}$ of nitrogen gas reacts with $45.0\mathrm{mL}$ of oxygen gas, what is the volume of ${\mathrm{N}}_2{\mathrm{O}}_3$ produced? Assume all gases are at the same temperature and pressure. $${\mathrm{N}}_2(g)+{\mathrm{O}}_2(g)⟶{\mathrm{N}}_2{\mathrm{O}}_3(g)$$

Short answer

45.0 mL of ${\text{N}}_2{\text{O}}_3$ is produced.

Step-by-step solution

Write the Balanced Equation

The balanced chemical equation is already provided: ${\text{N}}_2(g)+{\text{O}}_2(g)\to {\text{N}}_2{\text{O}}_3(g)$. This equation indicates that 1 mole of nitrogen gas reacts with 1 mole of oxygen gas to produce 1 mole of nitrogen trioxide gas.

Determine the Limiting Reactant

Use the provided volumes to determine the limiting reactant. Since gases at the same temperature and pressure have volumes proportional to moles, compare the given volumes. There are 70.0 mL of nitrogen and 45.0 mL of oxygen. Notice that the stoichiometry of the reaction is 1:1. Therefore, oxygen with only 45.0 mL is the limiting reactant.

Calculate Volume of Product Formed

Since the limiting reactant is oxygen and it reacts in a 1:1 ratio to produce ${\text{N}}_2{\text{O}}_3$, the volume of ${\text{N}}_2{\text{O}}_3$ formed is equal to the volume of oxygen used. Therefore, $45.0\mathrm{mL}$ of ${\text{N}}_2{\text{O}}_3$ is produced.

Key concepts

Stoichiometry

Stoichiometry is an essential concept in chemistry that involves calculating the quantities of reactants and products in chemical reactions. This is done using the balanced chemical equation, which shows the ratio of moles between them.
In a balanced equation, the coefficients that appear before each compound indicate the relative amounts needed for the reaction. For example, in the given reaction $${\text{N}}_2(g)+{\text{O}}_2(g)\to {\text{N}}_2{\text{O}}_3(g)$$ the coefficients (all implied as "1") mean that 1 mole of nitrogen reacts with 1 mole of oxygen to form 1 mole of nitrogen trioxide. Reactants and products follow these stoichiometric ratios. This balanced equation helps in understanding the exact proportions in which chemicals interact or transform. By using these ratios, you can determine the amount of product formed or the amount of each reactant needed.

Limiting Reactant

The limiting reactant in a chemical reaction is the reactant that is completely consumed first, thus determining the amount of product formed.
To find the limiting reactant, compare the mole ratios of the reactants in the balanced equation to those available for the reaction. In our example, the reaction uses a 1:1 ratio of nitrogen to oxygen. Let's consider the provided volumes: 70.0 mL of nitrogen and 45.0 mL of oxygen. Since both are measured at the same conditions of temperature and pressure, we can directly compare their volumes to find out which is less in terms of the stoichiometric requirements. The smaller volume of oxygen (45.0 mL) makes it the limiting reactant, meaning it will run out first and limit the amount of nitrogen trioxide produced. Understanding the limiting reactant is crucial for predicting how much product results from given amounts of reactants.

Gas Laws

Gas laws describe the behavior of gases and allow us to relate different properties such as pressure, volume, and temperature. In this exercise, the principle that equal volumes of gases at the same conditions of temperature and pressure contain an equal number of moles is used.
This principle supports the step where the volumes of nitrogen and oxygen can be directly compared to determine the limiting reactant.
A key gas law here is Avogadro's Law, which states that the volume of a gas is directly proportional to the number of moles when pressure and temperature are constant. Therefore, in a reaction, assuming constant temperature and pressure, the volume of gas produced will be directly proportional to the volume of the limiting reactant. This is why the final volume of nitrogen trioxide, $45.0\mathrm{mL}$, matches the volume of the limiting reactant, oxygen.