Question

If 1.00 mol of nitrogen monoxide gas and 1.00 mol of oxygen gas react, what is the limiting reactant and how many moles of \(\mathrm{NO}_{2}\) are produced from the reaction? $$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$$

Short answer

The limiting reactant is NO, and 1 mole of \(\text{NO}_2\) is produced.

Step-by-step solution

Understand the Balanced Equation

We start with the balanced chemical equation for the reaction: \[2 \text{NO}(g) + \text{O}_2(g) \rightarrow 2 \text{NO}_2(g).\] This equation tells us that 2 moles of NO react with 1 mole of \(\text{O}_2\) to produce 2 moles of \(\text{NO}_2\).

Determine the Moles of Reactants

We have 1.00 mol of NO and 1.00 mol of \(\text{O}_2\). With this in mind, check the stoichiometry from the balanced equation to compare the amount of reactants.

Identify the Limiting Reactant

According to the balanced equation, 2 moles of NO are needed to react with 1 mole of \(\text{O}_2\). Since we have 1 mole of \(\text{O}_2\), we would need 2 moles of NO to fully react with it, but we only have 1 mole of NO. Therefore, NO is the limiting reactant.

Calculate Moles of NO2 Produced

Since NO is the limiting reactant, the amount of \(\text{NO}_2\) produced will be based on its moles. The balanced equation shows 2 moles of NO produce 2 moles of \(\text{NO}_2\). Thus, 1 mole of NO will produce 1 mole of \(\text{NO}_2\).

Key concepts

Limiting Reactant

In chemical reactions, the limiting reactant is the substance that is entirely consumed first. This reactant limits the amount of product that can be formed from the chemical reaction. To determine the limiting reactant, compare the mole ratio of the reactants used in the reaction to the ratio in the balanced chemical equation.
For the reaction between nitrogen monoxide ( O) and oxygen ( O_2), the balanced chemical equation is:

• 2 NO + O_2 → 2 NO_2.

You need 2 moles of NO for every 1 mole of O_2. In our exercise, we have 1.00 mol of NO and 1.00 mol of O_2. We need 2 moles of NO to entirely use up the 1 mole of O_2 based on the stoichiometric ratio. Since there isn't enough NO to react with all the O_2, NO is the limiting reactant. This is crucial because it determines how much NO_2 can be produced.

Chemical Equations

A balanced chemical equation is a representation of a chemical reaction where the number of atoms for each element is the same on both the reactant and product sides. This balance is guided by the law of conservation of mass, which states that mass is conserved in a closed system.
The balanced equation for the reaction in our exercise is:

• 2 NO + O_2 → 2 NO_2.

This tells us that 2 moles of nitrogen monoxide react with 1 mole of oxygen to produce 2 moles of nitrogen dioxide. Each coefficient in the equation (such as the '2' in front of NO) indicates the number of moles that participate in the reaction. Balanced equations are essential for calculating and understanding the amounts of reactants and products involved.

Mole-to-Mole Conversions

Mole-to-mole conversions are a vital part of stoichiometry, helping us to calculate how many moles of a product can be formed from a given amount of reactant. To perform these conversions, use coefficients from a balanced chemical equation to form a conversion factor.
In our balanced reaction:

• 2 NO + O_2 → 2 NO_2,

the coefficients tell us that 2 moles of NO will produce 2 moles of NO_2. Therefore, the ratio of NO to NO_2 is 1:1. If we have 1 mole of NO, like in the exercise, it will produce 1 mole of NO_2. This 1:1 conversion ratio allows us to directly equate the amount of NO used to the amount of NO_2 produced. Understanding these conversions helps ensure accurate predictions about the outcome of chemical reactions.