Problem 83 - Chemistry

Question

Nitric oxide (NO) reacts with oxygen gas to form nitrogen dioxide \(\left(\mathrm{NO}_{2}\right)\), a dark-brown gas: $$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$$ In one experiment 0.886 mole of NO is mixed with 0.503 mole of \(\mathrm{O}_{2}\). Calculate which of the two reactants is the limiting reactant. Calculate also the number of moles of \(\mathrm{NO}_{2}\) produced.

Step-by-Step Solution

Answer

The limiting reactant is NO, and the number of moles of NO2 produced is 0.886 moles.

Step 1: Find the stoichiometric ratio between the reactants

From the balanced chemical equation, we can see that 2 moles of NO react with 1 mole of O2 to form 2 moles of NO2. Therefore, the stoichiometric ratio of NO to O2 is 2:1.

Step 2: Determine the actual ratio of the reactants

In this experiment, we have 0.886 moles of NO and 0.503 moles of O2. So, the actual ratio of NO to O2 is \(0.886 / 0.503 \approx 1.76\), which is less than the stoichiometric ratio (2). Therefore, NO is the limiting reactant because it will be consumed before O2.

Step 3: Determine the number of moles of NO2 produced

Since 2 moles of NO produce 2 moles of NO2, 1 mole of NO will produce 1 mole of NO2. Therefore, 0.886 moles (the amount of the limiting reactant, NO) will produce 0.886 moles of NO2.

Key Concepts

Stoichiometry

Stoichiometry is the section of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It is essentially the math behind chemistry, allowing scientists to predict how much product can be produced from a given amount of reactants or how much of a reactant is needed to create a desired quantity of product.

It all hinges on the balanced chemical equation, which provides the ratio of moles of reactants and products. For example, in the reaction of nitric oxide (NO) with oxygen (O₂) to form nitrogen dioxide (NO₂), the balanced equation clearly indicates that two moles of NO react with one mole of oxygen to produce two moles of NO₂. This type of stoichiometric calculation is invaluable when determining which reactant will run out first—the limiting reactant—which in turn limits the amount of product formed.

Chemical Reaction

A chemical reaction is a process that leads to the transformation of one set of chemical substances to another. In the context of the exercise involving nitric oxide and oxygen gas, it's a reaction where molecules of NO and O₂ interact to form NO₂, a nitrogen dioxide gas with a dark brown color.

Understanding chemical reactions involves knowing not just how molecules come together and apart, but also understanding the conditions that favor their interaction, such as temperature, pressure, and concentration. The rate of the reaction can vary based on these conditions along with the presence of catalysts. The reaction rate, however, does not affect the stoichiometry of the reaction—the amounts of reactants and products are always governed by the balanced chemical equation.

Mole Concept

The mole concept is a fundamental part of chemistry that provides a way to count particles at the atomic and molecular scale. A mole represents Avogadro's number (\(6.022 \times 10^{23}\) entities) of anything, usually atoms or molecules. This concept becomes especially useful in chemistry due to the incredibly small scale of atoms and molecules, making the mole a bridge between our macroscopic and microscopic worlds.

It allows chemists to use grams and liters, which are much more manageable quantities, to represent numbers of atoms or molecules that would otherwise be incomprehensibly large. In stoichiometry, the mole concept is key to converting between masses of reactants and products. For instance, in the exercise cited, the moles of nitric oxide and oxygen indicate how much of each reactant is present, thus determining the quantity of product that can be formed and which reactant is the limiting one.