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 mol of \(\mathrm{NO}\) is mixed with \(0.503 \mathrm{~mol}\) of \(\mathrm{O}_{2}\). Determine which of the two reactants is the limiting reactant. Calculate also the number of moles of \(\mathrm{NO}_{2}\) produced.

Short answer

NO is the limiting reactant; 0.886 moles of NO2 are produced.

Step-by-step solution

Write the Balanced Equation

The balanced chemical equation for the reaction is: \[ 2 \mathrm{NO}(g) + \mathrm{O}_2(g) \rightarrow 2 \mathrm{NO}_2(g) \] This shows that 2 moles of \(\mathrm{NO}\) react with 1 mole of \(\mathrm{O}_2\) to produce 2 moles of \(\mathrm{NO}_2\).

Determine Moles of NO Needed for Reaction

From the balanced equation, the stoichiometry dictates a 2:1 ratio. Given 0.503 moles of \( \mathrm{O}_2 \), the required moles of \( \mathrm{NO} \) needed is:\[ 0.503 \times 2 = 1.006 \text{ moles of } \mathrm{NO} \]

Compare Available Moles of NO

We only have 0.886 moles of \( \mathrm{NO} \) available, which is less than the needed 1.006 moles. Hence, \( \mathrm{NO} \) is the limiting reactant because there is not enough of it to fully react with the available \( \mathrm{O}_2 \).

Calculate Moles of NO2 Produced

Since \( \mathrm{NO} \) is the limiting reactant, it will determine the amount of \( \mathrm{NO}_2 \) formed. According to the reaction, the stoichiometry is 1:1 for \( \mathrm{NO} \) to \( \mathrm{NO}_2 \). Therefore, 0.886 moles of \( \mathrm{NO}_2 \) will be produced.

Key concepts

Chemical Reaction Stoichiometry

Understanding chemical reaction stoichiometry is crucial for solving exercises about limiting reactants in chemical reactions, like in the provided example. Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows you to predict how much of each substance is needed or produced in a reaction.
Imagine a recipe where two slices of bread and one slice of cheese make one sandwich. If you have only 3 slices of bread, no matter how much cheese you have, you can only make 1 sandwich. Similarly, in the given reaction, the equation \(2 \text{NO} + \text{O}_2 \rightarrow 2 \text{NO}_2\) provides the stoichiometric relationship between the reactants and products.
Key points of stoichiometry include:

• Balancing equations to relate moles of reactants to moles of products.
• Using ratios obtained from the balanced equation to identify limiting reactants.
• Determining the amount of products formed from given amounts of reactants.

In our example, the stoichiometry shows that 2 moles of NO react with 1 mole of \(\text{O}_2\) to produce 2 moles of \(\text{NO}_2\). This ratio guides you to find which reactant you will run out of first, also known as the limiting reactant.

Moles Calculation

Moles calculation is an essential skill in chemistry, as it allows us to convert amounts of substances into a usable form using the concept of a mole. A mole quantifies an amount of substance, based on the number of atoms or molecules, similar to how a dozen quantifies 12 items.
In chemical reactions, we use moles to determine how much of each substance is involved. For the given exercise, the reaction involves 0.886 moles of NO and 0.503 moles of \(\text{O}_2\). The stoichiometry from the balanced equation shows that 1 mole of \(\text{O}_2\) reacts with 2 moles of NO.
To find how many moles of NO should react with 0.503 moles of \(\text{O}_2\), we calculate:

• Required moles of NO = \(0.503 \times 2 = 1.006\) moles.

We compare this with the available 0.886 moles of NO. Since 0.886 is less than the required 1.006, NO is the limiting reactant, because it will not allow the full use of \(\text{O}_2\). This calculation helps us understand which reactant limits the reaction and how much of each product can form.

Balanced Chemical Equation

A balanced chemical equation is fundamental for understanding and predicting the outcomes of chemical reactions. It provides the exact proportion of reactants and products involved, ensuring matter is neither created nor destroyed, only transformed.
The key principle of a balanced equation is that the number of atoms of each element must be the same on both sides of the reaction. It acts like a scale that is perfectly balanced on both sides with an equal mass.
For instance, the balanced chemical equation \(2 \text{NO} + \text{O}_2 \rightarrow 2 \text{NO}_2\) confirms that 2 nitrogen atoms and 4 oxygen atoms are present before and after the reaction.
Having a correctly balanced equation allows you to:

• Identify the mole ratios between reactants and products.
• Use these ratios for calculations involving limiting reactants or amounts of products.
• Ensure calculations comply with the law of conservation of mass.

In this exercise, the balanced equation helps determine that 0.886 moles of NO can form 0.886 moles of \(\text{NO}_2\), given the 1:1 stoichiometric ratio between NO and \(\text{NO}_2\). Balancing is the foundation of solving any stoichiometric problem effectively.