Question

If \(5.00 \mathrm{~mol}\) of nitrogen gas and \(5.00 \mathrm{~mol}\) of oxygen gas react, what is the limiting reactant and how many moles of NO are produced from the reaction? $$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}(g)$$

Short answer

The limiting reactant is neither; both reactants are fully consumed, producing 10.00 moles of NO.

Step-by-step solution

Write the Balanced Chemical Equation

The given chemical equation is already balanced. It is as follows: \ \[ \mathrm{N}_{2}(g) + \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}(g) \] This equation tells us that 1 mole of nitrogen gas reacts with 1 mole of oxygen gas to produce 2 moles of nitric oxide.

Determine the Mole Ratio from the Equation

From the balanced equation, the mole ratio of nitrogen gas \((\mathrm{N}_{2})\) to oxygen gas \((\mathrm{O}_{2})\) is 1:1. Similarly, the mole ratio of nitrogen gas to nitric oxide \((\mathrm{NO})\) is 1:2.

Calculate Moles Required for Reaction Completion

Given that you have 5.00 moles of \(\mathrm{N}_{2}\) and 5.00 moles of \(\mathrm{O}_{2}\), use the mole ratio to determine how much of each reactant is required to fully react. According to the 1:1 ratio, 5.00 moles of \(\mathrm{N}_{2}\) will need exactly 5.00 moles of \(\mathrm{O}_{2}\) to react completely.

Identify the Limiting Reactant

Both \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) are present in the exact stoichiometric ratio required by the balanced equation. Thus, neither reactant is in excess. In this scenario, both reactants will be completely consumed, so neither one is an absolute limiting reactant; they limit each other.

Calculate Moles of NO Produced

According to the 1:2 ratio in the balanced equation, for every mole of \(\mathrm{N}_{2}\) or \(\mathrm{O}_{2}\) that reacts, 2 moles of NO are produced. Since 5.00 moles of \(\mathrm{N}_{2}\) or \(\mathrm{O}_{2}\) react, you will produce: \ \[ 5.00 \text{ moles of } \mathrm{N}_{2} \times \frac{2 \text{ moles of } \mathrm{NO}}{1 \text{ mole of } \mathrm{N}_{2}} = 10.00 \text{ moles of } \mathrm{NO} \] This means 10.00 moles of NO are produced.

Key concepts

Limiting Reactant

When dealing with chemical reactions, it's crucial to identify the limiting reactant because it determines the maximum amount of product that can be formed. In our given reaction, both nitrogen (\(\mathrm{N}_2\)) and oxygen (\(\mathrm{O}_2\)) start with 5.00 moles. The reaction requires them in a 1:1 ratio, meaning they will react completely without any leftovers.

Here’s how limiting reactants work:

• Compare the mole ratio needed for the reaction to the moles you have.
• If you have less of a reactant than necessary, it’s your limiting reactant.
• In this case, both react in exact required amounts, making each a limiting factor for the other.

In scenarios where one reactant is in excess, the limiting reactant runs out first, preventing more product from forming. Here, since both substances limit each other equally, they are both consumed at the same rate with this stoichiometric balance.

Balanced Chemical Equation

A balanced chemical equation is crucial for solving stoichiometry problems. It provides a recipe for how reactants convert into products. In our example, the balanced equation \[\mathrm{N}_2(g) + \mathrm{O}_2(g) \rightarrow 2\mathrm{NO}(g)\] perfectly illustrates:

• One molecule of nitrogen reacts with one molecule of oxygen to yield two molecules of nitric oxide.
• Each reactant has equal stoichiometric coefficients, maintaining atom balance across the reaction.

Balanced equations ensure:

• Conservation of mass: The same number of each type of atom is present on both sides of the equation.
• Correct mole relationships for calculations.

This equation shows the 1:1:2 relationship between reactants and product, which is essential for accurately determining amounts involved in the reaction.

Mole Ratio

Understanding mole ratio is fundamental in predicting the outcome of a reaction. In chemical equations, the mole ratio gives the proportional amount of reactants taking part in the reaction and products formed.

In the equation \[\mathrm{N}_2(g) + \mathrm{O}_2(g) \rightarrow 2\mathrm{NO}(g)\], the mole ratios are:

• 1 mole of \(\mathrm{N}_2\) to 1 mole of \(\mathrm{O}_2\) (1:1 ratio).
• 1 mole of either \(\mathrm{N}_2\) or \(\mathrm{O}_2\) produces 2 moles of \(\mathrm{NO}\) (1:2 ratio).

Mole ratios indicate:

• How many moles of one substance will react with another.
• The number of moles of products expected from given reactants.

For our 5 moles of reactants, using these ratios, we can predict 10 moles of \(\mathrm{NO}\) will be formed, exemplifying the importance of mole ratio in calculating product formation.