Question

Ammonia reacts with \(\mathrm{O}_{2}\) to form either \(\mathrm{NO}(g)\) or \(\mathrm{NO}_{2}(g)\) according to these unbalanced equations: $$ \begin{array}{l}{\mathrm{NH}_{3}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{H}_{2} \mathrm{O}(g)} \\\ {\mathrm{NH}_{3}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)}\end{array} $$ In a certain experiment 2.00 moles of \(\mathrm{NH}_{3}(g)\) and 10.00 moles of \(\mathrm{O}_{2}(g)\) are contained in a closed flask. After the reaction is complete, 6.75 moles of \(\mathrm{O}_{2}(g)\) remains. Calculate the number of moles of \(\mathrm{NO}(g)\) in the product mixture: Hint: You cannot do this problem by adding the balanced equations because you cannot assume that the two reactions will occur with equal probability.)

Short answer

The number of moles of \(\mathrm{NO}\) in the product mixture is \(4\) moles.

Step-by-step solution

Balance the reaction equations

Let's balance the two given unbalanced reactions. Reaction 1: \[\mathrm{4NH}_{3}(g)+\mathrm{5O}_{2}(g) \longrightarrow 4\mathrm{NO}(g)+6\mathrm{H}_{2}\mathrm{O}(g)\] Reaction 2: \[\mathrm{4NH}_{3}(g)+\mathrm{7O}_{2}(g) \longrightarrow 4\mathrm{NO}_{2}(g)+6\mathrm{H}_{2} \mathrm{O}(g)\]

Determine moles of \(\mathrm{O}_{2}\) consumed

Since we know that there are 10.00 moles of \(\mathrm{O}_{2}\) initially and 6.75 moles of \(\mathrm{O}_{2}\) left after the reaction, the moles of \(\mathrm{O}_{2}\) consumed can be calculated as follows: Moles of \(\mathrm{O}_{2}\) consumed = Initial moles of \(\mathrm{O}_{2}\) - Remaining moles of \(\mathrm{O}_{2}\) Moles of \(\mathrm{O}_{2}\) consumed = \(10.00 - 6.75 = 3.25\) moles

Calculate the moles of each product using the balanced reactions

In Reaction 1, we can notice that for every 5 moles of \(\mathrm{O}_{2}\) consumed, 4 moles of \(\mathrm{NO}\) are formed. In Reaction 2, we can notice that for every 7 moles of \(\mathrm{O}_{2}\) consumed, 4 moles of \(\mathrm{NO}_{2}\) are formed. Now, let's consider that 'a' moles of \(\mathrm{NO}\) are produced via Reaction 1, and 'b' moles of \(\mathrm{NO}_{2}\) are produced via Reaction 2. Since only 3.25 moles of \(\mathrm{O}_{2}\) are consumed in total, we can set up the following equation using the stoichiometric ratios in the balanced reactions: \[\frac{a}{5} + \frac{b}{7} = 3.25\]

Use moles of \(\mathrm{NH}_{3}\) to find 'a'

Since all \(\mathrm{NH}_{3}\) is consumed in the reactions, we can use its moles to find the value of 'a'. There are 2.00 moles of \(\mathrm{NH}_{3}\) initially. From Reaction 1, for every 4 moles of \(\mathrm{NH}_{3}\) consumed, 4 moles of \(\mathrm{NO}\) are produced. Therefore, \[\frac{a}{4} = 2\] Solve for 'a': \[a = 4\]

Find 'b' using 'a' value

Substitute the value of 'a' found in the previous step back into the equation for moles of \(\mathrm{O}_{2}\) consumed: \[\frac{4}{5} + \frac{b}{7} = 3.25\] Now, solve for 'b': \[\frac{b}{7} = 3.25 - \frac{4}{5}\] \[\frac{b}{7} = \frac{16.25 - 4}{5} = \frac{12.25}{5}\] \[b = \frac{85.75}{5}\] Since 'b' represents moles of \(\mathrm{NO}_{2}\) produced and we're only interested in the moles of \(\mathrm{NO}\) produced, the value of 'a' provides our final answer.

Final answer

The number of moles of \(\mathrm{NO}\) in the product mixture: \(a = 4\) moles.

Key concepts

Balanced Chemical Equation

Balancing a chemical equation is a core concept in stoichiometry that ensures mass conservation. Every element must have the same count of atoms on both the reactant and product sides of the equation. This concept maintains the integrity of the reaction by following the law of conservation of mass.
To illustrate this, consider the unbalanced equations of ammonia reacting with oxygen to form nitrogen monoxide (NO) and nitrogen dioxide (NO2). In the unbalanced form, the number of oxygen or hydrogen atoms on the reactant side does not match the number on the product side. By correctly balancing them:
- For the reaction forming NO: - 4 moles of NH3 react with 5 moles of O2 to produce 4 moles of NO and 6 moles of H2O. - For the reaction forming NO2: - 4 moles of NH3 react with 7 moles of O2 to produce 4 moles of NO2 and 6 moles of H2O.
This balanced state is crucial for accurately calculating the stoichiometric relationships, like the ratio of moles of reactants to products. Being proficient in balancing equations allows you to predict how much product can be formed from given quantities of reactants.

Moles of Reactants and Products

In chemical reactions, the concept of a mole provides a bridge between microscopic atoms and macroscopic quantities. Understanding how moles play into chemical equations is crucial to stoichiometry.
In the given problem, we started with a certain number of moles for reactants: 2.00 moles of ammonia (NH3) and 10.00 moles of oxygen (O2). After the reaction, 6.75 moles of O2 remain, indicating that 3.25 moles were consumed.
Using the balanced chemical equations, you can determine how many moles of each product form. With reaction one, for every five moles of O2 consumed, four moles of NO form, while for reaction two, seven moles of O2 form four moles of NO2.
These ratios illustrate the mole-to-mole conversions critical in stoichiometric calculations. Not only do these conversions help in predicting the amounts of products, but they also ensure efficient use of reactants.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products, and understanding this transformation is fundamental in chemistry. It starts with the knowledge of how molecules interact to form new substances.
In the context of the exercise, ammonia reacts with oxygen in a closed flask, which means it’s a controlled environment where no external influences can alter the outcome. This setup represents a typical reaction scenario in stoichiometry.

• Reaction pathways: Ammonia can react with oxygen in more than one way, forming either NO or NO2. Each pathway has its own balanced equation and stoichiometry.
• Determining reaction outcomes: By knowing how many moles of one product form, you can deduce the pathway and products of the reaction.
• Stoichiometry in reactions: This provides a quantitative means to predict how much product will be formed from particular amounts of reactants.

Understanding chemical reactions involves not just writing and balancing equations but also making informed predictions about the products and yields based on initial conditions.