Question

Solid copper can be produced by passing gaseous ammonia over solid copper(II) oxide at high temperatures. The other products of the reaction are nitrogen gas and water vapor. The balanced equation for this reaction is: $$ 2 \mathrm{NH}_{3}(g)+3 \mathrm{CuO}(s) \rightarrow \mathrm{N}_{2}(g)+3 \mathrm{Cu}(s)+3 \mathrm{H}_{2} \mathrm{O}(g) $$ What is the theoretical yield of solid copper that should form when \(18.1 \mathrm{~g}\) of \(\mathrm{NH}_{3}\) is reacted with \(90.4 \mathrm{~g}\) of \(\mathrm{CuO}\) ? If only \(45.3 \mathrm{~g}\) of copper is actually collected, what is the percent yield?

Short answer

The theoretical yield of solid copper is 72.2 g, and the percent yield for this reaction is approximately 62.7%.

Step-by-step solution

Calculate the moles of the reactants

We are given the mass of ammonia (NH₃) and copper(II) oxide (CuO). We will calculate the number of moles of each reactant using their molar masses. For NH₃: molar mass = 14.01 g/mol (N) + 3 × 1.01 g/mol (H) = 17.03 g/mol Moles of NH₃ = mass/molar mass = 18.1 g / 17.03 g/mol ≈ 1.063 mol For CuO: molar mass = 63.55 g/mol (Cu) + 16.00 g/mol (O) = 79.55 g/mol Moles of CuO = mass/molar mass = 90.4 g / 79.55 g/mol ≈ 1.136 mol

Determine the limiting reactant

In order to find the theoretical yield, we need to determine the limiting reactant, which will be consumed completely and determine the amount of product formed. The stoichiometry of the balanced equation for NH₃ and CuO is 2:3. Mole ratio (NH₃:CuO) = 2:3 Divide the moles of reactants by their respective coefficients: NH₃: 1.063 mol / 2 ≈ 0.5315 CuO: 1.136 mol / 3 ≈ 0.3787 Since CuO has the lowest ratio, it is the limiting reactant.

Calculate the theoretical yield of solid copper (Cu)

Now, we will use the limiting reactant, CuO, to determine the theoretical yield of solid copper (Cu). The stoichiometry of the balanced equation for CuO and Cu is 3:3. Moles of Cu = moles of CuO (as the ratio is 1:1) Moles of Cu = 1.136 mol Now, convert the moles of Cu to grams: Mass of Cu = moles × molar mass = 1.136 mol × 63.55 g/mol ≈ 72.2 g The theoretical yield of solid copper is 72.2 g.

Calculate the percent yield

We are given the actual yield of solid copper (45.3 g) and have calculated the theoretical yield (72.2 g). The percent yield can be calculated using the following formula: Percent yield = (actual yield / theoretical yield) × 100 Percent yield = (45.3 g / 72.2 g) × 100 ≈ 62.7% The percent yield for this reaction is approximately 62.7%.

Key concepts

Limiting Reactant

Understanding the concept of a limiting reactant is crucial in the field of chemistry, particularly when carrying out reactions where quantities of reagents must be precisely measured. A limiting reactant is the substance in a chemical reaction that is entirely consumed first and thus determines the amount of product that can be formed. It is akin to the number of cars that can be produced on an assembly line being limited by the number of tires available—if there are only enough tires for 100 cars, then only 100 cars can be made, regardless of how much metal or other parts you have.

For students grappling with the idea, an effective methodology includes clear step-by-step identification of the limiting reactant. Start by finding the molar mass of each reactant, then convert given weights to moles. The next step is to use the stoichiometry—ratios given by the balanced chemical equation—to compare the mole quantities in proportion. The reactant that runs out first—that will produce the least amount of product when the stoichiometry is applied—is your limiting reactant. This approach helps students identify limiting reactants and predict the amount of product formed during a reaction.

Stoichiometry

Stoichiometry lies at the heart of chemical reactions. This branch of chemistry deals with the quantitative relationships, or the ratio of amounts, of reactants and products in a chemical reaction as described by the balanced chemical equation. Students often visualize stoichiometry as a recipe: if you’re baking a cake, you need a certain number of eggs, cups of flour, and cups of sugar. If you double the eggs, you must double the other ingredients to keep the proportions correct for the cake to turn out right.

In the context of our exercise, stoichiometry is used to determine the theoretical yield of copper. By using the coefficients of the balanced equation, we can understand the proportionality of reactants to products. Therefore, understanding stoichiometry is essential for predicting the expected amount of each substance used and produced in a reaction. Having solid grasp on stoichiometry not only helps with theoretical predictions but also with practical applications in the lab, where it is vital for preparing the precise amounts of substances needed for a reaction to occur as intended.

Percent Yield

The calculation of percent yield is a way to measure the efficiency of a chemical reaction. It is the ratio of the actual yield—the amount of product you actually obtain—to the theoretical yield—the maximum amount of product that could be formed based on stoichiometry, considering all reactants fully convert to products. The formula for percent yield is \[\begin{equation}\text{Percent Yield} = \left( \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \right) \times 100%\text{.}\text{\end{equation}\]}For students, it's important to understand that the percent yield can never exceed 100%; that would mean you got more product than scientifically possible given the starting materials. Various factors such as reactions not proceeding to completion, side reactions, or loss of product during recovery can lower the percent yield. When one further contextualizes in a real lab scenario, it becomes clear why reactions might not be perfectly efficient. Emphasizing this connection helps students appreciate the concept of percent yield beyond mere numerical calculation and recognize it as a measure of how