Question

When gascous ammonia is passed over solid copper(II)oxide at high temperatures, nitrogen gas is formed. $$ 2 \mathrm{NH}_1(\mathrm{~g})+3 \mathrm{CuO}(s) \rightarrow \mathrm{N}_2(\mathrm{~g})+3 \mathrm{Cu}(s)+3 \mathrm{H}_2 \mathrm{O}(\mathrm{g}) $$ What is the limiting reagent when 34 grams of ammonia form 26 grams of nitrogen in a reaction that runs to completion? A. \(\mathrm{NH}_3\) B. CuO C. \(\mathrm{N}_2\) D. \(\mathrm{Cu}\)

Short answer

B. CuO

Step-by-step solution

Determine molar masses

Calculate the molar mass of each compound involved in the reaction. For ammonia (NH₃), the molar mass is approximately 17 g/mol. For nitrogen (N₂), it is approximately 28 g/mol.

Calculate moles of each reactant

Using the given mass of ammonia (NH₃), calculate the moles: \[ \text{Moles of NH}_3 = \frac{34 \text{ g}}{17 \text{ g/mol}} = 2 \text{ mol} \] For nitrogen (N₂), calculate the moles using its given mass: \[ \text{Moles of N}_2 = \frac{26 \text{ g}}{28 \text{ g/mol}} \text{ g/mol} = 0.929 \text{ mol} \]

Identify the stoichiometric ratio

From the balanced chemical equation: \[ 2 \text{ NH}_3 (\text{g}) + 3 \text{ CuO} (\text{s}) \rightarrow \text{ N}_2 (\text{g}) + 3 \text{ Cu} (\text{s}) + 3 \text{ H}_2\text{O} (\text{g}) \] The ratio is 2:3:1:3:3 respectively for NH₃, CuO, N₂, Cu, and H₂O.

Compare mole ratios

From the moles calculated:\[ \text{For NH}_3: 2 \text{ mol} \rightarrow \text{ expected N}_2: 1 \text{ mol} \]\[ \text{Given N}_2: 0.929 \text{ mol} \rightarrow \text{ expected NH}_3: 1.858 \text{ mol} \] The given moles of NH₃ (2 mol) are slightly more than twice the expected moles of NH₃ based on the actual N₂ formed (1.858 mol).

Determine the limiting reagent

Since more NH₃ was present than required to form the given amount of N₂, the limiting reagent must be CuO which isn't in excess. Therefore, CuO determines the amount of product formed.

Key concepts

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships of reactants and products in chemical reactions. It allows us to predict how much of each substance is involved in a reaction. To understand stoichiometry, it's important to:

• Write balanced chemical equations.
• Use molar ratios to convert between moles of different substances.
• Calculate mass, volume, or particles of reactants/products using molar relationships.

In the given problem, stoichiometry helps us find the limiting reagent. By balancing the reaction and using molecular weights, we can determine which reactant runs out first, limiting the amount of product formed.

Chemical Reactions

Chemical reactions involve the transformation of one or more substances into new substances. During a reaction, reactant molecules collide and bonds break, forming new products.

In the equation: \[2 \text{ NH}\text{₃} (\text{g}) + 3 \text{ CuO} (\text{s}) \rightarrow \text{ N}\text{₂} (\text{g}) + 3 \text{ Cu} (\text{s}) + 3 \text{ H}\text{₂O} (\text{g})\] ammonia (NH₃) reacts with copper(II) oxide (CuO) to produce nitrogen gas (N₂), copper (Cu), and water vapor (H₂O).

Key points to remember:

• Reactants are the starting materials; products are the substances formed.
• Balanced equations ensure the same number of each atom type exists on both sides.
• Coefficients in a balanced equation reflect the mole ratios of reactants and products.

Mole Calculations

The mole is a fundamental unit in chemistry that represents a specific number of particles, usually atoms, molecules, or ions. One mole equals Avogadro's number \[ (6.022 \times 10^{23}) \] of particles.

To find the limiting reagent, you calculate the moles of each reactant. For ammonia: \[ \text{Moles of NH}\text{₃} = \frac{34 \text{ g}}{17 \text{ g/mol}} = 2 \text{ mol} \] And for nitrogen: \[ \text{Moles of N}\text{₂} = \frac{26 \text{ g}}{28 \text{ g/mol}} = 0.929 \text{ mol}\]

Using these calculations, you can compare which reactant limits the reaction by seeing which one forms fewer products.

Inorganic Chemistry

Inorganic chemistry is the study of inorganic compounds, which generally do not contain carbon-hydrogen bonds. This branch covers compounds like salts, metals, and minerals.

In the problem, we deal with inorganic compounds: ammonia (NH₃), copper(II) oxide (CuO), nitrogen (N₂), copper (Cu), and water (H₂O).

These reactions are common in inorganic chemistry due to:

• Redox reactions, where electrons are transferred between substances.
• Formation of solid products from gaseous or liquid reactants.
• High-temperature reactions, changing reactants into more stable products.

Understanding these principles helps us predict reaction behaviors, such as identifying limiting reagents and determining the maximum amount of product formed.