Question

Consider the following reagents: zinc, copper, mercury (density 13.6 \(\mathrm{g} / \mathrm{mL}\) , silver nitrate solution, nitric acid solution. (a) Given a 500 -mL Erlenmeyer flask and a balloon, can you combine two or more of the foregoing reagents to initiate a chemical reaction that will inflate the balloon? Write a balanced chemical equation to represent this process. What is the identity of the substance that inflates the balloon? (b) What is the theoretical yield of the substance that fills the balloon? (c) Can you combine two or more of the foregoing reagents to initiate a chemical reaction that will produce metallic silver? Write a balanced chemical equation to represent this process. What ions are left behind in solution? (d) What is the theoretical yield of silver?

Short answer

(a) The chemical reaction between zinc and nitric acid produces hydrogen gas, which inflates the balloon. The balanced chemical equation is: \[Zn(s) + 2HNO_{3}(aq) \rightarrow Zn(NO_{3})_{2}(aq) + H_{2}(g)\] (b) With 1 mole of Zn and 2 moles of HNO3 reacting, the theoretical yield of H2 is 1 mole. (c) Copper and silver nitrate produce metallic silver. The balanced chemical equation is: \[Cu(s) + 2AgNO_{3}(aq) \rightarrow Cu(NO_{3})_{2}(aq) + 2Ag(s)\] (d) With 1 mole of Cu and 2 moles of AgNO3 reacting, the theoretical yield of Ag is 2 moles.

Step-by-step solution

Find the suitable reaction to inflate the balloon

We can combine zinc with nitric acid to produce hydrogen gas, which can inflate the balloon. The balanced chemical equation for this reaction is: \[Zn(s) + 2HNO_{3}(aq) \rightarrow Zn(NO_{3})_{2}(aq) + H_{2}(g)\] The substance that inflates the balloon is hydrogen gas (H2). (b) Calculating the theoretical yield of hydrogen gas:

Calculate the molar amounts of the reagents

To find the theoretical yield, we need to know the amounts (in moles) of zinc and nitric acid that are reacting. Assume we have: - 1 mole of Zinc (Zn) (65.38 g/mol) - 2 moles of Nitric acid (HNO3) (63.01 g/mol)

Determine the limiting reagent

As the balanced equation shows, 1 mole of Zn reacts with 2 moles of HNO3. Thus, the molar ratio of Zn:HNO3 is 1:2. In our case, we have 1 mole of Zn and 2 moles of HNO3, which matches the stoichiometric ratio. Therefore, there is no limiting reagent in this case.

Calculate the theoretical yield of H2

According to the balanced equation, 1 mole of Zn reacts to produce 1 mole of H2. Since we have 1 mole of Zn, the theoretical yield of H2 is also 1 mole. (c) Combining reagents to produce metallic silver and writing a balanced chemical equation:

Find the suitable reaction to produce metallic silver

We can combine copper with silver nitrate to produce metallic silver. The balanced chemical equation for this reaction is: \[Cu(s) + 2AgNO_{3}(aq) \rightarrow Cu(NO_{3})_{2}(aq) + 2Ag(s)\] (d) Calculating the theoretical yield of metallic silver:

Calculate the molar amounts of the reagents

To find the theoretical yield of silver, we need to know the amounts (in moles) of copper and silver nitrate that are reacting. Assume we have: - 1 mole of Copper (Cu) (63.55 g/mol) - 2 moles of Silver nitrate (AgNO3) (169.87 g/mol)

Determine the limiting reagent

As the balanced equation shows, 1 mole of Cu reacts with 2 moles of AgNO3. Thus, the molar ratio of Cu:AgNO3 is 1:2. In our case, we have 1 mole of Cu and 2 moles of AgNO3, which matches the stoichiometric ratio. Therefore, there is no limiting reagent in this case.

Calculate the theoretical yield of Ag

According to the balanced equation, 1 mole of Cu reacts to produce 2 moles of Ag. Since we have 1 mole of Cu, the theoretical yield of Ag is 2 moles.

Key concepts

Chemical Reactions

Chemical reactions are processes in which substances, known as reactants, transform into new substances called products. In the exercise, two separate reactions are considered. The first involves zinc reacting with nitric acid, producing hydrogen gas, which can inflate a balloon. This is represented by the balanced chemical equation:

def:chemical_equation1In the exercise, zinc (Zn) and nitric acid (2HNO_{3}) are the reactants, while zinc nitrate (Zn(NO_{3})_{2}) and hydrogen gas (H_{2}) are the products. The second reaction features copper and silver nitrate, leading to the formation of copper nitrate and metallic silver as follows:

def:chemical_equation2These reactions follow the law of conservation of mass, where the total mass of the reactants equals the total mass of the products. The equations are balanced to reflect this, with equal numbers of each atom on both sides of the reaction.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It is a key concept to understand when determining the theoretical yield in chemistry. In the exercise, the stoichiometry of the reactions is determined by the coefficients in the balanced equations, which represent the molar ratios of the reactants and products. For instance, in the reaction between zinc and nitric acid, the stoichiometric ratio is 1:2, meaning one mole of zinc requires two moles of nitric acid to complete the reaction.

With the knowledge of stoichiometry and the balanced chemical equations, one can calculate the theoretical yield, which is the maximum amount of product that can be obtained from a given amount of reactants under ideal conditions. In the exercise, the stoichiometry allows students to determine the theoretical yield of hydrogen gas and metallic silver by using the molar ratios from the equations:

def:stoichiometric_calculation1and

def:stoichiometric_calculation2In both reactions analyzed, the stoichiometric ratios match the amounts provided, suggesting no limiting reagent. Understanding stoichiometry is crucial for predicting the outcomes of chemical reactions and optimizing the use of reactants.

Limiting Reagent

The limiting reagent in a chemical reaction is the reactant that is completely consumed first, thereby limiting the amount of products formed. It dictates the theoretical yield of the reaction. Identifying the limiting reagent is vital for accurately calculating the theoretical yield.

In the exercise provided, students must analyze the molar amounts of reactants in the reactions to determine if there is a limiting reagent. As the stoichiometry reveals, both reactions under consideration do not have a limiting reagent since the reactants are present in amounts that perfectly match the stoichiometric ratios required for the reactions to proceed:

def:limiting_reagent_analysis1and

def:limiting_reagent_analysis2However, in real-world scenarios, it's common to have a limiting reagent due to non-ideal conditions or discrepancies in reactant amounts. Therefore, understanding how to identify the limiting reagent is essential for both theoretical calculations and practical applications in the laboratory.