Question

Consider the reaction between \(1.0 \mathrm{~L}\) of \(3.0 \mathrm{M} \mathrm{AgNO}_{3}(a q)\) and \(1.0 \mathrm{~L}\) of \(1.0 \mathrm{M} \mathrm{CuCl}_{2}(a q)\) according to the equation: $$ 2 \mathrm{AgNO}_{3}(a q)+\mathrm{CuCl}_{2}(a q) \rightarrow 2 \mathrm{AgCl}(s)+\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}(a q) $$ Which of the following will increase the amount of AgCl (s) produced? a. Adding another \(1.0 \mathrm{~L}\) of \(3.0 \mathrm{M} \mathrm{AgNO}_{3}(a q)\) b. Adding another \(1.0 \mathrm{~L}\) of \(1.0 \mathrm{M} \mathrm{CuCl}_{2}(a q)\) c. Adding \(1.0 \mathrm{~L}\) of water to the original \(\mathrm{AgNO}_{3}(a q)\) solution d. Allowing all of the water to evaporate from the resulting solution e. At least two of the above will increase the amount of \(\mathrm{AgCl}(s)\) produced.

Short answer

The short answer is: Adding another \(1.0 L\) of \(1.0 M\) \(CuCl_{2}(aq)\) (option b) will increase the amount of AgCl(s) produced because it increases the amount of the limiting reactant, \(CuCl_2\), allowing more reaction to take place.

Step-by-step solution

Identify the Limiting Reactant#

To do this, we compare the moles of each reactant, then divide it by its stoichiometric coefficient in the balanced reaction. For AgNO₃, we have \(1.0 L * 3.0 M = 3.0 moles\). Stoichiometric coefficient of AgNO₃ is 2. For CuCl₂, we have \(1.0 L * 1.0 M = 1.0 moles\). Stoichiometric coefficient of CuCl₂ is 1. Limiting reactant can be determined as: \(AgNO_3 = \frac{3.0}{2} = 1.5\) \(CuCl_2 = \frac{1.0}{1} = 1.0\) Since CuCl₂ has a lower value when divided by its stoichiometry coefficient, it is the limiting reactant. This means that CuCl₂ determines the amount of AgCl formed.

Discuss Each Option and Determine Results#

(a) Adding another 1.0 L of 3.0 M AgNO₃(aq): This option results in an excess of AgNO₃ but since CuCl₂ is still the limiting reactant, there will be no effect on the amount of AgCl produced. (Incorrect) (b) Adding another 1.0 L of 1.0 M CuCl₂(aq): This option increases the amount of the limiting reactant CuCl₂, thus allowing more reaction to take place, and an increase in the amount of AgCl produced. (Correct) (c) Adding 1.0 L of water to the original AgNO₃(aq) solution: This option simply dilutes the AgNO₃ solution. It doesn't affect the actual amount of each reactant, therefore it does not increase the amount of AgCl produced. (Incorrect) (d) Allowing all of the water to evaporate from the resulting solution: This option doesn't affect the actual amount of reactants, it just removes the solvent and changes the state of the solution. This does not increase the amount of AgCl produced. (Incorrect) (e) At least two of the above will increase the amount of AgCl(s) produced: Since only one option (b) increases the amount of AgCl, this statement is false. (Incorrect) The correct answer is option (b).

Key concepts

Stoichiometry

Stoichiometry is the section of chemistry that focuses on the quantitative relationships between the reactants and products in a chemical reaction. It involves using the coefficients from a balanced chemical equation to calculate the masses, volumes, and moles of substances. Understanding stoichiometry is essential for determining which reactant is the limiting reactant in a reaction—which is the reactant that will be completely used up first, thereby dictating the maximum amount of product that can be formed.

For example, in the problem we are considering, stoichiometry comes into play when you need to figure out how much silver chloride (AgCl) can be produced from the given quantities of silver nitrate (AgNO₃) and copper(II) chloride (CuCl₂). The coefficients in the balanced chemical equation imply the ratio in which the reactants combine, which is especially important when determining the correct answer to the multiple-choice question provided.

Chemical Reactions

Chemical reactions involve the transformation of substances through the breaking and forming of chemical bonds to create new substances. The reactants are the starting materials, and the products are the substances formed as a result of the reaction. Each chemical reaction is characterized by a balanced equation that shows the conservation of mass where the number of atoms of each element involved remains unchanged before and after the reaction.

When we look at the reaction between AgNO₃ and CuCl₂, we see that the reactants combine in a specific molar ratio to produce silver chloride (AgCl) and copper(II) nitrate (Cu(NO₃)₂). This ratio is guided by the reaction's stoichiometry. Predicting the outcome of mixing different quantities of reactants, such as in the exercise provided, requires a strong grasp of the principles governing chemical reactions.

Molar Concentration

Molar concentration, often represented as molarity and denoted by the symbol M, is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution. This concept is crucial in predicting how much product can be formed in a reaction when reactants are in a solution, as it allows you to estimate the number of moles of each reactant available to react.

In the exercise presented, the molar concentrations of AgNO₃ and CuCl₂ dictate the amounts of the reactants in solution. By knowing the volume of the solutions and their molarities, you can calculate the moles of each reactant and then use stoichiometry to determine the limiting reactant, which leads to answering the question about increasing the yield of AgCl. For instance, understanding that option (b) adds more moles of the limiting reactant (CuCl₂), allows students to deduce that this would increase the amount of AgCl produced.