Question

You mix \(100.0 \mathrm{~mL}\) of \(0.100 \mathrm{M}\) calcium chloride with \(100.0 \mathrm{~mL}\) of \(0.100 \mathrm{M}\) silver nitrate. What species are in solution when the reaction is complete? a. calcium ion, chloride ion, nitrate ion, water b. chloride ion, silver ion, nitrate ion, water c. calcium ion, chloride ion, silver ion, nitrate ion, water d. calcium ion, nitrate ion, water e. calcium ion, silver ion, nitrate ion, water

Short answer

The species present in the solution after the reaction are calcium ion (Ca2+), chloride ion (Cl-), nitrate ion (NO3-), and water (H2O). The correct answer is (a).

Step-by-step solution

Write the balanced chemical equation for the reaction

Calcium chloride (CaCl2) reacts with silver nitrate (AgNO3) to form calcium nitrate (Ca(NO3)2) and silver chloride (AgCl). Write the balanced chemical equation by including coefficients for the reactants and products: \[CaCl_{2} + 2AgNO_{3} \rightarrow Ca(NO_{3})_{2} + 2AgCl \]

Determine the moles of reactants

Given the volume and concentration of calcium chloride and silver nitrate, we can find the moles of each reactant. For calcium chloride: Moles = Volume × Molarity Moles = \(100.0 \mathrm{~mL} × 0.100 \mathrm{M}\) Moles = \(0.0100 \mathrm{~moles}\) For silver nitrate: Moles = Volume × Molarity Moles = \(100.0 \mathrm{~mL} × 0.100 \mathrm{M}\) Moles = \(0.0100 \mathrm{~moles}\)

Determine the limiting reactant

In the balanced chemical equation, 1 mole of calcium chloride reacts with 2 moles of silver nitrate. We have 0.0100 moles of each reactant. Since the mole ratio of calcium chloride to silver nitrate is 1:2, 0.0100 moles of calcium chloride would react with 0.00500 moles of silver nitrate. Therefore, silver nitrate is the limiting reactant, and calcium chloride is in excess.

Identify the ions after the reaction is complete

When the reaction is complete, all moles of silver nitrate have reacted and there are no more silver ions left. The silver ions react with the chloride ions and result in the formation of silver chloride (AgCl), which is a solid compound. Since calcium chloride is in excess, some calcium ions and chloride ions will still be present in the solution. Calcium nitrate is formed, and it is a soluble compound, so it ionizes to form calcium ions (Ca2+) and nitrate ions (NO3−) in the solution. Therefore, the species present in the solution after the reaction are: calcium ions (Ca2+), chloride ions (Cl-), nitrate ions (NO3-), and water (H2O). Which corresponds to answer choice (a).

Key concepts

Limiting Reactant

The concept of the limiting reactant is a fundamental aspect of chemical reaction stoichiometry, critical for understanding how reactions proceed. When two or more reactants are mixed together to produce a product(s), one reactant will be used up first; this is the limiting reactant. The limiting reactant determines the maximum amount of product that can be formed. Once the limiting reactant is fully consumed, the reaction cannot continue, even if other reactants are still present in excess.

Consider a simple analogy: if you are baking and have 5 eggs and 10 cups of flour, your recipe requires 2 eggs for every 1 cup of flour. Once you've used up all 5 eggs, you can't make more of your recipe, even though you have extra flour left. Similarly, in our exercise, although we have equal moles of calcium chloride and silver nitrate, due to the stoichiometry of 1:2, the silver nitrate is in lesser supply in proportion to what is needed, and thus it is the limiting reactant.

Balanced Chemical Equations

A balanced chemical equation provides a representation of a chemical reaction where the number of atoms for each element in the reactants equals the number of atoms for that element in the products. This is in accordance with the law of conservation of mass which states that matter cannot be created or destroyed in a chemical reaction.

To balance an equation, coefficients are placed before the chemical formulas to ensure that the atom count for each element is equal on both sides. In our exercise, the balanced chemical equation is:
\[CaCl_{2} + 2AgNO_{3} \rightarrow Ca(NO_{3})_{2} + 2AgCl \]
This indicates that one mole of calcium chloride reacts with two moles of silver nitrate to produce one mole of calcium nitrate and two moles of silver chloride. Note that the coefficients 1 and 2 help to balance the equation, ensuring that the number of chloride, silver, and nitrate ions are the same on both sides of the reaction.

Mole Concept

The mole concept is a bridging concept of chemistry that relates the mass of substances to the quantity of entities, such as atoms, ions, or molecules. One mole is defined as the amount of a substance that contains as many entities as there are atoms in 12 grams of isotopically pure carbon-12, which is approximately \(6.022 \times 10^{23}\) entities.

This number, known as Avogadro's number, provides a physical meaning to the mole concept. When dealing with chemical reactions, knowing the number of moles helps us understand the amounts of reactants and products involved. In our exercise, by multiplying the volume of the solutions by their molarity, we calculated the moles of each reactant involved in the reaction. This allows us to use the balanced chemical equation to find the proportion in which these reactants combine, leading us to identify the limiting reactant and predict the outcome of the reaction.