Question

What is the molarity of \(\mathrm{ZnCl}_{2}\) that forms when \(25.0 \mathrm{~g}\) of zinc completely reacts with \(\mathrm{CuCl}_{2}\) according to the following reaction? Assume a final volume of \(275 \mathrm{~mL}\). $$ \mathrm{Zn}(s)+\mathrm{CuCl}_{2}(a q) \longrightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{Cu}(s) $$

Short answer

The molarity of ZnCl2 is the ratio of moles of ZnCl2 formed to the volume of solution in liters.

Step-by-step solution

Write down the given information

Identify the given information: the mass of zinc is 25.0 g, and the final volume of solution is 275 mL. The balanced chemical equation is: \[\mathrm{Zn}(s)+\mathrm{CuCl}_{2}(aq) \longrightarrow \mathrm{ZnCl}_{2}(aq)+\mathrm{Cu}(s)\]

Calculate moles of Zn

Calculate the number of moles of zinc used in the reaction using its molar mass. The molar mass of zinc (\text{Zn}) is approximately 65.38 g/mol. Using the formula: \[\text{moles of Zn} = \frac{\text{mass of Zn}}{\text{molar mass of Zn}}\], we calculate the moles of Zn.

Determine moles of ZnCl2 formed

According to the balanced equation, 1 mole of Zn reacts to form 1 mole of ZnCl2. Therefore, the moles of ZnCl2 formed will be the same as the moles of Zn initially used.

Convert volume to liters

Convert the final volume of the solution from milliliters to liters by dividing by 1000 because there are 1000 milliliters in a liter. \[\text{Volume in liters} = \frac{275\, \text{mL}}{1000}\]

Calculate molarity of ZnCl2

Molarity is defined as moles of solute per liter of solution. Use the moles of ZnCl2 and the volume in liters to calculate the molarity of ZnCl2 with the formula: \[\text{Molarity} = \frac{\text{moles of ZnCl2}}{\text{volume in liters}}\].

Key concepts

Stoichiometry

Stoichiometry is a section of chemistry that involves calculating the quantities of reactants and products in a chemical reaction. It is based on the conservation of mass where the number of atoms of each element must be the same before and after the reaction. This means for every chemical reaction, there is a fixed ratio of reactants that combine to form a fixed ratio of products.

For example, in the reaction \[\mathrm{Zn}(s)+\mathrm{CuCl}_{2}(aq) \longrightarrow \mathrm{ZnCl}_{2}(aq)+\mathrm{Cu}(s)\],the stoichiometry shows that 1 mole of zinc reacts with 1 mole of copper(II) chloride to produce 1 mole of zinc chloride and 1 mole of copper. Using stoichiometry, we can relate the mass of zinc used in the reaction to the amount of zinc chloride produced.

Molar Mass

The molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is a critical concept in stoichiometry since it allows us to convert mass, which is easily measured, to moles, which is used in the balanced chemical equation.

The molar mass of an element can be found on the periodic table as the atomic weight. For compounds like \(\mathrm{ZnCl}_{2}\), the molar mass is calculated by adding the molar masses of all the atoms in the molecule. To solve our problem, we first determine the molar mass of zinc (65.38 g/mol). Knowing this, we can calculate the number of moles of zinc used in the reaction with the formula \[\text{moles of Zn} = \frac{\text{mass of Zn}}{\text{molar mass of Zn}}\].

Understanding the concept of molar mass and how to calculate it is vital for correctly solving stoichiometry problems.

Chemical Reaction

A chemical reaction is a process where substances, the reactants, undergo chemical change to form new substances, the products. Represented by chemical equations, reactions must be balanced, meaning the number of atoms for each element in the reactants must equal the atoms in the products. This allows for the precise calculations involved in stoichiometry.

In the given reaction \[\mathrm{Zn}(s)+\mathrm{CuCl}_{2}(aq) \longrightarrow \mathrm{ZnCl}_{2}(aq)+\mathrm{Cu}(s)\],zinc and copper(II) chloride are the reactants, and zinc chloride and copper are the products. The balanced equation tells us that the reaction proceeds in a 1:1:1:1 ratio. This ratio is the foundation of the stoichiometric calculations that follow, such as determining the molarity, which relies on knowing the amount of product formed in the reaction.