Problem 87 - General Chemistry: Principles and Modern Applications

Question

In an experiment, \(125 \mathrm{cm}^{3}\) of zinc and \(125 \mathrm{cm}^{3}\) of iodine are mixed together and the iodine is completely converted to \(164 \mathrm{cm}^{3}\) of zinc iodide. What volume of zinc remains unreacted? The densities of zinc, iodine, and zinc iodide are \(7.13 \mathrm{g} / \mathrm{cm}^{3}, 4.93 \mathrm{g} / \mathrm{cm}^{3}\) and \(4.74 \mathrm{g} / \mathrm{cm}^{3}\), respectively.

Step-by-Step Solution

Answer

The volume of unreacted zinc is approximately \(102.42 \mathrm{cm^{3}}\).

Step 1: Calculate the Mass of the Initial Substances

Use the volumes and densities of the initial substances (zinc and iodine) to calculate their masses. The mass is simply the volume times the density. Therefore, the mass of zinc and iodine can be calculated as: Mass_Zn = \(7.13 \mathrm{g/cm^3} \times 125 \mathrm{cm^3} = 891.25g\) Mass_I = \(4.93 \mathrm{g/cm^3} \times 125 \mathrm{cm^3} = 616.25g\)

Step 2: Calculate the Total Mass Before the Reaction

Add the masses of zinc and iodine calculated in Step 1 to get the total mass before the reaction: Total mass before = \(891.25g + 616.25g = 1507.5g\)

Step 3: Calculate the Mass of Zinc Iodide After the Reaction

Using the volume and density of zinc iodide, calculate its mass: Mass_ZnI2 = \(4.74 \mathrm{g/cm^3} \times 164 \mathrm{cm^3} = 777.16g\)

Step 4: Calculate the Mass of Unreacted Zinc

Subtract the mass of zinc iodide from the total mass before the reaction to find the mass of the unreacted zinc: Mass_Zn(unreacted) = \(1507.5g - 777.16g = 730.34g\)

Step 5: Convert the Mass of Unreacted Zinc to Volume

Use the density of zinc to convert the mass of the unreacted zinc to volume. Volume = mass / density. Thus, Volume_Zn(unreacted) = \(730.34g / 7.13 \mathrm{g/cm^3} = 102.42 \mathrm{cm^3}\)

Key Concepts

Mass-Volume Calculations

When dealing with chemical reactions, it's common to go back and forth between mass and volume. These transitions are often facilitated by a substance's density. Let's break down these types of calculations with practical examples.

To find mass from volume, multiply the volume by the substance's density. This gives us the mass because density (g/cm³) times volume (cm³) leads to mass in grams.

On the other hand, to find volume from a given mass, you divide the mass by the substance's density. Volume = mass / density allows you to rearrange the formula to solve for volume.

Understanding these basics will enable you to move seamlessly between mass and volume, which is crucial for stoichiometric calculations.

Density

Density is a measure of how much mass is contained in a given volume. It is crucial in stoichiometry because it allows conversions between mass and volume.

• Density = Mass / Volume
• A high density means a lot of mass in a small volume, while low density shows less mass in the same space.

Knowing the density of substances like zinc, iodine, and zinc iodide helps compute their respective masses when given their volumes.
For example, if you have 125 cm³ of zinc with a density of 7.13 g/cm³, the mass is calculated by multiplying 125 by 7.13, resulting in a mass of 891.25 grams.
Understanding the concept of density enables you to perform precise stoichiometric calculations and better understand the relationship between a substance's mass and volume.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products. This transformation follows the law of conservation of mass, meaning the mass of reactants equals the mass of products.

In the example with zinc and iodine reacting to form zinc iodide, zinc initially reacts with iodine to produce the compound. Any unreacted zinc remains leftover. By calculating the amount of zinc iodide formed, the law of conservation allows us to determine if all components were consumed.

This exercise also highlights the importance of stoichiometry in ensuring reactants are correctly proportioned to form products without excess, which can impact the efficiency of chemical processes.
Understanding these principles ensures more effective and accurate predictions in chemical equations and reactions.