Problem 91 - Chemistry: Atoms First

Question

Calculate these volumes. (a) What is the volume of \(25 \mathrm{g}\) iodine, density \(=4.93 \mathrm{g} / \mathrm{cm}^{3} ?\) (b) What is the volume of 3.28 g gaseous hydrogen, density \(=0.089 \mathrm{g} / \mathrm{L}\) ?

Step-by-Step Solution

Answer

The volume of iodine is approximately 5.07 cm³, and the volume of gaseous hydrogen is approximately 36.85 L.

Step 1: Calculate the Volume of Iodine

Use the formula for volume: Volume = Mass / Density. Given the mass of iodine is 25 g and its density is 4.93 g/cm³, the volume in cubic centimeters can be calculated as follows: Volume = 25 g / 4.93 g/cm³.

Step 2: Calculate the Volume of Gaseous Hydrogen

Again, use the formula for volume: Volume = Mass / Density. Given the mass of gaseous hydrogen is 3.28 g and its density is 0.089 g/L, the volume in liters can be calculated as follows: Volume = 3.28 g / 0.089 g/L.

Key Concepts

Density and Volume Relationship

Understanding the relationship between density and volume is essential when working with different materials in chemistry. Density is the measure of how much mass is contained in a given unit volume of a substance. The formula for density is \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). This formula highlights the inverse relationship between density and volume: as the density of a substance increases, the volume that a given mass occupies tends to decrease, assuming the mass remains constant.

For example, iodine has a high density, meaning a small volume of iodine would have a significant mass. Conversely, gaseous hydrogen has a very low density, which implies that a relatively large volume would be necessary to encompass a mass similar to that of a much smaller volume of iodine.

Mass to Volume Conversion

The conversion from mass to volume is a straightforward application of the density formula, which is often needed in chemical calculations. To find the volume when the mass and density are known, we rearrange the density formula to \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \). This conversion is useful when you have a specific amount of a substance, perhaps a reactant in a reaction, and you need to know how much space it will occupy.

Considering the solved textbook exercise, this conversion allowed us to determine that 25 g of iodine, which is quite dense, occupies a smaller volume than one might intuitively expect. Likewise, even a small mass of gaseous hydrogen fills a large volume due to its very low density. Knowing how to perform mass to volume conversions is key in preparing chemicals and solutions as well as in the analysis of reaction products.

Volume Calculation Formula

The volume calculation formula expressed as \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \) is crucial for many laboratory and industrial applications. To use this formula effectively, it is essential to have the mass of the substance and its density. These values must be in compatible units, such as grams for mass and grams per cubic centimeter or grams per liter for density, depending on whether the substance is a solid or a gas.

In our textbook example, knowing how to use the correct units allowed for the precise calculation of volume in both solid iodine and gaseous hydrogen. Remember that for solid materials, the standard volume unit is cubic centimeters (\(\text{cm}^3\)), while for gases, it is often liters (L). To become proficient in these conversions, it's recommended to practice with various substances and scenarios to understand how changes in mass and density influence the volume outcome.