Problem 164 - General Chemistry

Question

Zinc ore (zinc sulfide) is treated with sulfuric acid, leaving a solution with some undissolved bits of material and releasing hydrogen sulfide gas. If \(10.8 \mathrm{~g}\) of zinc ore is treated with \(50.0 \mathrm{~mL}\) of sulfuric acid (density \(1.153 \mathrm{~g} / \mathrm{mL}\) ), \(65.1 \mathrm{~g}\) of solution and undissolved material remains. In addition, hydrogen sulfide (density \(1.393 \mathrm{~g} / \mathrm{L}\) ) is evolved. What is the volume (in liters) of this gas?

Step-by-Step Solution

Answer

The volume of hydrogen sulfide gas evolved is approximately 2.40 liters.

Step 1: Identify the Masses

First, calculate the mass of sulfuric acid. Given the volume of sulfuric acid is \(50.0 \text{ mL}\) and the density is \(1.153 \text{ g/mL}\), the mass of sulfuric acid is \((50.0 \text{ mL}) \times (1.153 \text{ g/mL}) = 57.65 \text{ g}\).

Step 2: Apply Mass Conservation

The total initial mass is the sum of the masses of zinc ore and sulfuric acid, which is \(10.8 \text{ g} + 57.65 \text{ g} = 68.45 \text{ g}\). The final mass (given) is \(65.1 \text{ g}\).

Step 3: Calculate Mass of Evolved Gas

Use the law of conservation of mass. The mass of the hydrogen sulfide gas evolved is the difference between the initial and final mass: \[ 68.45 \text{ g} - 65.1 \text{ g} = 3.35 \text{ g}. \]

Step 4: Convert Mass of Gas to Volume

Given the density of hydrogen sulfide gas is \(1.393 \text{ g/L}\), use the formula for density \(\text{Density} = \frac{\text{Mass}}{\text{Volume}}\) to find the volume:\[ \text{Volume} = \frac{3.35 \text{ g}}{1.393 \text{ g/L}} \approx 2.40 \text{ L}. \]

Key Concepts

Mass Conservation

The law of mass conservation is a fundamental principle in chemistry, suggesting that mass remains constant in a closed system. It doesn't disappear or appear out of thin air.
In our case, during the chemical reaction between zinc ore and sulfuric acid, the mass we start with equals the mass we end with. The initial mass comprises the sum of zinc ore and sulfuric acid.

By calculating this sum, you can better understand how the system compensates for any changes:

• The mass of zinc ore: 10.8 g
• The mass of sulfuric acid: 57.65 g

The total initial mass is thus 68.45 g.
The remaining mass, after the reaction, is 65.1 g, involving the leftover solution and material.
This allows us to deduce that the mass that vanished is conserved as hydrogen sulfide gas, which amounts to 3.35 g. This kind of understanding helps you see the invisible exchanges happening in chemical processes!

Density Calculations

Density is a central concept in chemistry, explaining how much mass fits in a given volume.
Here, density is expressed as mass per unit volume, which helps us determine how dense an object or substance is. The formula for density is:\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]If you know two of these elements, you can always calculate the third.

In the exercise, sulfuric acid has a density of 1.153 g/mL, allowing us to convert the given volume of 50.0 mL into its corresponding mass.
This results in a mass calculation of:\[ \text{Mass} = 50.0 \text{ mL} \times 1.153 \text{ g/mL} = 57.65 \text{ g} \]Similarly, the density for hydrogen sulfide gas is 1.393 g/L. With the mass of the evolved gas, you can backtrack to find the volume. Understanding how density relates mass and volume helps in converting these particle amounts into relatable numbers.

Gas Volume Conversion

Converting the mass of a gas to its volume involves using its density, turning abstract numbers into familiar measurements.
In this situation, to find out how much space 3.35 g of hydrogen sulfide occupies, we use its density: 1.393 g/L.

The process involves using the rearranged density formula for volume:\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]So for hydrogen sulfide, we calculate:\[ \text{Volume} = \frac{3.35 \text{ g}}{1.393 \text{ g/L}} \approx 2.40 \text{ L} \]
This conversion gives insight not only into the amount of gas but also the principles of gas laws and helps confirm the behavior of gases in different contexts. When practicing this conversion, remember it's all about finding relationships between elements of a chemical equation.