Question

If \(2.02\) g of hydrogen gas occupies \(22.4\) liters, calculate the density of hydrogen gas in grams per milliliter.

Short answer

The density of hydrogen gas is approximately \(0.00009018\) g/mL.

Step-by-step solution

Extract given information

We are given the mass and volume of hydrogen gas: - Mass = 2.02 g - Volume = 22.4 L

Calculate density in g/L

Use the formula for density: density = mass/volume Density (g/L) = 2.02 g / 22.4 L = 0.09018 g/L

Convert density to g/mL

Since there are 1000 mL in 1 L, we can convert the density to g/mL: Density (g/mL) = 0.09018 g/L * (1 L / 1000 mL) = 0.00009018 g/mL To summarize, the density of hydrogen gas is approximately 0.00009018 g/mL.

Key concepts

Hydrogen Gas

Hydrogen gas, often represented as H₂, is one of the most abundant elements in the universe. It is a colorless, odorless, and highly flammable gas. Hydrogen is the lightest element known, which is part of why it is often used as a reference point for discussions about gases and their properties. It is made up of molecules consisting of two hydrogen atoms bonded together. This simplicity and low molecular weight make hydrogen gas an important subject of study, particularly when discussing concepts like density and the mass-to-volume relationship of substances.

Grams per Milliliter

When calculating density, we often use the unit grams per milliliter (g/mL) to express how much mass is contained within a given volume. This measurement reveals the compactness of a substance.

• If a substance has a high density, that means more mass is packed into a given volume.
• If it has a low density, less mass occupies that same space.

In the exercise, the density of hydrogen gas is given in grams per milliliter, converted from grams per liter to account for smaller quantities. Understanding this conversion is essential for accurately interpreting substance properties, especially in chemistry and physics.

Mass and Volume Relationship

The relationship between mass and volume forms the backbone of understanding density. Mass refers to the amount of matter an object contains, while volume refers to the amount of space that object occupies. Both of these measurements are crucial in density calculations.

• A higher mass in a given volume generally indicates a higher density.
• Conversely, the same mass in a larger volume suggests a lower density.

In the exercise, you are given the mass of hydrogen gas (2.02 g) and its volume (22.4 L). Despite its light weight, hydrogen gas occupies a significant amount of space due to its low density and gaseous state, which is a fundamental quality that can be measured and calculated.

Density Formula

The formula for density is quite straightforward, where density equals mass divided by volume: \(\text{Density} = \frac{\text{Mass}}{\text{Volume}} \)To solve for density, use the given mass and volume values in this formula. The exercise instructs us to first calculate density in grams per liter:\[\frac{2.02 \text{ g}}{22.4 \text{ L}} = 0.09018 \text{ g/L} \]Then, convert this result to grams per milliliter by dividing by 1000, as 1 liter equals 1000 milliliters:\[0.09018 \text{ g/L} \times \frac{1 \text{ L}}{1000 \text{ mL}} = 0.00009018 \text{ g/mL} \]This conversion ensures accuracy in measurements, especially when precise calculations are necessary in laboratory settings.