Question

A gas cylinder having a volume of 10.5 L contains 36.8 g of gas. What is the density of the gas?

Short answer

The density of the gas is 3.5 g/L.

Step-by-step solution

Write down the formula for density

We start by writing down the formula for density: Density = Mass/Volume

Plug in the given values

Now, we plug in the given values: Density = \( \frac{36.8 \,\text{g}}{10.5 \,\text{L}}\)

Calculate the density

Now, we simply divide the mass by the volume to find the density: Density = \( \frac{36.8 \,\text{g}}{10.5 \,\text{L}} = 3.5 \,\frac{\text{g}}{\text{L}}\) The density of the gas is 3.5 g/L.

Key concepts

Density Formula

Understanding the concept of density is vital in the field of chemistry. Density is defined as the mass of an object divided by its volume. This fundamental relationship allows us to quantify how much matter is packed into a given space.

The formula for calculating density is expressed as:
density = \( \frac{mass}{volume} \) where:

• density is measured in units of mass per unit volume (e.g., g/L, kg/m³)
• mass is the amount of matter in the object, typically measured in grams (g) or kilograms (kg)
• volume is the space occupied by the object, often measured in liters (L) or cubic meters (m³)

When dealing with gases, accurate measurements of the mass and volume will lead to a precise calculation of density. A common error in such calculations is the unit mismatch, so always ensure that mass and volume units are compatible before performing the division.

Mass-Volume Ratio

The mass-volume ratio is an essential concept in density and stoichiometry. It tells us how many grams of substance are present in one unit of volume. In the exercise example, we determine how many grams of a gas are in a liter of volume. The ratio is directly used to calculate the density.

The ratio is calculated through the division of mass by volume, as shown in the formula:
density = \( \frac{mass}{volume} \)
This simple yet powerful ratio is integral when it comes to characterizing substances, especially in the field of stoichiometry where reactions are quantified. Calculations involving the mass-volume ratio require careful attention to the units used, to ensure an accurate depiction of the substance's characteristics.

Chemistry Problem Solving

Solving problems in chemistry often involves a systematic approach that integrates various concepts. When addressing a question such as the density of a gas, gathering the correct formulas and understanding the relationships between units are key steps.

An effective problem-solving strategy includes:

• Identifying the known quantities and required units
• Choosing the correct formula that relates these quantities
• Performing dimensional analysis to ensure unit consistency
• Carrying out the numerical calculations carefully

For instance, in the provided exercise, ensuring the mass is in grams and the volume in liters is crucial before applying the density formula. Accuracy in these initial steps helps to avoid common mistakes and leads to the correct solution.

Stoichiometry

Stoichiometry is the study of quantitative relationships in chemical reactions, and it involves mass-volume ratios as part of its core principles. It provides tools to predict the outcomes of reactions and to quantify the reactants and products involved.

In the context of gas density calculation, stoichiometry may extend to determining how a gas's density affects reaction yields or how much of a gas is produced or consumed in a reaction. To solve stoichiometric problems with gases, one might also need to apply the ideal gas law, since the state of the gas (pressure, temperature, and volume) can affect its density.

Mastering stoichiometric techniques is vital for chemists in analyzing and predicting chemical processes. It's all about the conservation of mass and the predictable ratio in which chemicals react, which are foundational concepts traced back to the idea of the mass-volume relation in density.