Question

Suppose a 5.00 L sample of \(O_{2}\) at a given temperature and pressure contains \(1.08 \times 10^{23}\) molecules. How many molecules would be contained in each of the following at the same temperature and pressure? a. 5.0 \(LH_{2}\) b. 5.0 \(LCO_{2}\) c. 10.0 \(L NH_{3}\)

Short answer

Each 5.0 L sample contains \(1.08 \times 10^{23}\) molecules. A 10.0 L sample contains \(2.16 \times 10^{23}\) molecules.

Step-by-step solution

Understand the Problem

The problem provides the number of molecules in a 5.00 L sample of \(O_2\). We need to find the number of molecules in different volumes of other gases under the same temperature and pressure.

Use Avogadro's Law

Avogadro's Law states that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules. Therefore, the number of molecules in a 5.00 L sample of any gas will be the same as in 5.00 L of \(O_2\).

Calculate Molecules in 5.0 L of Different Gases

Since 5.00 L of \(O_2\) contains \(1.08 \times 10^{23}\) molecules, the same is true for 5.0 L of \(H_2\) and 5.0 L of \(CO_2\).

Calculate Molecules in 10.0 L of a Gas

For 10.0 L of \(NH_3\), we need to double the number of molecules because the volume is twice that of the 5.00 L sample of \(O_2\). Therefore, the number of molecules in 10.0 L of \(NH_3\) is \(2 \times 1.08 \times 10^{23} = 2.16 \times 10^{23}\).

Key concepts

Molecule Calculations

In the given exercise, understanding molecule calculations is key. Molecules are the tiny particles that make up gases. According to Avogadro's Law, at constant temperature and pressure, equal volumes of any gas contain the same number of molecules. This fundamental principle is used to solve the problem.

For example, if 5.00 liters (L) of oxygen gas (\(O_2\)) contains 1.08 × 10^23 molecules, then 5.00 L of any other gas, such as hydrogen (\(H_2\)) or carbon dioxide (\(CO_2\)), will also contain exactly 1.08 × 10^23 molecules under the same conditions.

To calculate molecules in different gas volumes:

• Use the given molecule number for a specified volume (e.g., 5.00 L).
• Apply Avogadro's Law to find the number of molecules for the asked volumes of other gases.

This straightforward relationship is what makes Avogadro's Law so powerful in chemistry.

Gas Volume

Gas volume plays a crucial role in understanding gas behavior and calculations. It is the space that gas particles occupy, and in any given container, the gas volume can be measured in liters (L).

Avogadro's Law links gas volume directly to the number of gas molecules. This law states that at constant temperature and pressure, equal volumes of all gases contain the same number of molecules. Hence, if the volume doubles, the number of molecules also doubles.

For instance, in the exercise:

• A 5.00 L sample of \(O_{2}\) contains 1.08 × 10^23 molecules.
• A 10.00 L sample of \(NH_{3}\) will contain twice as many molecules as a 5.00 L sample, which is 2 × 1.08 × 10^23 = 2.16 × 10^23 molecules.

This shows how changing the volume of the gas, while keeping temperature and pressure constant, changes the number of molecules accordingly.

Temperature and Pressure

Temperature and pressure are essential factors that can affect the behavior of gases. In the context of Avogadro's Law, these conditions must remain constant for the law to be applicable.

Temperature measures the kinetic energy of gas molecules. Higher temperatures increase energy, leading to more energetic collisions among molecules. Conversely, lower temperatures reduce the kinetic energy and the associated collisions.

Pressure is the force that the gas molecules exert on the walls of their container. When considering Avogadro's Law, maintaining consistent pressure ensures that changes in gas volume reflect only a change in the number of molecules and not other physical forces.

To keep temperature and pressure constant:

• Perform gas calculations at the same conditions throughout the problem.
• Use standard temperature and pressure (STP) conditions, if unspecified, which are 0°C (273.15 K) and 1 atm.

By understanding and controlling these conditions, you can accurately apply Avogadro's Law to determine gas volume and molecule count accurately.