Question

Carbon dioxide and carbon monoxide are very different gases. For example, you exhale CO_2. but \(C O\) is extremely toxic. Suppose you have two balloons, one filled with \(1.00\) mole of CO and the other filled with 1 mole of \(\mathrm{CO}_{2}\). Both gases are at \(1.00 \mathrm{~atm}\) and \(25.0^{\circ} \mathrm{C}\). (a) What is the volume in liters of each balloon? (b) What did you learn about gases from doing this problem?

Short answer

(a) The volume of each balloon filled with CO and CO_2 is 24.47 liters. (b) We learned that under the same temperature and pressure conditions, equal amounts of different gases (in moles) will occupy the same volume, in accordance with Avogadro's Law.

Step-by-step solution

Convert temperature to Kelvin

The given temperature is 25.0°C. To convert it to Kelvin, we add 273.15 to the Celsius value: \(T = 25.0 + 273.15 = 298.15 \, K\)

Recall the Ideal Gas Law and constants

The Ideal Gas Law is given by \(PV = nRT\), where P is the pressure in atm, V is the volume in liters, n is the number of moles, R is the gas constant (0.0821 L atm/mol K), and T is the temperature in Kelvin. For both balloons: The pressure, P = 1.00 atm The number of moles, n = 1.00 mole The gas constant, R = 0.0821 L atm/mol K The temperature, T = 298.15 K

Calculate the volume of each balloon using the Ideal Gas Law

Since the number of moles, pressure, and temperature are the same for both balloons, we can directly calculate the volume using the Ideal Gas Law: \(V = \frac{nRT}{P}\) \(V = \frac{(1.00\,mol)(0.0821\,L\,atm/mol\,K)(298.15\,K)}{1.00\,atm}\) \(V = 24.47\,L\) Both balloons have a volume of 24.47 liters.

Analyze the results

(a) The volume of each balloon is 24.47 liters. (b) From this problem, we learned that under the same temperature and pressure conditions, equal amounts of different gases (in moles) will occupy the same volume. This observation is in alignment with Avogadro's Law, which states that equal volumes of gas at the same temperature and pressure contain the same number of particles (in this case, moles).

Key concepts

Avogadro's Law

Avogadro's Law is a principle that helps us understand the behavior of gases. It tells us that equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules or particles. This law is fundamental for anyone studying chemistry because it simplifies calculations in gas-related problems.

When you look at the example of two balloons filled with different gases, carbon monoxide (CO) and carbon dioxide (CO₂), both containing 1 mole of gas, you see Avogadro's Law in action. Each balloon ends up with the same volume of gas, 24.47 liters, due to the same number of moles and identical conditions of temperature and pressure. This shows us that the type of gas doesn't matter when it comes to volume, as long as the conditions are identical.

Here are a few key takeaways from Avogadro's Law:

• It holds true for ideal gases under standard conditions.
• Applicable when comparing gases at the same temperature and pressure.
• Makes it easier to predict and understand gas behavior in chemical reactions.

Gas Properties

Gases have unique properties that differentiate them from solids and liquids. These properties are crucial for various scientific and practical applications. Understanding these properties helps us predict how gases will behave under different conditions.

One of the most notable characteristics of gases is their ability to expand and fill any container they are in. This expansion occurs because the gas particles are always in constant and random motion. They move freely at high speeds, which allows them to spread out evenly in any available space.

Additionally, gases can be compressed, unlike liquids or solids. This compressibility is due to the vast space between gas molecules, allowing them to be packed closer together when pressure is applied.

Gases are also affected by temperature changes significantly. As temperature increases, the kinetic energy of the particles increases, causing the gas to expand. Conversely, a decrease in temperature will slow down the particles and cause the gas to contract.

Key points about gas properties:

• Gases expand to fill their containers.
• They are highly compressible.
• They have a variable volume that depends on temperature and pressure.
• They have lower densities compared to solids and liquids.

Mole Concept

The mole is a basic unit used in chemistry to measure the amount of substance. It provides a bridge between the atomic scale and the macroscopic quantities we can observe and measure. A mole is defined as exactly 6.022 x 10²³ particles, which is Avogadro's number.

In the context of gases, the mole concept is particularly useful. In the exercise example, both balloons contained 1 mole of gas, illustrating the simplicity the mole concept brings to calculations with gases. When using the Ideal Gas Law, knowing the number of moles directly helps in calculating the volume, pressure, or temperature of a gas.

Here are a few crucial aspects of the mole concept:

• Helps in determining the stoichiometry of chemical reactions.
• Facilitates the conversion between atoms/molecules and grams; it's a handy tool in calculations.
• When combined with Avogadro's Law, it simplifies calculations involving gases.

By using the mole concept, chemists can easily correlate mass, volume, and number of particles in their studies, making it an essential part of chemistry.