Question

Equal volumes of two gases are kept in separate containers at the same temperature and pressure. Then (1) Masses of the two gases are same (2) Molecular structure of two gases would be similar (3) The two gases contain the same number of molecules (4) The two gases if allowed to diffuse would do so at the same rate

Short answer

The two gases contain the same number of molecules.

Step-by-step solution

Identify the given conditions

The gases are kept in separate containers with equal volumes, the same temperature, and the same pressure.

Apply the Ideal Gas Law

According to the Ideal Gas Law, under the same conditions of temperature, pressure, and volume, the number of molecules (or moles) of gases will be the same.

Match statements with the conclusion

The statement that matches the conclusion from the Ideal Gas Law is: (3) The two gases contain the same number of molecules.

Key concepts

moles of gas

Understanding the concept of 'moles of gas' is essential in grasping many principles in chemistry. A mole is a fundamental unit in chemistry that measures the amount of substance. One mole contains exactly Avogadro’s number of particles (approximately 6.022 x 10^23 particles). This could refer to atoms, molecules, ions, or electrons.
When we talk about gases, the Ideal Gas Law helps us relate moles to other properties of the gas. The equation is given by:
\[ PV = nRT \]
where:

• P = pressure
• V = volume
• n = number of moles
• R = ideal gas constant (8.314 J/(mol K))
• T = temperature in Kelvins

Because the Ideal Gas Law helps correlate the state variables of a gas, it's very easy to determine the amount in moles if you know the pressure, volume, and temperature. For example, if we know two gases are at the same temperature, pressure, and volume, we can infer that they contain the same number of moles. This conclusion stems directly from the application of the Ideal Gas Law.

gas diffusion

Gas diffusion is the process by which gas molecules spread from areas of high concentration to areas of low concentration. This phenomenon can be studied using Graham's Law of Diffusion. Graham's Law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. Mathematically, it is:
\[ \frac{rate\text{ }A}{rate\text{ }B} = \frac{\text{Molar mass of gas } B}{\text{Molar mass of gas } A} \bigg)^{1/2} \]
Here, the masses or weights of two gases come into play.
Key points to remember:

• Lighter molecules will diffuse faster than heavier molecules.
• Diffusion is influenced by temperature—the higher the temperature, the faster the diffusion.

Understanding this is essential, particularly when considering the different rates at which gases mix and spread.

temperature and pressure relationships

The relationship between temperature and pressure is a critical concept in the study of gases. These state variables are closely related and follow various gas laws. For instance, Boyle's Law states that the pressure of a gas is inversely proportional to its volume, when the temperature is held constant:
\[ PV = k onumber \]
Charles's Law indicates that the volume of a gas is directly proportional to its temperature at constant pressure:
\[ V \bigg/ T = k onumber \]
These relationships are particularly significant when considering scenarios where gases are held at a constant volume, pressure, or temperature.
Important points:

• If the temperature increases and the volume remains constant, the pressure will increase.
• If the volume increases and the temperature remains constant, the pressure will decrease.
• If the pressure decreases and the volume remains constant, the temperature will decrease.

Understanding these principles ensures a comprehensive grasp of gas behavior under various conditions.