Mean free path and Avogadro’s number - One Line Questions
1.
Avogadro's number is approximately equal to the number of atoms in: —
12 grams of Carbon-12
2.
What is the value of the Boltzmann constant (k_B) if the universal gas constant (R) is 8.314 J/(mol·K) and Avogadro's number (N_A) is 6.022 x 10^23 mol^-1? —
1.38 x 10^-23 J/K
3.
How many moles are there in 10 grams of water (Molar mass of H_2O = 18 g/mol)? —
10 / 18 moles
4.
What is the total number of molecules in 2 moles of any gas at STP? —
2 * N_A
5.
Avogadro's number (N_A) represents the number of particles (atoms or molecules) in one mole of a substance. What is its approximate value? —
6.022 x 10^23
6.
According to the kinetic theory of gases, the mean free path (λ) is inversely proportional to which quantity? —
Number density (n)
7.
What is the number of molecules in 1 mole of water (H_2O)? —
Approximately 6.022 x 10^23
8.
If the temperature of a gas is kept constant, but the pressure is increased, the number density (n) of molecules: —
Increases.
9.
Avogadro's hypothesis states that equal volumes of all gases, at the same temperature and pressure, contain: —
Equal numbers of molecules.
10.
Which of the following is a direct consequence of Avogadro's hypothesis? —
Equal volumes of all gases at the same temperature and pressure contain the same number of molecules.
11.
Consider two gases at the same temperature and pressure. If Gas A has smaller molecules than Gas B, what can be said about their mean free paths? —
Gas A has a longer mean free path.
12.
The concept of mean free path is crucial in understanding phenomena like: —
Viscosity and diffusion of gases.
13.
The mean free path (λ) is inversely proportional to the number density (n). If the number density is halved, the mean free path is: —
Doubled.
14.
If you have one mole of Helium gas and one mole of Oxygen gas at the same temperature and pressure, how do their number of molecules compare? —
They have the same number of molecules.
15.
If the number density of a gas is constant, and the molecular diameter is doubled, the mean free path will: —
Decrease by a factor of 4.
16.
Consider a gas at constant temperature and volume. If the number of moles of gas is increased, the mean free path will: —
Decrease.
17.
The mean free path is related to the average distance between molecules. If the average distance between molecules decreases, the mean free path generally: —
Decreases.
18.
If the number density of gas molecules in a container is doubled, how does the mean free path change, assuming temperature and molecular diameter remain constant? —
It halves.
19.
The mean free path of gas molecules is inversely proportional to the square of the molecular diameter (d). If the diameter is halved, how does the mean free path change? —
It becomes four times.
20.
How does an increase in the absolute temperature affect the mean free path of gas molecules, assuming pressure and molecular diameter are constant? —
It remains unchanged.
21.
If the temperature of a gas is increased at constant volume, what happens to the mean free path? —
It remains the same.
22.
If the pressure of a gas is increased at constant temperature, what happens to the mean free path? —
It decreases.
23.
If the volume of a container holding a gas is decreased at constant temperature and number of moles, what happens to the mean free path? —
It decreases.
24.
Which of the following statements about Avogadro's number is INCORRECT? —
It is the number of atoms in 12 grams of Carbon-12.
25.
Which of the following is a unit of number density? —
m^-3
26.
Avogadro's number is a fundamental constant that bridges the macroscopic and microscopic worlds. It relates the number of entities to: —
Amount of substance (moles)
27.
What is the SI unit for Avogadro's number? —
mol^-1
28.
Which of the following is a correct expression for the number of moles (n) of a substance with mass (m) and molar mass (M)? —
n = m / M
29.
What is the relationship between the number of molecules (N), Avogadro's number (N_A), and the number of moles (n)? —
N = n * N_A
30.
The total number of molecules in a given sample of gas is related to the number of moles (n) and Avogadro's number (N_A) by which formula? —
N = n * N_A
31.
How is the number density (n) of gas molecules related to the total number of molecules (N) and the volume (V) they occupy? —
n = N / V
32.
What is the relationship between Avogadro's number (N_A) and the number of molecules (N) in 'n' moles of a substance? —
N = n * N_A
33.
If the temperature of a gas is increased at constant pressure, what happens to the number density (n) and thus the mean free path (λ)? —
n decreases, λ increases.
34.
How many molecules are there in 1 gram of Hydrogen gas (Molar mass of H_2 = 2 g/mol), given Avogadro's number? —
N_A / 2
35.
In the formula for mean free path λ = 1 / (√2 πnd²), what does 'n' represent? —
Number density of molecules
36.
The mean free path formula λ = 1 / (√2 πnd²) is derived under the assumption that molecules are: —
Rigid spheres of finite diameter.
37.
The mean free path is dependent on the size of the molecules. Larger molecules generally have: —
Shorter mean free paths.
38.
Which factor, when increased, leads to a decrease in the mean free path of gas molecules? —
Pressure
39.
Which of the following is NOT a direct factor influencing the mean free path of gas molecules? —
Molar mass
40.
What is the definition of the mean free path of a gas molecule? —
The average distance traveled by a molecule between two consecutive collisions.
41.
The molar mass of a substance is defined as: —
The mass of one mole of the substance.
42.
The value of Avogadro's number is primarily determined by: —
Experimental measurements relating macroscopic properties to the number of particles.
43.
Avogadro's number is defined as the number of constituent particles (usually atoms or molecules) that are contained in one mole of a substance. What is the exact definition related to Carbon-12? —
The number of atoms in 12 grams of Carbon-12.
44.
The term 'collision frequency' in the context of gas molecules refers to: —
The number of collisions per unit time per molecule.
45.
Which physical quantity is numerically equal to the number of particles per mole? —
Avogadro's Number (N_A)
46.
At very low pressures, the mean free path of gas molecules becomes: —
Very large.
47.
If the molecular diameter of gas molecules is very small, the mean free path would tend to be: —
Very large.
48.
The formula for the mean free path (λ) of gas molecules, considering them as hard spheres of diameter 'd' and number density 'n', is approximately: —
λ = 1 / (√2πnd²)
49.
The mean free path (λ) is directly proportional to the average speed of the molecules (ν_avg) and inversely proportional to the collision frequency (Z). What is the relation? —
λ = ν_avg / Z