suppose you have two 1-L flasks one containing N2 at STP the other containg CH4 at STP how do these systems compare with respect to a)number of molecules B)density c)average kinetic energy of the molecules d)rate of effusion through a pinhole leak?
To compare the two systems, we need to consider some basic principles of ideal gases. Let's address each aspect one by one:
a) Number of molecules:
The number of molecules in a gas can be determined using Avogadro's law, which states that equal volumes of gases, at the same temperature and pressure, contain an equal number of particles. Since both flasks have the same volume (1 liter) and are at the same temperature and pressure (STP - standard temperature and pressure conditions), the number of molecules in each flask will be the same. Therefore, the two systems have an equal number of molecules.
b) Density:
Density is defined as the mass of a substance per unit volume. To compare the densities of the two systems, we need to consider their molecular weights. The molecular weight of nitrogen (N2) is approximately 28 g/mol, while the molecular weight of methane (CH4) is approximately 16 g/mol. Since both flasks have the same volume (1 L), the system with CH4 will have a lower density compared to the system with N2, as it has a lower molecular weight.
c) Average kinetic energy of the molecules:
The average kinetic energy of gas molecules can be determined using the formula KE_average = (3/2) * k * T, where k is the Boltzmann constant and T is the temperature. Since both systems are at the same temperature (STP), the average kinetic energy of the molecules will be the same for both flasks.
d) Rate of effusion through a pinhole leak:
The rate of effusion, which is the escape of gas through a small hole, depends on the molar mass of the gas. According to Graham's law of effusion, the rate of effusion is inversely proportional to the square root of the molar mass. Since the molar mass of N2 is higher than that of CH4, the rate of effusion for N2 will be slower compared to CH4.
In summary:
a) Both systems have the same number of molecules.
b) The system with CH4 has a lower density compared to the system with N2.
c) The average kinetic energy of the molecules is the same for both systems.
d) The rate of effusion for N2 is slower compared to CH4.