Two rigid containers of equal volume hold hydrogen and argon gases respectively at the same temperature and pressure. Which of the following statements is(are) false ?
A) The two containers hold an equal mass of gas.
B) The two containers hold an equal number of gas particles.
C) The molecules in each container have the same average kinetic energy.
D) The two containers hold an equal number of atoms.
E) The two containers hold an equal number of moles of gas.
Think about this.
PV = nRT for each gas, therefore, if we solve for n = PV/RT then
(PV/RT)<Ar = (PV/RT)H2. Then, since
n = grams/molar mass, we can write
(PV/RT)Ar = (PV/RT)H2 = (g/MM)Ar = (g/MM)H2. Since P, V, R, and T are the same, we can dispense with the PV/RT and just write
(g/MM)Ar = (g/MM)H2.
To determine which of the statements is false, let's analyze each statement one by one:
A) The two containers hold an equal mass of gas.
To determine if this statement is true, we need to consider the molar masses of hydrogen (H₂) and argon (Ar). The molar mass of argon is much higher than the molar mass of hydrogen. Since the containers have equal volumes, the container holding argon will have a higher mass of gas compared to the container holding hydrogen. Therefore, statement A is false.
B) The two containers hold an equal number of gas particles.
Since the containers have equal volumes, the number of gas particles in each container would be the same, regardless of the type of gas. This is because the volume of a gas is directly proportional to the number of particles (as long as temperature and pressure are constant). Therefore, statement B is true.
C) The molecules in each container have the same average kinetic energy.
The average kinetic energy of gas molecules is determined by their temperature, not the type of gas. Since the temperature is the same in both containers, the average kinetic energy of the molecules in each container will be the same. Therefore, statement C is true.
D) The two containers hold an equal number of atoms.
To determine if this statement is true, we need to consider the atomic structure of the two gases. Hydrogen gas (H₂) is composed of two hydrogen atoms, while argon gas (Ar) is composed of a single argon atom. Therefore, the number of atoms in the containers will be different, and statement D is false.
E) The two containers hold an equal number of moles of gas.
To determine the number of moles, we need to know the mass of each gas. As mentioned earlier, the container holding argon will have a higher mass of gas compared to the container holding hydrogen. Since the containers have equal volumes, the two containers will not hold an equal number of moles of gas. Therefore, statement E is false.
In conclusion, statements A, D, and E are false, while statements B and C are true.