Question

Consider two gas cylinders of the same volume and temperature, one containing 1.0 mol of propane, C3H8, and the other 2.0 mol of methane, CH4. Which of the following statements is true?

(a) The C3H8 and CH4 molecules have the same urms
(b) The C3H8 and CH4 molecules have the same average kinetic energy
(c) The rate at which the molecules collide with the cylinder walls is the same for both cylinders
(d) The gas pressure is the same in both cylinders

Answer 1

(b) The C3H8 and CH4 molecules have the same average kinetic energy

Step-by-step explanation:

The expression for the root mean square speed is:

`C_(rms)=\sqrt {\frac {3RT}{M}}`

R is Gas constant having value = 8.314 J / K mol

M is the molar mass of gas

Molar mass of
`CO_2` = 0.04401 kg/mol

Thus, it depends on the molecular mass which is not the same for both species. Hence, a is not the answer.

The expression for the kinetic energy is:-

`K.E.=(3)/(2)* K* T`

k is Boltzmann's constant =
`1.38* 10^(-23)\ J/K`

T is the temperature

Thus, kinetic energy is only proportional to the temperature. Hence, there is same value of kinetic energy for both the gases and hence, b is the answer.

Since, the velocity are different for both gases, the rate cannot be same. Hence, c is not the answer.

Considering ideal gas equation as:

`PV=nRT`

where,

P is the pressure

V is the volume

n is the number of moles

T is the temperature

R is Gas constant having value = 0.0821 L atm/ K mol

Thus, pressure is directly proportional to the number of moles and hence, they don't not have same pressure. Thus, d is not the answer.