Consider two gas cylinders of the same volume and temperature, one containing 1.0 mol of propane, c3h8,c3h8, and the other 2.0 mol of methane, ch4.ch4. which of the following statements is true?
a. the c3h8c3h8 and ch4ch4 molecules have the same urmsurms
b. the c3h8c3h8 and ch4ch4 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

B

Explanation:

Statement A

Vrms (root-mean-square velocity) is defined as follows.

Vrms = √(2RT/Mm), where R is the ideal gas constant, T is the temperature, and Mm is the molar mass of the gas. R and T are the same for both gases, but the molar mass is different, so Vrms for the two gases is different

Statement B

Kinetic energy KE of a molecule is related to temperature as follows:

KE = 3/2KbT, where Kb is the Boltzmann's constant and T is the temperature. The temperature is the same for both gases, so KE is the same for both.

Statement C

The rate depends on the number of molecules present. Since there are twice as many molecules of methane as propane, the rate is different for both gases.

Statement D

Pressure is directly proportional to the number of moles, based on the ideal gas law (pV = nRT). The volume and temperature are the same for both gases, so since there are twice as many molecules of methane as propane, the pressure is twice as great in the cylinder of methane.

in the given question, the partial pressure is calculated by using the ideal gas equation, that is, pv = nrt

here, p is pressure, v is volume = 25 l, n is number of moles = 0.0104 moles, r is gas constant = -0.0821 l.atm / mol.k

t is temperature = 273 k

p = nrt / v

p = (0.0104 mol × 0.0821 l.atm / mol.k × 273 k) / 25 l

= 0.0093 atm

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