At 200K, the particles of gas X have an average velocity equal to that of Argon at 400K. What is the identity of X?

He
CO
HF
HBr
F2

To find the identity of gas X, we can use the relationship between average kinetic energy and temperature in gases. The average kinetic energy of a gas is directly proportional to its absolute temperature. The formula for average kinetic energy is:

KE = (1/2) * m * v^2

Where:
KE = average kinetic energy of the gas
m = mass of the gas particle
v = velocity of the gas particle

Since it is stated that at 200K, the particles of gas X have an average velocity equal to that of Argon at 400K, we can equate the average kinetic energy of gas X at 200K to the average kinetic energy of Argon at 400K.

(1/2) * mX * vX^2 = (1/2) * mAr * vAr^2

Cancelling out the common terms, we have:

mX * vX^2 = mAr * vAr^2

Since we are looking for the identity of gas X, we can use the molar mass of each gas to represent their masses.

mX * vX^2 / molar mass of X = mAr * vAr^2 / molar mass of Ar

Simplifying further:

(vX^2 / molar mass of X) = (vAr^2 / molar mass of Ar)

We are given that the average velocity of gas X at 200K is equal to the average velocity of Argon at 400K. Therefore, vX = vAr.

(vAr^2 / molar mass of Ar) = (vAr^2 / molar mass of Ar)

Thus, the molar masses of Ar and X are equal. By comparing the molar masses of the given gases, we can determine the identity of gas X.

The molar masses of the given gases are:
He: 4 g/mol
CO: 28 g/mol
HF: 20 g/mol
HBr: 81 g/mol
F2: 38 g/mol

Since the molar mass of Argon is approximately 40 g/mol, we can conclude that the molar mass of gas X is also approximately 40 g/mol. Therefore, the identity of gas X is F2.