Calculate the relative rate of effusion for the orange to blue spheres. The root-mean-square speed for the orange spheres is 565.0 m/s. The root-mean-square speed for the blue spheres is 369.0 m/s.

The rate of effusion of blue is 1.53 times that of orange

Explanation:

Rate of effusion of a gas at a given temperature is directly proportional to the speed of the gas and inversely proportional to their masses.

At equal temperature, two gases will have equal amount of kinetic energy.

K. E = ½mv²

K. E = 3/2 KT

MV² = 3KT

V² = 3KT / M (single molecule of a gas)

U² = 3RT / M (mole of molecule)

3RT = MU²

RT = constant,

M1U²1 = M2U²2 for different gases at equal temperature.

Relationship between speed and rate of effusion =

m1r²1 = m2r²2 (speed is equal to the rate of effusion)

M1 / M2 = r²2 / r²1

M (blue) / M (orange) = r² (orange) / r² (blue)

M (blue) / M (orange) = 565 / 369

M (blue) / M (orange) = 1.53

The molar mass of the blue gas is 1.53 times heavier than the orange gas.

Relative rate of effusion for the orange to blue spheres = 1.531

Explanation:

Rate of effusion of Orange / Rate of effusion of blue = [Mblue / Morange]^1/2

Vrms = sqrt [ (3RT/M) ]

Vorange / Vblue = [ Mblue / Morange]^1/2

Rate of effusion of Orange / Rate of effusion of blue = 565 / 369 = 1.531