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.

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