Select the gas with the largest molecular speed (most fast) at 28°C.

Question

Select the gas with the larges molecular speed ( most fast) at 28 degrees C

A NO3

B NO2

C COs

D CO

Answer 1

You are going to use Graham's Law to find the rates of diffusion/effusion. The 28 ^oC temperature is just there to distract you. Ignore it.

The basic formula is r(M)^½ = constant ===> r = 1/M^1/2

or when comparing 2 gases, r_{Gas A}/r_{Gas B} = (M_{Gas B})^½/(M_{Gas A})^½

Next find the molar mass for each compound.

^NO₃ = (14x1) + (16x3) = 62 g/mol

NO₂ = (14x1) + (16x2) = 46 g/mol

CO₂ = (12x1) + (16x2) = 44 g/mol

CO = (12x1) + (16x1) = 28 g/mol.

Intuitively, you should see that the lower massed compound will have the faster speed at a given temperature. Think of pushing a car, a motorcycle, a bicycle, or a skateboard, if the same force is applied to all of them, the skateboard should have the fastest speed because it has less mass and is easier to get moving. Same principle applies here, lighter gas molecules move faster. We can plug it into the equation and find out.

rNO₃ = 62^(-1/2) = 0.127 m/sec

rNO₂ = 46^(-1/2) = 0.147 m/sec

rCO₂ = 44^(-1/2) = 0.150 m/sec

rCO = 28^(-1/2) = 0.188 m/sec.

The answer is CO is the fastest.

If we compared using the second version of the equation, then,

rCO/rNO₃ = 62^^1/2 / 28^^1/2 = 1.48, so CO is 1.48x faster than NO₃.

rCO/rNO₂ = 46^1/2 / 28^^1/2 = 1.28, so CO is 1.28x faster than NO₂.

rCO/rCO₂ = 44^^1/2 / 28^^1/2 = 1.25, so CO is 1.25x faster than CO₂.