Which of the following gases will diffuse fastest when passed through a porous plug?
[H = 1, C = 12, N = 14, O = 16]
The rate of diffusion is inversely proportional to the square root of the relative molecular mass; in other words, lighter molecules diffuse faster than heavier ones.
The relationship between diffusion rate and molecular mass is an inverse one. This means that as the molecular mass of a substance increases, its diffusion rate decreases. Conversely, substances with lower molecular masses will diffuse more quickly.
Relative molecular mass of :
(a) Propane, C\(_3\)H\(_8\) = (12 x 3) + (1 x 8) = 36 + 8 = 44
(b) Oxygen, O\(_2\) = 16 x 2 = 32
(c) Methane, CH\(_4\) = 12 + (1x4) = 12 + 4 = 16
(d) Ammonia, NH\(_3\) = 14 + (1 x 3) = 17
Since CH\(_4\) has the least molecular mass compared to other options, it has the highest diffusion rate.
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