from dimensional analysis derive the unit of 'M' in the equation Pv =WRT/M where the symbols have their usual meaning
Answers
The unit of M in given equation is g/mol.
From dimensional analysis, we have to derive the unit of M in the equation, PV = WRT/M, where the symbols have their usual meaning.
solution : method 1 : We know from gaseous equation, PV = nRT
but here PV = WRT/M
so, WRT/M = nRT
⇒W/M = n
⇒M = W/n
here W is weight and n is no of moles.
so, unit of W = g and unit of n = mol
then unit of M = g/mol
Therefore the unit of M in equation PV = WRT/M, is g/mol
method 2 : in equation, PV = WRT/M
P = pressure ⇒dimensions of P = [ML¯¹T¯²]
V = volume ⇒ dimensions of V = [L³]
W = weight in g ⇒dimensions of W = [M]
R = universal gas constant ⇒dimensions of R = [ML²T¯²θ¯¹mol¯¹],
T = temperature ⇒dimensions of T = [θ]
now,
[ML¯¹T¯²][L³] = [M][ML²T¯²θ¯¹mol¯¹][θ]/M
⇒[ML²T¯²] = [M²L²T¯²mol¯¹]/M
⇒M = [M mol¯¹]
Therefore the unit of M = unit of Mass/unit of mole = g/mol.
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