If `chi_(M), chi_(P)" and "chi_(V)` are mole fraction, pressure fraction and volume fraction respectively of a gaseous mixture, then

Options

A. `chi_(M) = (1)/(chi_(P)) xx (1)/(chi_(V))`
B. `(1)/(chi_(M)) = chi_(P) xx (1)/(chi_(V))`
C. `chi_(M) = chi_(P) xx chi_(V)`
D. `(1)/(chi_(P)) = (1)/(chi_(M)) xx (1)/(chi_(V))`

Answer

C

Explanation

`{:("moles" ,, "pressure" ,, "volume" ,, "temperature"), (n_(1) ,, P_(1) ,, V_(1) ,, T) , ("Total" (n_(2))/(n_(T)) ,, (P_(2))/(P_(T)) ,, (V_(2))/(V_(T)) ,, T) , (P_(1) = (n_(1) RT)/(V_(1)) , ,, P_(T) = (n_(T) RT)/(V_(T)) ,, implies (P_(1))/(P_(T)) = (n_(1))/(n_(T)) xx (V_(T))/(V_(1))):}`
`therefore chi_(M) = chi_(p) xx chi_(v)`