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Which of the following relationships bet...

Which of the following relationships between partial pressure , volume and temperature is correct ?
(i) `P = (nRT)/(V)`
(ii) `P_("total") = P_(1) + P_(2) + P_(3)`
(iii) `P_("total") = (n_(1) + n_(2) + n_(3)) (RT)/(V)`

A

(i) and (ii)

B

(i) and (iii)

C

(ii) and (iii)

D

(i) , (ii) and (iii)

Text Solution

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The correct Answer is:
D
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Examine the following plots and predict whether in (i) P_(1) lt P_(2) "and" T_(1) gt T_(2) , in (ii) T_(1) = T_(2)ltT_(3) , in (iii) V_(1) gt V_(2), "in" (iv) P_(1) gt P_(2) "or" P_(2) gt P_(1)

2.^(n)P_(3)=^(n+1)P_(3)

When a liquid is completely miscible with another liquid, a homogeneous solution consisting of a single phase is formed. If such a solution is placed in a closed evacuated vessel, the total pressure exerted by the vapour, after the system attained equilibrium will be equal to the sum of partial pressures of the constituents. A solution is said to be ideal if its constituents follow Raoult's law under all conditions of concentrations, i.e., where p_(i) is the partial pressures of the constituent i, whose mole fraction in the solution is x_(i) and p_(i)^(@) is the corresponding vapour pressure of the pure constituent. The change in the thermodynamic functions when an ideal solution is formed by mixing pure components is given by the following expression. Delta_(mix) = G = n_("total") RT sum_(i) x_(i) In x_(i) ...(i) where, n_("total") is the total amount of all the constituents present in the solution. Delta_(mix)F =- n_("total") R sum_(i) x_(i) In x_(i) ......(ii) Delta_(mix)H =- n_("total") RT sum_(i) x_(i) In x_(i) - n_("total") R sum_(i) x_(i) In x_(i) = 0 ........(iii) Delta_(mix) U = 0 .........(iv) Since botli the components of an ideal binary system follow Raoult's law of the entire range of the compositions, the partial pressure exerted by the vapours of these constituents over the solution will be given by p_(A) = x_(A) p_(A)^(@) ..........(v) p_(B) = x_(B) p_(B)^(@) .........(vi) where, x_(A) and x_(B) are the mole fractions of the two constituents in the liquid phase and p_(A)^(@) and p_(B)^(@) are the respective vapour pressure of the pure constituents. The total pressure (p) over the solution will be the sum of the partial pressure. The composition of the vapour phase (y_(A)) can be determined with the help of Dalton's law of partial pressures. For an ideal solution in which p_(A)^(@) gt p_(B)^(@) , the plot of total pressure (p) us the mole fraction of A at constant temperature in the vapour phase is:

Find the value of n such that "(i) "^(n)P_(5) =42 xx ""^(n)P_(3), n gt 4 " (ii) "(""^(n)P_(4))/(" "^(n-1)P_(4))=(5)/(3), n gt 4.

Find n if .^(n-)P_(3): .^(n)P_(4) = 1:9 .

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