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Question
PA and PB are the vapour pressure of pure liquid components, A and B, respectively of an ideal binary solution. If xA represents the mole fraction of component A, the total pressure of the solution will be
Options
A.PA + xA ( PB - PA )
B.PA + xA ( PA - PB )
C.PB + xA ( PB - PA )
D.PB + xA ( PA - PB )
Solution
Total pressure,
PT = P′A + P′B .....(i)
We know that, P′A = PA xA
P′B = PB xB
Substituting the value of P′A and P′B in Eq. (i)
PT = PA xA + PB xB
[ xA + xB = 1 ⇒ xA = 1 - xB or xB = 1 - xA]
= PA xA + PB (1 - xA )
= PA xA + PB - PB xA
∴ PT = PB + xA (PA - PB )
PT = P′A + P′B .....(i)
We know that, P′A = PA xA
P′B = PB xB
Substituting the value of P′A and P′B in Eq. (i)
PT = PA xA + PB xB
[ xA + xB = 1 ⇒ xA = 1 - xB or xB = 1 - xA]
= PA xA + PB (1 - xA )
= PA xA + PB - PB xA
∴ PT = PB + xA (PA - PB )
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