1.

For an ideal binary solution (A) and (B), `y_(A)` is the mole fraction of A in vapour phase. Which of the following plot should be linear?A. `P_("Total") vs y_(A)`B. `P_("Total") vs y_(B)`C. `(1)/(P_("Total")) vs y_(A)`D. `(1)/(P_("Total"))vs (y_(B)+y_(A))`

Answer» Correct Answer - C
`P_("Total") = x_(A)p_(A)^(@) +x_(B)p_(B)^(@)`
`= x_(A)p_(A)^(@) +(1-x_(A))p_(B)^(@)`
`= x_(A) (p_(A)^(@) -p_(B)^(@)) +p_(B)^(@)`
`x_(A) = (P_("Total")-p_(B)^(@))/((p_(A)^(@)-p_(B)^(@)))` ...(i)
Now, `y_(A) = (p_(A))/(P_("Total")) = (x_(A)p_(A)^(@))/(P_("Total"))`
`x_(A) = (y_(A)P_("Total"))/(p_(A)^(@))` ...(ii)
Eliminate `x_(A)` between (i) and (ii)
`(P_("Total")-p_(B)^(@))/(p_(A)^(@)-p_(B)^(@))=(y_(A)P_("Total"))/(p_(A)^(@))`
`(P_("Total")-p_(B)^(@))/(P_("Total"))=((p_(A)^(@)-p_(B)^(@))/(p_(A)^(@)))y_(A)`
`1 -(p_(B)^(@))/(P_("Total")) = ((p_(A)^(@)-p_(B)^(@))/(p_(A)^(@)))y_(A)`
`(p_(B)^(@))/(P_("Total")) = 1- ((p_(A)^(@)-p_(B)^(@))/(p_(A)^(@)))y_(A)`
`(1)/(P_("Total")) =(1)/(p_(B)^(@)) -(p_(A)^(@)-p_(B)^(@))/(p_(A)^(@)p_(B)^(@))`
`(1)/(P_("Total"))` is a linear function of `y_(A)`.


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