Benzene and toluene form two ideal solution A and B at 313 K, Solution A(total pressure `"P"_("A")`) contains equal mole fo toluene and benzene. Solution B contains equal masse of both(total pressure `"P"_("B")`). The vapour pressure of benzene and toluene are 160 and 60 mm of Hg respectively at 313 K. Calculate the value of `"P"_("A")//"P"_(B")`.

Answer

0.964

Explanation

Benzene-B, Toluene-T
`"P"_("A")="X"_("B")"P"_("B")^(0)+X_("T")"P"_("T")^(0)`
`"n"_("B")="n"_("T")="n"`
`"P"_("solution")=("n")/(2"n")xx160+("n")/(2"n")xx60`
`"P"_("solution")=110"mm Hg"`
Now for solution B
`"w"_("B")="w"_("T")="w"`
`"X"_("b")=(("w")/(78))/(("w")/(78)+("w")/(92)),"X"_("t")=1-(46)/(85)`
`=(92)/(170)" "=(39)/(85)`
`=(46)/(86)`
`"P"_("solution")^(1)="X"_("b")"P"_("b")^(0)+"X"_("t")"P"_("t")^(0)`
`46/85xx160+39/85xx60=1940/17`