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Answer :
Answer: mole fraction of hexane = 0.61 and mole fraction of cyclohexane = 0.39
Explanation:
According to Raoult's law, the vapor pressure of a component at a given temperature is equal to the mole fraction of that component multiplied by the vapor pressure of that component in the pure state.
[tex]p_1=x_1p_1^0[/tex] and [tex]p_2=x_2P_2^0[/tex]
where, x = mole fraction
[tex]p^0[/tex] = pressure in the pure state
According to Dalton's law, the total pressure is the sum of individual pressures.
[tex]p_{total}=p_1+p_2[/tex][tex]p_{total}=x_Ap_A^0+x_BP_B^0[/tex]
[tex]x_{hexane}=\frac{\text {moles of hexane}}{\text {moles of hexane+moles of cyclohexane}}=\frac{1}{1+1}=0.5[/tex],
[tex]x_{cyclohexane}=\frac{\text {moles of cyclohexane}}{\text {moles of hexane+moles of cyclohexane}}=\frac{1}{1+1}=0.5[/tex],
[tex]p_{hexane}^0=151.4torr[/tex]
[tex]p_{cyclohexane}^0=97.6torr[/tex]
[tex]p_{total}=0.5\times 151.4torr+0.5\times 97.6torr=124.5torr[/tex]
[tex]y_{hexane}[/tex] = mole fraction of hexane in vapor phase [tex]y_{hexane}=\frac{p_{hexane}}{p_{total}}=\frac{0.5\times 151.4}{124.5}=0.61[/tex]
[tex]y_{cyclohexane}=1-y_{hexane}=1-0.61=0.39[/tex]
Thus the mole fraction of hexane in the vapor above the solution is 0.61 and mole fraction of cyclohexane in the vapor above the solution is 0.39
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