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Heptane (C7H16) and octane (C8H18) are constitutents of gasoline. At 80 degree celsius, the vapor pressure of heptane is 428mmHg and the vapor pressure of octane is 175mmHg. What Xheptane in a mixture of heptane and octane that has a vapor pressure of 305mmHg and 80 degree celsius?

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meerkat18
Looking at this equation P= (pa*pb)/ (pa+(pb-pa)) ya  where pa=vap press a and ya= vap composition a and P= total pressure,it relates vapor pressure mixture to vapor composition. This is derived using the combination of Dalton's and Raoult's laws.

Answer: The mole fraction of heptane at 80°C is 0.506

Explanation:

We are given:

Vapor pressure of heptane at 80°C = 428 mmHg

Vapor pressure of octane at 80°C = 175 mmHg

Total pressure at 80°C = (428 + 175) = 603 mmHg

To calculate the mole fraction of heptane at 80°C, we use the equation given by Raoult's law, which is:

[tex]p_{heptane}=p_T\times \chi_{heptane}[/tex]

where,

[tex]p_A[/tex] = partial pressure of heptane = 305 mmHg

[tex]p_T[/tex] = total pressure  = 603 mmHg

[tex]\chi_A[/tex] = mole fraction of heptane = ?

Putting values in above equation, we get:

[tex]305mmHg=603mmHg\times \chi_{heptane}\\\\\chi_{heptane}=0.506[/tex]

Hence, the mole fraction of heptane at 80°C is 0.506