Answer :
According to the statement the vapor pressure of ethanol at 84.6 °C is approximately 56.6 mmHg.
To find the vapor pressure of ethanol at 84.6 °C, we can use the Clausius-Clapeyron equation:
ln(P2/P1) = (-∆Hvap/R) x (1/T2 - 1/T1)
where P1 is the known vapor pressure at 45.9 °C (108 mmHg), P2 is the vapor pressure at 84.6 °C (what we're trying to find), ∆Hvap is the heat of vaporization (given as 39.3 kJ/mol), R is the gas constant (8.314 J/mol-K), T1 is the known temperature (45.9 °C + 273.15 K = 319.3 K), and T2 is the temperature we're trying to find (84.6 °C + 273.15 K = 357.3 K).
Plugging in these values and solving for P2, we get:
ln(P2/108) = (-39.3/(8.314))(1/357.3 - 1/319.3)
ln(P2/108) = -0.0386
P2/108 = e^-0.0386
P2 = 108 x e^-0.0386
P2 = 56.6 mmHg
Therefore, the vapor pressure of ethanol at 84.6 °C is approximately 56.6 mmHg.
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