At its normal boiling point of 126°C n-octane, C8H18, has a vapor pressure of 760 torr. What is its vapor pressure at 25°C? the enthalpy of vaporization of n-octane is 39.07 kj/mol.

To find the vapor pressure of n-octane at 25°C, we can use the Clausius-Clapeyron equation. The equation is given by:

ln(P2/P1) = (-ΔHvap/R) * (1/T2 - 1/T1)

Where:
P1 = vapor pressure at the boiling point (760 torr)
P2 = vapor pressure at 25°C (unknown)
ΔHvap = enthalpy of vaporization (39.07 kJ/mol)
R = gas constant (8.314 J/(mol·K))
T1 = boiling point temperature in Kelvin (126°C + 273.15 = 399.15 K)
T2 = 25°C in Kelvin (25°C + 273.15 = 298.15 K)

Let's plug in the values and calculate:

ln(P2/760) = (-39.07 * 10^3 J/mol) / (8.314 J/(mol·K)) * (1/298.15 K - 1/399.15 K)

Calculating the right-hand side of the equation:

(-39.07 * 10^3 J/mol) / (8.314 J/(mol·K)) * (1/298.15 K - 1/399.15 K)
= -14.62

Now, rearranging the equation to solve for P2:

ln(P2/760) = -14.62
P2/760 = e^(-14.62)
P2 = 760 * e^(-14.62)

Calculating P2:

P2 ≈ 0.001 torr

Therefore, the vapor pressure of n-octane at 25°C is approximately 0.001 torr.

To calculate the vapor pressure of n-octane (C8H18) at 25°C, we can use the Clausius-Clapeyron equation:

ln(P2/P1) = -(ΔHvap/R) * (1/T2 - 1/T1)

Where:
P1 = vapor pressure at the boiling point (760 torr)
P2 = vapor pressure at the desired temperature (25°C)
ΔHvap = enthalpy of vaporization (39.07 kJ/mol)
R = ideal gas constant (8.314 J/mol·K)
T1 = boiling point temperature (in Kelvin)
T2 = desired temperature (in Kelvin)

First, let's convert the temperatures from Celsius to Kelvin.

T1 = 126°C + 273.15 = 399.15 K
T2 = 25°C + 273.15 = 298.15 K

Next, we need to convert the enthalpy of vaporization from kJ/mol to J/mol.

ΔHvap = 39.07 kJ/mol * 1000 J/kJ = 39,070 J/mol

Substituting these values into the equation:

ln(P2/760) = -(39,070 J/mol / 8.314 J/(mol·K)) * (1/298.15 K - 1/399.15 K)

Simplifying:

ln(P2/760) = -4704.62 * (-0.003358 + 0.002507)

ln(P2/760) = -4704.62 * -0.000851

ln(P2/760) = 4.00

Now, we can solve for P2 by taking the exponential of both sides:

P2/760 = e^4.00

P2 = 760 * e^4.00

Using a calculator, we find:

P2 ≈ 760 * 54.6

P2 ≈ 41,496 torr

Therefore, the vapor pressure of n-octane (C8H18) at 25°C is approximately 41,496 torr.

What's wrong with using the Arrhenius equation?

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