Question

Ethanol has a heat of vaporization of 38.56 kJ/mol and a normal boiling point of 78.4 oC. What is the vapor pressure of ethanol at 15.0 oC? (Hint: 1 atm = 760 torr)

Answer 1

Answer:

238.3 torr

Explanation:

We'll use the Clausius-Clapeyron Equation which allows us to calculate the vapour pressure of a liquid at a certain temperature, given that the enthalpy of vaporization and the vapor pressure at another temperature is known.

㏑$(\frac{P_{1} }{P_{2} } )$ = $\frac{H_{vap} }{R}$ $(\frac{1}{T_{1} } - \frac{1}{T_{2} } )$

T₁ (temperature)= (50.0+ 273.15) K = 323.15 K (convert temperature to kelvin)

P₁ (vapor pressure) = ???

T₂ (temperature) = (78.4+ 273.15) K = 351.55 K  (convert temperature to kelvin)

P₂ (vapor pressure) = 760 torr  

R = Ideal gas constant = 8.314  J⋅K ⁻¹mol⁻¹

$H_{vap}$ (heat of vaporization) = 38.56 kJ⋅mol⁻¹ = 38560 J⋅mol⁻¹

㏑ $(\frac{760 torr}{P_{2} } )$ = $\frac{38560 J.mol^{-1} }{8.314 J.K^{-1} mol^{-1} }$  $(\frac{1}{323.15 K } - \frac{1}{351.55 } )$

㏑ $(\frac{760 torr}{P_{2} } )$ = 4638 X 2.5 X $10^{-4$

㏑ $(\frac{760 torr}{P_{2} } )$ = 1.159

$(\frac{760 torr}{P_{2} } )$ = $e^{1.159}$

$(\frac{760 torr}{P_{2} } )$ = 3.188

$P_{2}$ = $\frac{760 torr}{3.188}$ = 238.3 torr

Answer 2

The vapor pressure of Ethanol at 15°C is calculated as 237.88torr

HOW TO CALCULATE VAPOR PRESSURE:

• The vapor pressure of ethanol in this question can be calculated using Clausius-Clapeyron Equation as follows:

• ln (P1/P2) = ∆H vap/R (1/T2 - 1/T1)

Where;

1. T₁ (temperature)= (50°C + 273.15) K = 323.15K
2. P₁ (vapor pressure) = ?
3. T₂ (temperature) = (78.4°C + 273.15) K = 351.55K
4. P₂ (vapor pressure) = 760 torr
5. R = Ideal gas constant = 8.314 J⋅K ⁻¹mol⁻¹
6. ∆H (heat of vaporization) = 38.56 kJ⋅mol⁻¹ = 38560 J⋅mol⁻¹

Hence;

• ln (P1/760) = 38560/8.314 (1/351.55 - 1/323.15)

• ln (P1/760) = 4637.96 (0.002845 - 0.003095)

• ln (P1/760) = 4637.96 × - 0.00025

• ln (P1/760) = -1.16

• P1/760 = exp (-1.16)

• P1/760 = 0.313

• P1 = 760 × 0.313

• P1 = 237.88torr.

• Therefore, vapor pressure of Ethanol at 15°C is calculated as 237.88torr

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