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11 May, 00:39

The vapor pressure of liquid antimony is 400 mm Hg at 1.84*103 K. Assuming that its molar heat of vaporization is constant at 115 kJ/mol, the vapor pressure of liquid Sb is 394.98 mm Hg at a temperature of 1.81*103 K. Find the vapor pressure of liquid Sb?

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  1. 11 May, 00:51
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    Vapor pressure of liquid Sb = 8.19 x 10⁴ mm Hg

    Explanation:

    The vapor pressure can be calculated by using Clausius-Clapeyron equation.

    ln (p₁/p₂) = (-ΔHvap/R) (1/T₁ - 1/T₂)

    Where

    p₁ is the vapor pressure at T₁ (Initial Temperature)

    p₂ is the vapor pressure at T₂ (final Temperature)

    ΔHvap is molar heat of vaporization of the substance

    R is the real gas constant = 8.314 x 10⁻³ kJ/mol. K

    Data Given:

    p₁ = ?

    p₂ = 394.98 mm Hg

    T₁ = 1.84*10³ K

    T₂ = 1.81*10³ K

    ΔHvap = 115 kJ/mol

    Put the values in the Clausius-Clapeyron equation

    ln (p₁/p₂) = (-ΔHvap/R) (1/T₁ - 1/T₂)

    ln (p₁/394.98 mm Hg) = (-115 kJ/mol / 8.314 x 10⁻³ kJ/mol. K) (1/1.84*10³ K - 1/1.81*10³ K)

    ln (p₁ / 394.98 mm Hg) = ( - 13.8321 x 10³) (-0.5519)

    ln (p₁ / 394.98 mm Hg) = 7633.936

    ln cancel out by E, e is raise to a power x

    So,

    p₁/394.98 mm Hg = e^7633.936

    p₁ / 394.98 mm Hg = 20.75 x 10³

    p₁ = 20.75 x 10³ x 394.98 mm Hg

    p₁ = 8.19 x 10⁴ mm Hg

    Vapor pressure of liquid Sb = 8.19 x 10⁴ mm Hg
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