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17 December, 18:38

A solution is 40.00% by volume benzene (C6H6) in carbon tetrachloride at 20°C. The vapor pressure of pure benzene at this temperature is 74.61 mmHg and its density is 0.87865 g/cm3; the vapor pressure of pure carbon tetrachloride is 91.32 mmHg and its density is 1.5940 g/cm3. If this solution is ideal, its total vapor pressure at 20°C is

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  1. 17 December, 18:53
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    The total vapor pressure is 84.29 mmHg

    Explanation:

    Step 1: Data given

    Solution = 40.00 (v/v) % benzene in CCl4

    Temperature = 20.00 °C

    The vapor pressure of pure benzene at 20.00 °C = 74.61 mmHg

    Density of benzene is 0.87865 g/cm3

    The vapor pressure of pure carbon tetrachloride is 91.32 mmHg

    We suppose the total volume = 100 mL

    Step 2: Calculate volume benzene and CCl4

    40 % benzene = 40 mL

    60 % mL CCl4 = 60 mL

    Step 3: Calculate mass benzene

    Mass = density * volume

    Mass of benzene = 40.00 mL * 0.87865 g/mL = 35.146 g

    Step 4: Calculate moles of benzene

    Moles = mass / molar mass

    Number of moles of benzene = 35.146 grams / 78 g/mol = 0.45059 mol

    Step 5: Calculate mass of CCl4

    Mass of CCl4 = 60 mL * 1.5940 g/mL = 95.64 g

    Step 6: Calculate moles CCl4

    Number of moles of CCl4 = 95.64 grams / 154g/mol = 0.62104 mol

    Step 7: Calculate total number of moles

    Total number of moles = moles benzene + moles CCl4

    0.45059 moles + 0.62104 moles = 1.07163 mol

    Step 8: Calculate mole fraction benzene and CCl4

    Mole fraction = moles benzene / total moles

    Mole fraction of benzene = 0.45059 / 1.07163 = 0.4205

    Mole fraction of CCl4 = 0.62104 / 1.07163 = 0.5795

    Step 9: Calculate partial pressure

    Partial pressure of benzene = 0.4205 * 74.61 = 31.37 mmHg

    Partial pressure of CCl4 = 0.5795 * 91.32 = 52.92 mmHg

    Total vapor pressure = 31.37 + 52.92 = 84.29 mmHg

    The total vapor pressure is 84.29 mmHg
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