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To an evacuated vessel with movable piston under external pressure of 1 atm, 0.1 mole of He and 1.0 mole of an unknown compound (vapour pressure 0.68 atm at 0°C) are introduced. Considering the ideal gas behaviour, the total volume (in litre of the gases Of 0°C is close to)
(2011, Integer Type)
    Correct answer is '7'. Can you explain this answer?
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    To an evacuated vessel with movable piston under external pressure of ...
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    Solution:

    Given:
    - External pressure on the evacuated vessel = 1 atm
    - Number of moles of He gas = 0.1 mole
    - Number of moles of the unknown compound = 1.0 mole
    - Vapour pressure of the unknown compound at 0°C = 0.68 atm

    We need to find the total volume of the gases at 0°C.

    Using the Ideal Gas Law:

    The ideal gas law equation is given by:

    PV = nRT

    Where:
    - P is the pressure
    - V is the volume
    - n is the number of moles
    - R is the ideal gas constant
    - T is the temperature in Kelvin

    Step 1: Convert temperature from Celsius to Kelvin:

    The given temperature is 0°C. To convert it to Kelvin, we use the following equation:

    T(K) = T(°C) + 273.15

    T(K) = 0 + 273.15 = 273.15 K

    Step 2: Calculate the volume of the unknown compound:

    Using the ideal gas law equation, we can rearrange it to solve for volume:

    V = (nRT) / P

    For the unknown compound:
    - Number of moles (n) = 1.0 mole
    - Pressure (P) = vapour pressure at 0°C = 0.68 atm
    - Temperature (T) = 273.15 K
    - Ideal gas constant (R) = 0.0821 L.atm/(mol.K)

    V = (1.0 mol * 0.0821 L.atm/(mol.K) * 273.15 K) / 0.68 atm
    V ≈ 11.19 L

    Step 3: Calculate the total volume of the gases:

    The total volume is the sum of the volume of the unknown compound and the volume of He gas.

    Total volume = Volume of unknown compound + Volume of He

    Total volume = 11.19 L + 0.1 L (since 0.1 mole of He occupies 0.1 L at STP)

    Total volume ≈ 11.29 L

    Step 4: Convert the volume to the nearest integer:

    The total volume is approximately 11.29 L. Rounding it to the nearest integer gives us 11 L.

    Therefore, the correct answer is 11, which is not equal to the given correct answer of 7. It is possible that there is an error in the given answer.
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    To an evacuated vessel with movable piston under external pressure of 1 atm, 0.1 mole of He and 1.0 mole of an unknown compound (vapour pressure 0.68 atm at 0°C) are introduced. Considering the ideal gas behaviour, the total volume (in litre of the gases Of 0°C is close to)(2011, Integer Type)Correct answer is '7'. Can you explain this answer?
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