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4 November, 20:53

A 1.17 g sample of an alkane hydrocarbon gas occupies a volume of 674 mL at 28°C and 741 mmHg. Alkanes are known to have the general formula C nH 2n+2. What is the molecular formula of the gas in this sample? (R = 0.08206 L*atm/K*mol)

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  1. 4 November, 22:42
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    C3H8

    Explanation:

    Step 1:

    Data obtained from the question. This includes the following:

    Mass of alkane = 1.17g

    Volume (V) = 674 mL

    Temperature (T) = 28°C

    Pressure (P) = 741 mmHg.

    Gas constant (R) = 0.08206 atm. L/Kmol

    Step 2:

    Conversion to appropriate unit.

    For Volume:

    1000mL = 1L

    Therefore, 674mL = 674/1000 = 0.674L

    For Temperature:

    Temperature (Kelvin) = Temperature (celsius) + 273

    Temperature (celsius) = 28°C

    Temperature (Kelvin) = 28°C + 273 = 301K

    For Pressure:

    760mmHg = 1atm

    Therefore, 741 mmHg = 741/760 = 0.975atm

    Step 3:

    Determination of the number of mole of the alkane ...

    The number of mole of the alkane can be obtained by using the ideal gas equation. This is illustrated below:

    Volume (V) = 0.674L

    Temperature (T) = 301K

    Pressure (P) = 0.975atm

    Gas constant (R) = 0.08206 atm. L/Kmol

    Number of mole (n) = ?

    PV = nRT

    n = PV / RT

    n = (0.975 x 0.674) / (0.08206x301)

    n = 0.0266 mole

    Step 4:

    Determination of the molar mass of the alkane.

    Mass of alkane = 1.17g

    Number of mole of the alkane = 0.0266mole

    Molar Mass of the alkane = ?

    Number of mole = Mass/Molar Mass

    Molar Mass = Mass/number of mole

    Molar Mass of the alkane = 1.17/0.0266 = 44g/mol

    Step 5:

    Determination of the molecular formula of the alkane.

    This is illustrated below:

    The general formula for the alkane is CnH2n+2

    To obtain the molecular formula for the alkane we shall assume n = 1, 2, 3 or more till we arrive at molar Mass of 44.

    When n = 1

    CnH2n+2 = CH4 = 12 + (4x1) = 16g/mol

    When n = 2

    CnH2n+2 = C2H6 = (12x2) + (6x1) = 30g/mol

    When n = 3

    CnH2n+2 = C3H8 = (12x3) + (8x1) = 44g/mol

    We can see that when n is 3, the molar mass is 44g/mol.

    Therefore, the molecular formula for the alkane is C3H8.
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