A 10.0 g sample of an unknown liquid is vaporized at 120.0°C and 5.0 atm. The volume of the vapour is found to be 568.0 mL. The liquid is determined to be made up of 84.2% carbon and 15.8% hydrogen. What is the molecular formula for the liquid?

C8H16

Explanation:

First thing to do here is to calculate the molar mass of the compound

Mathematically;

molar mass = mass/number of moles

we can calculate the number of moles using the ideal gas equation

Mathematically;

PV = nRT

n = PV/RT

where p is the pressure at 5 atm

V is the volume at 568 ml = 568/1000 = 0.568 L

R is the molar gas constant which is 0.0821

T is the temperature which is 120+ 273 = 393k

Inserting these values into the equation, we have

n = (5 * 0.568)/(0.0821 * 393)

n = 0.088 moles

So the molar mass = 10/0.088

= 114 g/mol

Now let’s go to the percentages

C = 84.2/12 = 7.016666666666667

H = 15.8/1 = 15.8

divide by the smallest

C = 7.016666666666667/7.016666666666667 = 1

H = 15.8/7.016666666666667 = 2 approximately

The empirical formula is CH2

So for the molecular formula, we have;

(12 + 2)n = 114

14n = 114

n = 114/14 = approximately 8

So the molecular formula of the liquid will be (CH2)n = C8H16

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