A 100.00g sample of the gaseous hydrocarbon ethane is a gaseous hydrocarbon, with 79.89g of carbon and
20.11g of hydrogen. Ethylene is a different gas phase hydrocarbon. A 100.00g sample of ethylene has 85.63g
of carbon with 14.37 of hydrogen. A sample of a hydrocarbon has 64.580g of carbon has 35.420g of hydrogen.
a. Use the mass percents and the law of constant composition to prove that all three compounds are different.
b. Prove that ethane and ethylene obey the law of multiple proportions.
a. Since you have a 100 g sample for all three gases, the percent C and H is the same as grams; i.e.,
ethane:
79.89% C
20.11% H
ethylene:
85.63% C
14.37% H
third hydrocarbon:
64.580% C
35.420% H
Look up the law of constant composition: it says that the amount of an element in a given compound doesn't change. You see that the percents are different for both C and H in all three compounds; therefore, they must be different substances.
b.
For ethane: C79.89H20.11.
Divide by 79.89 to make that C1H0.2517.
For ethylene: C85.63H14.37
Divide by 85.63 to make that
C1H0.1678.
The law of multiple proportions (look it up) says that when two elements form more than one compound that the mass of one element that combines with a fixed mass of the other will always be in the ratio of small whole numbers. So I divided to make the fixed mass 1g for C, now the ratio of H is 0.2517 to 0.1678 and that ratio is 0.2517/0.1678 =1.5 and 1:1.5 is the same as 2:3 and that is in the ratio of small whole numbers. That agrees with the Law of Multiple Proportions.
a. To prove that all three compounds are different, we can compare the mass percentages of carbon and hydrogen in each compound.
For the gaseous hydrocarbon ethane:
- Mass of carbon = 79.89g
- Mass of hydrogen = 20.11g
To calculate the mass percentage of carbon in ethane:
- Mass percentage of carbon = (Mass of carbon / Total mass of compound) * 100
- Mass percentage of carbon in ethane = (79.89g / 100.00g) * 100 = 79.89%
To calculate the mass percentage of hydrogen in ethane:
- Mass percentage of hydrogen = (Mass of hydrogen / Total mass of compound) * 100
- Mass percentage of hydrogen in ethane = (20.11g / 100.00g) * 100 = 20.11%
For the gas phase hydrocarbon ethylene:
- Mass of carbon = 85.63g
- Mass of hydrogen = 14.37g
To calculate the mass percentage of carbon in ethylene:
- Mass percentage of carbon = (Mass of carbon / Total mass of compound) * 100
- Mass percentage of carbon in ethylene = (85.63g / 100.00g) * 100 = 85.63%
To calculate the mass percentage of hydrogen in ethylene:
- Mass percentage of hydrogen = (Mass of hydrogen / Total mass of compound) * 100
- Mass percentage of hydrogen in ethylene = (14.37g / 100.00g) * 100 = 14.37%
For the unknown hydrocarbon:
- Mass of carbon = 64.580g
- Mass of hydrogen = 35.420g
To calculate the mass percentage of carbon in the unknown hydrocarbon:
- Mass percentage of carbon = (Mass of carbon / Total mass of compound) * 100
- Mass percentage of carbon in the unknown hydrocarbon = (64.580g / (64.580g + 35.420g)) * 100 = 64.58%
To calculate the mass percentage of hydrogen in the unknown hydrocarbon:
- Mass percentage of hydrogen = (Mass of hydrogen / Total mass of compound) * 100
- Mass percentage of hydrogen in the unknown hydrocarbon = (35.420g / (64.580g + 35.420g)) * 100 = 35.42%
By comparing the mass percentages of carbon and hydrogen in each compound, we can see that they are different for all three compounds. This proves that all three compounds are different.
b. To prove that ethane and ethylene obey the law of multiple proportions, we need to compare the ratios of the masses of carbon to hydrogen in each compound.
For ethane:
- Mass ratio of carbon to hydrogen = Mass of carbon / Mass of hydrogen = 79.89g / 20.11g = 3.97
For ethylene:
- Mass ratio of carbon to hydrogen = Mass of carbon / Mass of hydrogen = 85.63g / 14.37g = 5.97
The ratio of the masses of carbon to hydrogen in ethylene is approximately 1.5 times greater than in ethane. This shows that the ratio of carbon to hydrogen atoms in ethylene differs from that in ethane by a consistent factor.
Therefore, by comparing the mass ratios of carbon to hydrogen in ethane and ethylene, we can conclude that they obey the law of multiple proportions.