Question

A compound containing only carbon and hydrogen has a carbon-to-hydrogen mass ration of 11.89. Which carbon-to-hydrogen mass ratio is possible for another compound composed only of carbon and hydrogen? a) 2.50 b) 3.97 c) 4.66 d) 7.89 Why is the answer b?

Answer 1

Carbon to hydrogen mass ratio of 11.89

Carbon has a mass of 12

hydrogen has a mass of 1

Suppose we take 100 g of the compound its carbon content will be

100-hydrogen mass = carbon mass

100-hydrogen mass/hydrogen mass = 11.89

11.89hydrogen mass = 100 - hydrogen mass

12.89hydrogen mass = 100

hydrogen mass = 100/12.89

hydrogen mass = 7.75g converting to moles it is 7.75 moles

carbon mass = 92.24g converting to moles it is 92.24/12 = 7.6866 moles

ratio of moles of hydrogen = 7.75/7.6866 = 1.008

ratio of moles of carbon = 1

to get the molecular formul these have to be rounded to the nearest integer so the formula becomes C₁₂₅H₁₂₆ ~C_nH_n

Similarly for CH of 2.5

100-hydrogen mass = carbon mass

100-hydrogen mass/hydrogen mass = 2.5

2.5hydrogen mass = 100 - hydrogen mass

3.5hydrogen mass = 100

hydrogen mass = 100/3.5

hydrogen mass = 28.57g converting to moles it is 28.57 moles

carbon mass = 71.43g converting to moles it is 71.43/12 = 5.95 moles

ratio of moles of hydrogen = 28.57/5.95 = 4.799~4.8

ratio of moles of carbon = 1

C5H24 The amount of hydrogen is too high in this. C_nH_(4n+4)

Similarly for CH of 3.97

100-hydrogen mass = carbon mass

100-hydrogen mass/hydrogen mass = 3.97

3.97hydrogen mass = 100 - hydrogen mass

4.97hydrogen mass = 100

hydrogen mass = 100/4.97

hydrogen mass = 20.12g converting to moles it is 20.12moles

carbon mass = 79.88g converting to moles it is 79.88/12 = 6.65moles

ratio of moles of hydrogen = 20.12/6.65 = 3

ratio of moles of carbon = 1

C2H6 is a proper organic compound - C_nH_(2n+2)

Similarly for CH of 4.66

100-hydrogen mass = carbon mass

100-hydrogen mass/hydrogen mass = 4.66

4.66hydrogen mass = 100 - hydrogen mass

5.66hydrogen mass = 100

hydrogen mass = 100/5.66

hydrogen mass = 17.67g converting to moles it is 17.67moles

carbon mass = 82.33g converting to moles it is 82.33/12 = 6.86moles

ratio of moles of hydrogen = 17.67/6.86 = 2.57~2.60

ratio of moles of carbon = 1

C5H13 - C_nH_(2n+3)

Similarly for CH of 7.89

100-hydrogen mass = carbon mass

100-hydrogen mass/hydrogen mass = 7.89

7.89hydrogen mass = 100 - hydrogen mass

8.89hydrogen mass = 100

hydrogen mass = 100/8.89

hydrogen mass = 11.24g converting to moles it is 11.24moles

carbon mass = 88.75g converting to moles it is 88.75/12 = 7.39moles

ratio of moles of hydrogen = 11.24/7.39 = 1.52~1.5

ratio of moles of carbon = 1

C4H6 - C_nH_(2n-2)

As you can see that from these two of the answers are possible

b) and d) possible because

general formula for hydrocarbons are
Cn H(2n+2) ALKANE
Cn H2n ALKENE
Cn H(2n-2) ALKYNE
CnHn AROMATIC HYDROCARBONS