A compound was found to have 85.7% carbon and 14.3% hydrogen. Its molecular mass is 84. What is its empirical formula? What is its molecular formula?

Question

A compound was found to have 85.7% carbon and 14.3% hydrogen. Its molecular mass is 84.  What is its empirical formula? What is its molecular formula?

Caleb Adams · Accepted Answer

#"empirical formula"# #=# #CH_2#.

#"molecular formula"# #=# #C_6H_12# AS with all these problems, we assume (for simplicity) #100*g# of unknown compound. And thus there are #(85.7%xx100*g)/(12.011*g*mol^-1)# with respect to carbon, i.e. #7.14*mol*C# And #(14.3%xx100*g)/(1.00794*g*mol^-1)# with respect to hydrogen, i.e. #14.1*mol*H#. And thus the #"empirical formula"#, the simplest whole number ratio that defines constituent elements in a species is #CH_2#. Now the #"molecular formula"# is alway a whole number multiple of the #"empirical formula"#: #"empirical formula"xxn# #=# #"molecular formula"# So #(12.011*g*mol^-1+2xx1.00794*g*mol^-1)xxn=84*g*mol^-1.# So #n=6#, and #"molecular formula"# #=# #6xxCH_2# #=# #C_6H_12#

Wyatt Atkins · Answer

undefined To find the empirical formula, we need to determine the ratio of atoms in the compound.

Given:
- Percentage of carbon (C) = 85.7%
- Percentage of hydrogen (H) = 14.3%

First, we assume we have 100 g of the compound for easier calculation.

- Number of moles of C = 85.7 g / 12.01 g/mol = 7.14 mol
- Number of moles of H = 14.3 g / 1.008 g/mol = 14.18 mol

To find the simplest whole-number ratio, we divide by the smallest number of moles, which is 7.14:

- C: $ \frac{7.14}{7.14} $ ≈ 1
- H: $ \frac{14.18}{7.14} $ ≈ 2

So, the empirical formula is CH2.

Next, to find the molecular formula, we need to know the molecular mass of the empirical formula, which is 12 (C) + 2 (H) = 14.

Given the molecular mass of the compound is 84, we divide 84 by 14 to find the multiplier:

- $ \frac{84}{14} $ = 6

Thus, the molecular formula is 6 times the empirical formula: C6H12.