Question

The elemental analysis of penicillin is, `"carbon, 57.47%; hydrogen, 5.43%; nitrogen, 8.38%; oxygen, 19.14%; sulphur, 9.59%."` What is the empirical formula?

Answer 1

Divide the mass of the element present by the molecular mass, and multiply this by one hundred percent....

Explanation:

We gots...`C_16H_18N_2O_4S`, whose molecular mass is `334.39*g*mol^-1`...

And so `%C=(16xx12.011*g*mol^-1)/(334.39*g*mol^-1)xx100%=57.5%`

`%H, %N, %O, %S` are...???

Answer 2

Carbon: `57.47%`
Hydrogen: `5.43%`
Nitrogen: `8.38%`
Oxygen: `19.14%`
Sulfur: `9.59%`

Explanation:

The mass percent of an element in a compound is basically this: Given any amount of a compound, what percentage of mass will that element take up?

We can find that using this formula:

`"Mass percent" = "Mass of element"/"Mass of compound"`

Let's say the amount of penicillin G is `1` mole.
The mass of that would be:

`C_16H_18N_2O_4S = 16xxC + 18xxH + 2xxN + 4xxO + S`
`"= 16"xx12.01 + 18xx1.008 + 2xx14.01 + 4xx16.00 + 32.06`
`"= 334.384 g/mol"`

If there's `1` mole of penicillin G, there must be `16` moles of carbon because `C` has a subscript of `16` in `C_16H_18N_2O_4S`.

That means that the mass of carbon is:

`16xxC = 16xx12.01 = 192.16`

With this, we can find the mass percent of carbon in penicillin G.

`"Mass of element"/"Mass of compound" = 192.16 / 334.384 = 0.5747 = 57.47%`

We can use the same method to figure out the mass percents of the other elements in penicillin G:

• Hydrogen is `(18xx1.008) / 334.384 = 0.0543 = 5.43%`.
• Nitrogen is `(2xx14.01) / 334.384 = 0.0838 = 8.38%`.
• Oxygen is `(4xx16.00) / 334.384 = 0.1914 = 19.14%`.
• Sulfur is `(1xx32.06) / 334.384 = 0.0959 = 9.59%`.

To confirm this, we can add these up; if our calculations were correct, they should add up to `100%`.

`57.47% + 5.43% + 8.38% + 19.14% + 9.59% = 100%`

Yay! :)