Empirical Formula of a Compound with only percentages given

[dacoolguy]

Homework Statement

Determine the Empirical Formula of a compound which, when analyzed, is shown to consist of 62.07% carbon, 27.59% oxygen and 10.34% hydrogen.
The answer is supposedly C₃OH₆

Homework Equations

The Attempt at a Solution

First,I started by writing the ratio: C : O : H
Then, under each, I wrote the respective percentages.
I divided everything by the lowest percentage (10.34), giving me a ratio of 6:2.668:1, (C₆O₃H).
I have no real idea of what to do or where I went wrong. Thanks so much for your help!

 

[dacoolguy]

I'm really sorry- worked it out from another thread:)

Percent to mass,
Mass to mole,
Divide by small,
Multiply 'til whole.

Assume 100g of compound. Change % to g. Divide these masses by their molar masses to get moles. Divide each mole amount by the smallest mole quantity of the group. You'll get numbers that are either close to a whole number or close to half (such as 1.5, 2.5, etc.) multiply all of the numbers by a common factor until they are all whole numbers, and this will be the empirical formula.
Thanks to Gannon on thread: https://www.physicsforums.com/showthread.php?t=224348 :)

PS: how do I delete a thread once I found the solution (before any posts)?

 

[Blueshift5]

Based on the given percentages, we can assume that we have a compound with a total mass of 100 grams. This means that we have 62.07 grams of carbon, 27.59 grams of oxygen, and 10.34 grams of hydrogen.

To determine the empirical formula, we need to find the smallest whole number ratio between the elements. In this case, we can divide all the masses by the molar mass of each element: 12.01 g/mol for carbon, 16.00 g/mol for oxygen, and 1.01 g/mol for hydrogen.

This gives us a ratio of 5.17:1.72:10.24. We can round these numbers to the nearest whole number, giving us a ratio of 5:2:10.

This means that the empirical formula of the compound is C5O2H10. However, this is not the simplest ratio between the elements. We can divide all the numbers by 2 to get the simplest ratio of 2.5:1:5.

Finally, we can multiply all the numbers by 2 to get whole numbers, giving us an empirical formula of C5O2H10, which can be simplified to C3OH6.

So, the answer is indeed C3OH6. Your approach of dividing by the lowest percentage was correct, but you needed to take into account the molar masses of each element to get the simplest ratio.