Empirical formula determination from percentage composition

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The percentage composition of a compound leads directly to its empirical formula.

An empirical formula for a compound is the formula of a substance written with the smallest integer subscript.

To obtain the molecular formula of a substance , you need two pieces of information

(1) the percentage composition from which empirical formula can be determined.

(2) The molecular weight

 

The empirical formula from the composition:

The empirical formula of a compound shows the ratios of numbers of atoms in the compounds.You  can find this formula from the composition of the compound by converting masses of the elements to moles.Lets take a look at some examples;

Determing the empirical formula from percentage composition:

A compound of nitrogen and oxygen is analyzed and a sample weighing 1.587 g is found to contain 0.483 g N and 1.104 g O.What is empirical formula of the compound?

Solution: You convert masses of each element to moles,because these quantities will be proportional to the subscripts in the empirical formula.To obtain the smallest integers from the moles, you divide each by the smallest one.If the results are all whole numbers,they will be the subscripts in the formula.

You convert masses to moles;

0.483g N x 1 mol N/14.0 g N = 0.0345 mol N

1.104 g O x 1 mol O/16.00g O = 0.06900 mol O

Now divide each mole number by the smaller one (0.0345 mol).For N, you get 1.00 ; for O , you get 2.00.Thus ,the ratio of number of N atoms to the number of O atoms is 1 to 2.Hence,the empirical formula is NO2.

Problem 2: An analysis of sodium dichromate gives the following mass percentage:17.5% Na, 39.7% Cr and 42.8%.What is empirical formula of this compound.

Solution: Assume for the purpose of this calculation that you have 100.0 g of substace.Then,the mass of each element in the sample equals the numerical value of the percentage.For example, the quantity of sodium in sodium dichromate is 17.5 g, since the substance is 17.5% Na.Now convert the masses to moles and divide each mole number by the smallest.In this example,you do not obtain a series of integers, or whole numbers,from this division.You will need to find a whole-number factor to multiply these results by to obtain integers.Normally, this factor will be 2 or 3 though it might be larger.

Of the 100.0 g of sodium dichromate, 17.5 g is Na, 39.7 g is Cr, and 42.8 g is O.You convert these amounts of moles.

17.5 g Na x 1 mol Na /23.0 g Na = 0.761 mol Na

39.7 g Cr x 1 mol Cr/52.0 g Cr = 0.763 mol Cr

42.8 O x 1 mol o/16.0 g O = 2.68 mol O

Now you divide all the mole numbers by the smallest one.

For Na ; 0.761 mol/0.761 mol = 1.0

For Cr; 0.763/0.761 mol = 1.00

For O : 2.68 mol /0.761 mol = 3.52

you must decide whether these numbers are integers.If you round off last digit,which is subject to experimental error,you get N1.0C1.0O3.5 . In this, case, the subscripts are not all integers.However they can be made into integers by multiplying each one by 2 ;you get Na2.0Cr2.0O7.0 . Thus, empirical formula Na2Cr2O7.