Question

10 emprical formula on numerical

Answer 1

Calculate empirical formula when given percent composition data

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Calculate empirical formula when given mass data

Determine identity of an element from a binary formula and a percent composition

Determine identity of an element from a binary formula and mass data

Determine the formula of a hydrate

Notice below how I do the first problem with some attention to using proper atomic weights, as well as keeping close to the proper number of significant figures. Then, notice how I get away from that (as well as being real consistent with units) in the following problems.

Notice also how it really doesn't make much of a difference. The trick is to know when to do that and it comes only via experience. Generally speaking, in empirical formula problems, C = 12, H = 1, O = 16 and S = 32 are sufficient.

There are times when using 12.011 or 1.008 will be necessary. If you hit a problem that just doesn't seem to be working out, go back and re-calculate with more precise atomic weights. These problems, however, are fairly uncommon.

For what it is worth, one piece of advice on rounding: don't round off on the moles if you see something like 2.33 or 4.665. That first one can be rendered as two and one-third (or seven thirds) and the second one as four and two-thirds (or fourteen thirds). In a situation like that, you would multiply by three to reach the smallest whole-number ratio rather than dividing by the smallest.

I know it's easy to say, harder to demonstrate. Some of the problems below involve this thirds issue. Look for a problem involving citric acid. Just be aware that rounding off too early and/or too much is a common problem in this type of problem.

Problem #1: A compound is found to contain 50.05 % sulfur and 49.95 % oxygen by weight. What is the empirical formula for this compound? The molecular weight for this compound is 64.07 g/mol. What is its molecular formula?

Solution:

1) Assume 100 g of the compound is present. This changes the percents to grams:

S ⇒ 50.05 g
O ⇒ 49.95 g

2) Convert the masses to moles:

S ⇒ 50.05 g / 32.066 g/mol = 1.5608 mol
O ⇒ 49.95 g / 16.00 g/mol = 3.1212 mol

3) Divide by the lowest, seeking the smallest whole-number ratio:

S ⇒ 1.5608 / 1.5608 = 1
O ⇒ 3.1212 / 1.5608 = 2

4) Write the empirical formula:

SO2

5) Compute the "empirical formula weight:"

32 + 16 + 16 = 64

6) Divide the molecule weight by the "EFW:"

64.07 / 64 = 1

7) Use the scaling factor computed just above to determine the molecular formula:

SO2 times 1 gives SO2 for the molecular formula

Problem #2: A compound is found to contain 64.80 % carbon, 13.62 % hydrogen, and 21.58 % oxygen by weight. What is the empirical formula for this compound? The molecular weight for this compound is 74.14 g/mol. What is its molecular formula?

Solution:

1) Assume 100 g of the compound is present. This changes the percents to grams:

C ⇒ 64.80 g
H ⇒ 13.62 g
O ⇒ 21.58 g

2) Convert the masses to moles:

C ⇒ 64.80 g / 12 = 5.4
H ⇒ 13.62 g / 1 = 13.62
O ⇒ 21.58 g / 16 = 1.349

3) Divide by the lowest, seeking the smallest whole-number ratio:

C ⇒ 5.4 / 1.349 = 4
H ⇒ 13.62 / 1.349 = 10
O ⇒ 1.349 / 1.349 = 1

4) Write the empirical formula:

C4H10O

5) Determine the molecular formula:

"EFW" ⇒ 48+10+16 = 74 74.14 / 74 = 1 molecular formula = C4H10O

Problem #3: A compound is found to contain 31.42 % sulfur, 31.35 % oxygen, and 37.23 % fluorine by weight. What is the empirical formula for this compound? The molecular weight for this compound is 102.2 g/mol.