# 7.2.3: Practice Empirical and Molecular Formulas

#### Percent Composition Problems

Exercise $$\PageIndex{1}$$

What is the percent composition of Co(NO3)2?

Hint: What is formula mass?

Co mass  $$=1 \times 58.93 = 58.93$$ amu

N mass  $$=2 \times 14.01 = 28.02$$ amu

O mass  $$=6 \times 16.00 = 96.00$$ amu

Total = 182.95 amu

Co mass percent =$$\dfrac{58.93amu}{182.95amu}\times 100$$ % = 32.21 %

N mass percent =$$\dfrac{28.02amu}{182.95amu}\times 100$$ % = 15.32 %

O mass percent =$$\dfrac{96.00amu}{182.95amu}\times 100$$ % = 52.47 %

What is the percent composition of Ni2(SO4)3?

Hint: What is formula mass?

Ni mass  $$=2 \times 58.69 = 117.38$$ amu

S mass  $$=3 \times 32.07 = 96.21$$ amu

O mass  $$=12 \times 16.00 =192.00$$ amu

Total = 405.59 amu

Ni mass percent =$$\dfrac{117.38amu}{405.59amu}\times 100$$ % = 28.94 %

S mass percent =$$\dfrac{96.21amu}{405.59amu}\times 100$$ % = 23.72 %

O mass percent =$$\dfrac{192.00amu}{405.59amu}\times 100$$ % = 47.34 %

You analyze a sample and find that it contains 22.46 g of Fe and 42.76 g Cl.  What is the percent composition of this sample?

Hint: What is total mass?

Your sample is 22.46 g + 42.76 g = 65.22 g

Fe mass percent =$$\dfrac{22.46g}{65.22g}\times 100$$ % = 34.44 %

Cl mass percent =$$\dfrac{42.76g}{65.22g}\times 100$$ % = 65.56 %

#### Empirical Formula from Percent Composition

Exercise $$\PageIndex{1}$$

What is the empirical formula of a compound that is 73.42 % Co and 26.58% O by mass?

Hint

Convert 73.42 g Co to moles Co (Co = 58.93 g/mol) and 26.58 g O to moles O (O = 16.00 g/mol).

At first, you get 1.246 mol Co and 1.661 mol O.  Divide both of these by the smaller number (1.246)

This gives 1 mol Co and 1.33 mol O.  Now multiply both of these by 3.

This gives 3 mol Co and 4 mol O.

Co3O4

What is the empirical formula of a compound that is 26.52 % Cr, 24.53 % S, and 48.95% O by mass?

Hint

Convert 26.52 g Cr to moles Cr (Cr = 52.00 g/mol), 24.53 g S to moles S (S = 32.07 g/mol), and 48.95 g O to moles O (O = 16.00 g/mol).

At first, you get 0.5100 mol Cr, 0.7649 mol S, and 3.059 mol O.  Divide all of these by the smallest number (0.5100)

This gives 1 mol Cr, 1.5 mol S, and 6 mol O.  Now multiply all of these by 2.

This gives 2 mol Cr, 3 mol S, and 12 mol O.

Cr2S3O12 (this is actually the compound Cr2(SO4)3)

#### Empirical and Molecular Formulas

Exercise $$\PageIndex{1}$$

For each formula below, give the empirical formula.  Sometimes the formula given is the same as the empirical, sometimes it is different.

a)  C3H6O3

b)  N2O4

c)  Mg3N2

d)  C7H14O2

e)  P2O5

f)  C4H8N2

CH2O and NO2

Mg3Nand C7H14O2

P2O5 and C2H4

What is the molecular formula for a compound with empirical formula of CH2O and molecular mass of 150.15 amu?

C5H10O5  (Molecular mass is five times as big as empirical formula mass.)

What is the molecular formula for a compound with empirical formula of CH2NO2 and molecular mass of 180.12 amu?

C3H6N3O6  (Molecular mass is three times as big as empirical formula mass.)

What is the molecular formula for a compound with a molecular mass of 86.18 amu that is found to be 83.62 % C and 16.38 % H by mass? (Must find empirical formula first using percent composition.)

Empirical Formula

C3H7

At first, you get 6.963 mol C and 16.22 mol H.  Divide both of these by the smallest number (6.963)

This gives 1 mol C and 2.33 mol H.  Now multiply both of these by 3.

This gives 3 mol C and 7 mol H.

Molecular Formula

C6H14  (Molecular mass is two times as big as empirical formula mass.)