Benzene contains only carbon and hydrogen and has a molar mass of 78.1 g/mol. analysis shows the compound to be 7.44% hydrogen by mass. find the empirical and molecular formula of benzene.

Explanation:

From the question given above, the following data were obtained:

Molar mass of benzene = 78.1 g/mol

Hydrogen (H) = 7.44%

Empirical formula =?

Molecular formula =?

Next, we shall determine percentage of carbon in the compound. This can be obtained as follow:

Percentage of compound = 100%

Hydrogen (H) = 7.44%

Carbon = (Percentage of compound) – (Hydrogen)

Carbon = 100 – 7.44

Since we know the percentage composition of both carbon and hydrogen in the compound, thus, we can obtain the empirical and molecular formula of the compound as illustrated below:

1. Determination of the empirical formula

Carbon (C) = 92.56%

Hydrogen (H) = 7.44%

Divide by their molar mass

C = 92.56 / 12 = 7.71

H = 7.44 / 1 = 7.44

Divide by the smallest

C = 7.71 / 7.44 = 1

H = 7.44 / 7.44 = 1

2. Determination of the molecular formula

Molar mass of benzene = 78.1 g/mol

Empirical formula = CH

Molecular formula = Empirical formula × n

Molecular formula = molar mass

Thus,

Empirical formula × n = molar mass

[CH]n = 78.1

[12 + 1]n = 78.1

13n = 78.1

Divide both side by 13

n = 78.1 / 13

n = 6

Molecular formula = [CH]ₙ

Molecular formula = [CH]₆

1. Empirical formula of benzene is CH

2. Molecular formula of benzene is C₆H₆

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Hydrogen - 7.44%

Carbon - (100-7.44)% = 92.56%

Lets take 100 g of benzene, then we have

Hydrogen - 7.44 g

Carbon - 92.56 g

n - number of moles

n(H) = 7.44g *1 mol/1.0g = 7.44 mol

n(C) = 92.56 g* 1mol/12.0 g ≈ 7.713 mol

n(C) : n(H) = 7.713 mol : 7.44 mol = 1:1

Empirical formula is CH.

M(CH) = (12.0+ 1.00) g/mol = 13.0 g/mol

M (benzene) = 78.1 g/mol

M (benzene)/M(CH)= 78.1 g/mol/13.0 g/mol = 6

So, molecular formula of benzene is C6H6.