What is the molecular formula of a compound that contains 38.6% C, 45% N, and 16.4% H, if 0.158 g of the compound occupies 125 mL with a pressure of 0.982 atm at 22oC?

Molecular formula => CH₅N

Explanation:

We'll begin by calculating the number of mole of the compound. This can be obtained as follow:

Pressure (P) = 0.982 atm

Volume (V) = 125 mL = 125 / 1000 = 0.125 L

Temperature (T) = 22 °C = 22 + 273 = 295 K

Gas constant (R) = 0.0821 atm.L/Kmol

Number of mole (n) =?

PV = nRT

0.982 × 0.125 = n × 0.0821 × 295

0.12275 = n × 24.2195

Divide both side by 24.2195

n = 0.12275 / 24.2195

n = 0.0051 mole

Next, we shall determine the molar mass of the compound.

Mass of compound = 0.158 g

Mole of compound = 0.0051 mole

Molar mass of compound =?

Mole = mass /molar mass

0.0051 = 0.158 / molar mass

Cross multiply

0.0051 × molar mass = 0.158

Divide both side by 0.0051

Molar mass = 0.158 / 0.0051

Molar mass of compound = 31 g/mol

Next, we shall determine the empirical formula of the compound. This can be obtained as follow:

C = 38.6%

H = 16.4%

N = 45%

Divide by their molar mass

C = 38.6 / 12 = 3.217

H = 16.4 / 1 = 16.4

N = 45 / 14 = 3.214

Divide by the smallest

C = 3.217 / 3.214 = 1

H = 16.4 / 3.214 = 5

N = 3.214 / 3.214 = 1

Empirical formula => CH₅N

Finally, we shall determine the molecular formula of the compound. This can be obtained as follow:

Empirical formula = CH₅N

Molar mass of compound = 31 g/mol

Molecular formula = Empirical × n = molar mass of compound

[CH₅N]ₙ = 31

[12 + (5×1) + 14]n = 31

[12 + 5 + 14]n = 31

31n = 31

Divide both side by 31

n = 31 / 31

n = 1

Molecular formula => [CH₅N]ₙ

Molecular formula => [CH₅N]₁

Molecular formula => CH₅N