Answer:
Molecular formula => CH₅N
Step-by-step 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