The molecular formula of the compound is N₂H₄
we'll begin by calculating the number of mole of the unknown gas. This can be obtained as follow:
Volume (V) = 200 mL = 200 / 1000 = 0.2 L
Pressure (P) = 1.81 atm
Temperature (T) = 25 °C = 25 + 273 = 298 K
Gas constant (R) = 0.0821 atm.L/Kmol
PV = nRT
1.81 × 0.2 = n × 0.0821 × 298
0.362 = n × 24.4658
Divide both side by 24.4658
[tex]n \: = \frac{0.362}{24.4658} [/tex]
mole of compound = 0.0148 mole
mass of compound = 0.473 g
[tex]molar \: mass \: = \frac{mass}{mole} \\ \\ molar \: mass \: = \frac{0.473}{0.0148} \\ \\ [/tex]
Nitrogen (N) = 0.414 g
Hydrogen (H) = 0.0591 g
Divide by their molar mass
N = 0.414 / 14 = 0.0296
H = 0.0591 / 1 = 0.0591
Divide by the smallest
N = 0.0296 / 0.0296 = 1
H = 0.0591 / 0.0296 = 2
Therefore, the empirical formula of the compound is NH₂
Molar mass of compound = 31.96 g/mol
Empirical formula = NH₂
Molecular formula = Empirical formula × n = Molar mass
[NH₂]n = 31.96
[14 + (2×1)]n = 31.96
16n = 31.96
Divide both side by 16
n = 31.96 / 16
n = 2
Molecular formula = [NH₂]n
Molecular formula = [NH₂]₂
Thus, the molecular formula of the compound is N₂H₄
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