Agaseous compound is 30.4 % n and 69.6% o. a 5.25 g sample of the gas occupies a volume of 1.00 l and exerts a pressure of 958 mm of hg at –4.0 c. which of the following is its molecular formula?

a) no
b) no2
c) n3o6
d) n2o4
e) n2o5

The molecular formula = N2O4 (option D)

Explanation:

Step 1: Data given

Compound has 30.4 % N and 69.6 % O

Mass of the sample = 5.25 grams

Volume = 1L

Pressure = 958 mmHg = 1.26 atm

Temperature = -4°C = 269 Kelvin

Molar mass of N = 14 g/mol

Molar mass of O = 16 g/mol

Step 2: Calculate mass of N

Mass of N = 5.25 grams * 0.304 = 1.596 grams

Step 3: Calculate mass of O = 5.25 grams * 0.696 = 3.654 grams

Step 4: Calculate number of moles N

Number of moles = Mass of N/ Molar mass of N

Moles of N = 1.596 grams / 14g/mol

Moles of N = 0.114 moles

Step 5: Calculate moles of O

Moles O = 3.654 grams /16 g/mol

Moles 0 = 0.2884 moles

Step 6: Divide number of moles by the smallest number of mol

N : 0.114 / 0.114 = 1

O: 0.2284 / 0.114 = 2

⇒ This means the empirical formule = NO2

Step 7: Calculate number of moles of 5.25 g sample via gas law:

p*V = nRT

with p = the pressure = 1.26 atm

with v = 1.00 L

with n = the number of moles = TO BE DETERMINED

with R = the gasconstant = 0.08206 L*atm/ K*mol

with T = the temperature = 269 K

n = p*V/R*T

n = (1.26*1L)/(0.08206*269)

n = 0.057 mol  

Step 8: Calculate molar mass of the gas

This means 5.25 grams of the gas = 0.057 moles

So 1 mol = 5.25 / 0.057 = 92.11 g/mol

Step 9: Calculate molar mass of the empirical formula

The empirical formule NO2 has a molar mass of 46 g/mol

Step 10: Calculate molecular formula

92.11 / 46 = 2

This means the empirical formula should be multiplied by 2

2(NO2) = N2O4

The molecular formula = N2O4

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