Answer:
The molecular formula = N2O4
Explanation:
<u>Step 1</u>: Data given
A gaseous compound is 30.4 % N and 69.6%
Mass of the compound = 5.25 grams
Volume of the gas = 1.00 L
Pressure of the gas = 958 mmHg = 1.26 atm
Temperature of the gas = -4 °C = 273 -4°C = 269 Kelvin
Molar mass of N = 14 g/mol
Molar mass of O = 16 g/mol
<u>Step 2</u>: Calculate mass of N
Mass of Nitrogen = 5.25 grams * 0.304 = 1.596 grams
<u>Step 3:</u> Calculate mass of O
Mass of Oxygen = 5.25 grams * 0.696 = 3.654 grams
<u>Step 4:</u> Calculate number of moles N
Number of moles N = Mass of N/ Molar mass of N
Moles of N = 1.596 grams / 14g/mol
Moles of N = 0.114 moles N
<u>Step 5:</u> Calculate moles of O
Moles O = 3.654 grams / 16 g/mol
Moles 0 = 0.2884 moles
<u>Step 6:</u> Calculate empirical formule
We calculate the empirical formule by dividing number of moles by the smallest number of mol
N : 0.114 / 0.114 = 1
O: 0.2284 / 0.114 = 2
Empirical formule = NO2
<u>Step 7: </u>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 gas constant = 0.08206 L*atm/ K*mol
⇒ with T = the temperature = 269 K
number of moles n = (p*V)/(R*T)
n = (1.26*1L)/(0.08206*269)
n = 0.057 mol
<u>Step 8:</u> Calculate molar mass of the compound
This means 5.25 grams of the gas = 0.057 moles
So 1 mol of the compound has a molar mass of: 5.25 / 0.057 = 92.11 g/mol
<u>Step 9</u>: Calculate molar mass of the empirical formula NO2
N = 14 g/mol
O = 16 g/mol
NO2 = 14 + 16 + 16 = 46 g/mol
The empirical formule NO2 has a molar mass of 46 g/mol
<u>Step 10</u>: Calculate molecular formula
92.11 / 46 = 2
This means the empirical formula should be multiplied by 2
2*(NO2) = N2O4
The molecular formula = N2O4
