Question

A sample of a gaseous compound of nitrogen and oxygen weighs 5.25 g and occupies a volume of 1.00 L at a pressure of 1.26 atm and temperature of -4.0 °C. Which of the following molecular formulas could be that of the compound?

Answer is N₂O₄

_{Please show work, thank you!}

Answer 1

Ideal Gas Equation: PV = nRT :

We have Pressure P = 1.26 atm;
Volume V = 1L
R = 0.08205 L atm / mol·K
T = -4.0^oC = -4.0 + 273 = 269K

(1.26 atm) (1.00 L) = (n) (0.08205 L atm / mol·K ) (269 K)

n = 0.0570 mol

Now, we have no. moles and also given the mass of the gas m = 5.25 g
Therefore, we calculate the molecular weight:
no. of moles = mass/mol.wt
mol.wt = mass/no.moles
       = 5.25 g / 0.057 mol
       = 92.1 g/mol

Now we have to find the empirical formula, but there is no further information about the how much % of each element
contributes. Therefore, the information is not complete in this problem.
We need mass percent of each element in the gas to determine the empirical formula.
From the empirical formula and molecular weight, you can determine the molecular formula.

Suppose, the contains 30.6% nitrogen and 69.4% oxygen by mass,

Let's assume 100 g of the gas is present.

N: 30.6g/14.007g/mol = 2.1846 mol
O: 69.4g / 16.00g/mol = 4.3375 mol

N: 2.1846/2.1846 = 1
O: 4.3375/2.1846 = 1.985 = 2

The Empirical formula = NO₂

Empirical formula wt = 14 + 2(16) = 46

Therefore, molecular wt/empirical formula wt= 92.1 / 46 ~ 2
Therefore the molecular formula is : (NO₂)₂ = N₂O₄