Atoxic gas. a, consists of 53.8% nitrogen and 46.2% carbon by mass. at 273 k and 1.01 x 10^5 pa, 1.048g of a occupies 462 cm^3. determine the empirical formula of a. calculate the moral mass of the compound and determine its molar mass

The molecular formula of the compound is C2N2.

From the ideal gas equation;

PV = nRT

P = 1.01 x 10^5 Pa or 1.01 atm

V = 462 cm^3 or 0.462 L

R = 0.082 atm Lmol-1K-1

T = 273 K

n = ?

n = PV/RT

n = 1.01 atm × 0.462 L/ 0.082 atm Lmol-1K-1 × 273 K

n =0.467 /22.386

n = 0.02086 moles

Now;

Molar mass of the compound  is obtained from;

number of moles  = mass/molar mass

molar mass = mass/number of moles

molar mass =  1.048g/0.02086 moles

molar mass = 50.24 g/mol

The empirical formula of the compound is;

C - 53.8%/12,         N - 46.2%/14

C - 4.48,                 N - 3.3

Dividing through by the lowest ratio

C -4.48/3.3            N - 3.3/3.3

C - 1                       N - 1

The empirical formula is CN

The molecular formula is obtained thus;

[12 + 14]n = 50.24

n = 50.24/26

n = 2

The molecular formula of the compound is C2N2

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By the mass percentage, grams of the sample would contain

Which corresponds to

Hence the approximate ratio and the empirical formula .

Apply the idea gas formula to determine the number of moles of the gas molecules present in the sample:

Thus

which is approximately twice of , formula mass for the empirical formula . Hence the molecular formula

first one is the correct answer

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