Question

What is the molecular formula of a compound that contains 39% C, 45% N, and 16% H if 0.157 g of the compound occupies 125 mL with a pressure of 99.5 kPa at 22°C?

Answer 1

1st find the molar mass:

we have:

P= 99.5 kPa

= (99.5*1000) pa

= 99500.0 Pa

= 99500.0 Pa

= (99500.0/101325) atm

= 0.982 atm

V = 125.0 mL

= (125.0/1000) L

= 0.125 L

T = 22.0 oC

= (22.0+273) K

= 295 K

find number of moles using:

P * V = n*R*T

0.982 atm * 0.125 L = n * 0.08206 atm.L/mol.K * 295 K

n = 5.071*10^-3 mol

mass of solute = 0.157 g

we have below equation to be used:

number of mol = mass / molar mass

5.071*10^-3 mol = (0.157 g)/molar mass

molar mass = 30.96 g/mol

we have mass of each elements as:

C: 39 g

N: 45 g

H: 16 g

Divide by molar mass to get number of moles of each:

C: 39/12.01 = 3.2473

N: 45/14.01 = 3.212

H: 16/1.008 = 15.873

Divide by smallest to get simplest whole number ratio:

C: 3.2473/3.212 = 1

N: 3.212/3.212 = 1

H: 15.873/3.212 = 5

  

So empirical formula is:CNH₅

Molar mass of CNH5 = 1*MM(C) + 1*MM(N) + 5*MM(H)

= 1*12.01 + 1*14.01 + 5*1.008

= 31.06 g/mol

Now we have:

Molar mass = 30.96 g/mol

Empirical formula mass = 31.06 g/mol

Multiplying factor = molar mass / empirical formula mass

= 30.96/31.06

= 1

So molecular formula is:CNH₅