Question

 

A gaseous hydrogen and carbon containing compound is decomposed and found to contain 82.66% carbon and 17.34% hydrogen by mass. The mass of 158 mL of the gas, measured at 556 mmHg and 25 °C, was found to be 0.275 g. What is the molecular formula of the compound?

 

Answer 1

step 1: calculate the molar mass

we have:

P = 556.0 mm Hg

= (556.0/760) atm

= 0.7316 atm

V = 158.0 mL

= (158.0/1000) L

= 0.158 L

T = 25.0 oC

= (25.0+273) K

= 298 K

find number of moles using:

P * V = n*R*T

0.7316 atm * 0.158 L = n * 0.08205 atm.L/mol.K * 298 K

n = 4.727*10^-3 mol

mass of solute = 0.275 g

we have below equation to be used:

number of mol = mass / molar mass

4.727*10^-3 mol = (0.275 g)/molar mass

molar mass = 58.17 g/mol

step 2: calculate empirical formula and then molecular formula

we have mass of each elements as:

C: 82.66 g

H: 17.34 g

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

C: 82.66/12.01 = 6.8826

H: 17.34/1.008 = 17.2024

Divide by smallest:

C: 6.8826/6.8826 = 1

H: 17.2024/6.8826 = 2.5

multiply by 2 to get simplest whole number ratio:

C : 1*2 = 2

H : 2.5*2 = 5

So empirical formula is:C2H5

Molar mass of C2H5 = 2*MM(C) + 5*MM(H)

= 2*12.01 + 5*1.008

= 29.06 g/mol

Now we have:

Molar mass = 58.17 g/mol

Empirical formula mass = 29.06 g/mol

Multiplying factor = molar mass / empirical formula mass

= 58.17/29.06

= 2

So molecular formula is:C₄H₁₀