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# A gaseous compound containing hydrogen and carbon is ISBN: 9780321910295 34

## Solution for problem 103P Chapter 11

Introductory Chemistry | 5th Edition

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Problem 103P

PROBLEM 103P

A gaseous compound containing hydrogen and carbon 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 mm Hg and 25 °C, is 0.275 g. What is the molecular formula of the compound?

Step-by-Step Solution:

Solution 103P

Here, we are going to find the molecular formula of the given compound.

Step 1:

Molecular formula gives the total number of atoms in a molecule.

Step 2:

In order to determine the whole number ratio of C and H in the formula, the following table is drawn:

 Element % Relative number of atoms(% / atomic mass) Simple ratio Whole number ratio C 82.66 82.66/12 = 6.89 6.89/6.89 = 1 x 2 = 2 H 17.34 17.34/1 = 17.34 17.34/6.89 = 2.5 x 2 = 5

Hence, empirical formula of the compound is C2H5.

Empirical formula mass = (2 x 12) + (5 x 1) = 24 + 5 = 29

Step 3:

Again, from ideal gas equation, we have,

pV = nRT        ----(1)

Where, p = pressure

V = volume of the gas

n =  number of moles of the gas

R =  universal gas constant and its value is 0.0821 L atm K-1 mol-1

T =  temperature

Here, p = 556 mm Hg = 556 / 760 atm = 0.73 atm

V = 158 mL = 158 / 1000 L = 0.158 L

T =  25oC = 25 + 273 K = 298 K

Substituting the values in equation (1), we get,

n = pV / RT

n = (0.73 atm x 0.158 L) / (298 K x 0.0821 L atm K-1 mol-1)

= (0.11534 L atm) / (24.4658 L atm mol-1)

n = 0.0047 mol.

Step 4 of 6

Step 5 of 6

##### ISBN: 9780321910295

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