Question

Estimate the mole ratio of O2 to the sample(benzoic acid, sucrose) and compare the estimate with the stoichiometric ratio for the combustion. The volume of the bomb is 0.3dm^3. Use T=300K and 30atm for the pressure of O2. As a first approximation use the ideal gas law, but more a more refine estimate, use the compressibility factor for O2 at 30atm and 300K as calculated from the Van der Waals equation. Assume ideal behaviour on the part of oxygen.

Combustion of benzoic Acid:

C6H5COOH(s) + 15/2 O2(g)--> 7 CO2(g) + 3 H2O(l)

Combustion of sucrose:

C12H22O11 + 12 O2 >> 12 CO2 + 11 H2O  

Answer 1

The mole ratio of benzoic acid to O2 is 1: 7.5

The mole ratio of sucrose to O2 is 1:12

The volume of the bomb is 0.3 dm³ which is 300 mL or 0.3 L

PV=nRT

30 atm x 0.3 L =n x 0.082057 L atm K⁻¹ mol⁻¹ x 300 K

n = 0.365 moles

The Van der Waals equation of states is

[p + (an²/V²)] (V – nb) = nRT

for oxygen a and b are 1.382 L²atm/mol² and 0.03186 L/mol

[30 atm + (1.382 n²/0.3²)][0.3- (nx0.03186)] = n x 0.082057 L atm K⁻¹ mol⁻¹ x 300 K

from this solving for n we get n = 0.3519 moles