Question

A renewable energy company is testing the combustion of biobutanol, C4H10O. It is sequestering the CO2 and solidifying it using high pressure. The plant burns 500.0 kg of biobutanol every day. Given that the density of dry ice (solid CO2) is 1.56 g/cm3, calculate the diameter in meters of a dry ice ball that would be produced daily by this company.

Answer 1

The equation of biobutanol combustion:

C₄H₁₀O + 6O₂ → 4CO₂ + 5H₂O

m(C₄H₁₀O) = 500.0 kg = 500000 g;

M(C₄H₁₀O) = 74.1216 g/mol;

M(CO₂) = 44.0095 g/mol;

Density ρ(CO₂) = 1.56 g/cm³;

Solution:

$\nu$(C₄H₁₀O) = m/M= (500000 g)/(74,1216 g/mol) = 6745.67 mol;

Proportion according to the equation:

1 mole C₄H₁₀O — 4 moles CO₂

6745.67 moles C₄H₁₀O — x moles CO₂

x = 26982.68 moles ($\nu$(CO₂));

m = $\nu$×M;

m(CO₂) = 26982.68 moles × 44.0095 g/mol = 1187494.6 g;

Density ρ=m/V;

V=m/ρ;

V(CO₂) = (1187494.6 g)/(1.56 g/cm³) = 761214.48 cm³;

The formula for the volume of a sphere (ball) is

V = 4/3×π×r³;

761214.48 cm³ = (4/3)×3.14×r³;

181819.03 cm³ = r³;

r = 56.6517 cm;

Diameter d = 2r = 2×56.6517 = 113.3 cm = 1.13 m;

Answer: 1.13 m