How much air is required to burn coal weighing 10 kg. The volume fraction of oxygen in the air is 21%.

How much air is required to burn coal weighing 10 kg. The volume fraction of oxygen in the air is 21%. Coal contains carbon (mass fraction 96%) sulfur 0.8% and non-combustible mixtures. Calculate the volume of air at a temperature of 30 degrees centigrade and a pressure of 202.6 kPa.

Given:
m (coal) = 10 kg = 10000 g
φ (O2) = 21%
ω (C) = 96%
ω (S) = 0.8%
T = 30 ° C = 303K
P = 202.6 kPa

To find:
V (air) -?

1) C + O2 => CO2;
S + O2 => SO2;
2) m (C) = ω (C) * m (coal) / 100% = 96% * 10000/100% = 9600 g;
3) n (C) = m (C) / M (C) = 9600/12 = 800 mol;
4) n1 (O2) = n (C) = 800 mol;
5) m (S) = ω (S) * m (coal) / 100% = 0.8% * 10000/100% = 80 g;
6) n (S) = m (S) / M (S) = 80/32 = 2.5 mol;
7) n2 (O2) = n (S) = 2.5 mol;
8) n total (O2) = n1 (O2) + n2 (O2) = 800 + 2.5 = 802.5 mol;
9) Vn total. (O2) = n total (O2) * Vm = 802.5 * 22.4 = 17976 l;
10) Vn (air) = Vn (O2) * 100% / φ (O2) = 17976 * 100% / 21% = 85600 l;
11) V1 = Pn * Vn * T1 / (Tn * P1) = 101.3 * 85600 * 303 / (273 * 202.6) = 47503.3 l = 47.5 m3.

Answer: The air volume is 47.5 m3.