A new grill has a mass of 30.0 kg. You put 3.0 kg of charcoal in the grill. You burn all the charcoal and the grill has a mass of 30.0 kg. What is the mass of the gases given off? (Assume that the charcoal is pure carbon solid and that it burns completely in oxygen.)

11 kg of gas are emmited to the atmosphere

Explanation:

The problem consists in calculating the total mass of the gases produced in the combustion reaction of the carcoal.

In this case we consider the simple combustion reaction:

C+O2 - > CO2

In relation 1:1 molar with the oxygen.

In this case, the limitant reactant is the carbon, so we make the calculations based in the 3kg of carbon combusted.

First we convert the mass of carbon into mol of carbon

m, C=3kg=3000 g of C

Then we have the mol

n, C=3000g / (12 g/mol) = 249.77 mol C

This number also corresponds to the number of oxygen mol reacting with the charcoal. Therefore we calculate the mass of oxygen.

m, O2=249.77 mol * (32 g/mol) = 7990 g = 7.99 kg, aproximately 8 kg

Then the total mass of gas is the mass of charcoal plus the mass of oxygen

m, total=3kg + 8kg=11kg