Use stoicheometry

Question

A certain sample of coal contains 1.4% sulfur by mass. When the coal is burned, the sulfur is converted to sulfur dioxide. To prevent air pollution, this sulfur dioxidr is treated with calcium oxide (CaO) to form calcium sulfite (CaSO3). Calculate the daily mass (In kilograms) of CaO needed if a power plant uses 9.10 x 10^6 kg of coal per day.

Answer 1

Since the problem asks how much CaO is needed, the key reaction is going to be the reaction between sulfur dioxide and calcium oxide to form calcium sulfite:

SO₂ + CaO -> CaSO₃

We first check that all the elements in the reaction are balanced, and they are in this case.

In order to find the amount of CaO, it would be helpful to know the amount of SO₂ since they are in a 1:1 mole ratio in the reaction. We can find the amount of SO₂ using the percent mass of sulfur given at the beginning of the problem.

We are given that 9.10*10^6 kg of coal is used. If 1.4% of that mass is sulfur, then the mass of sulfur is:

9.10*10^6 kg * 0.014 = 127,400 kg of S, or 127,400,000 g. Note this is elemental sulfur, NOT SO₂.

To be able to use stoichiometry we need to convert to moles. We take the mass of S and divide by its molar mass:

127,400,000 g / (32.06 g/mol) = 3,973,799 mol S

But our chemical reaction involves SO₂, not just S. How do we account for this? First, we are told that all of the sulfur is converted to SO2. Since there is 1 sulfur atom in every SO₂ molecule, this means that the same number of moles of SO₂ must be produced - 3,973,799 mol.

Or written as a calculation with a mole ratio:

3,973,799 mol S * (1 mol SO₂ / 1 mol S) = 3,973,799 mol SO₂

Now we return to our reaction:

SO₂ + CaO -> CaSO₃

Based on the coefficients, for every 1 mol of SO₂ consumed, 1 mol of CaO is also consumed.

3,973,799 mol SO₂ * (1 mol CaO / 1 mol SO₂) = 3,973,799 mol CaO

As a final step, convert these moles to grams using the molar mass of CaO:

3,973,799 mol CaO * 56.08 g/mol = 222,850,648 g CaO = 222,850,648 kg CaO.

Most of these types of problems involve using the percent mass to find the mass of some element or compound you care about, then converting that mass to moles, then using the key chemical reaction to find moles of the final compound you want.