A certain sample of coal contains 1.6 percent sulfur by...

A certain sample of coal contains 1.6 percent sulfur by mass. When the coal is burned, the sulfur is converted to sulfur dioxide. To prevent air pollution, this sulfur dioxide is treated with calcium oxide $(\mathrm{CaO})$ to form calcium sulfite $\left(\mathrm{CaSO}_{3}\right)$. Calculate the daily mass (in kilograms) of CaO needed by a power plant that uses $6.60 \times 10^{6} \mathrm{~kg}$ of coal per day.

Key Concepts

Percent Composition

Percent composition refers to the percentage by mass of a particular element contained in a substance. In this context, knowing that the coal contains 1.6% sulfur by mass allows us to calculate the actual mass of sulfur present in a given mass of coal, which is an essential step in determining the amount of reactant needed in subsequent chemical reactions.

Stoichiometry

Stoichiometry involves using the relationships between the amounts of reactants and products in a balanced chemical equation. It is used to convert the mass of sulfur derived from the coal into the mass of calcium oxide required, ensuring that the reactants are present in the proper proportions for the reaction that converts sulfur into its treated compound.

Chemical Reaction Balancing

Balancing chemical equations is the process of ensuring that the number of atoms for each element is the same on both sides of a chemical reaction. This balance provides the necessary stoichiometric coefficients used in the calculations to determine how much calcium oxide reacts with the sulfur dioxide produced from sulfur combustion.

Molar Mass Calculation

Molar mass calculation involves determining the mass of one mole of a given substance by adding together the atomic masses of its constituent elements. This calculation is crucial for converting between the mass of the reactants (such as sulfur and calcium oxide) and the number of moles, which is necessary for applying stoichiometric ratios in the reaction.

Transcript

00:01 So for this problem, we have some chemical reactions that involve coal, sulfur, and then ultimately caaso3, or calcium sulfite.

00:11 And our goal is to find the mass of cao, calcium oxide, required for a power plant that uses 6 .60 times 10 to the 6 kilograms of coal every day.

00:26 So our first job is going to actually write out the chemical equations that occur.

00:31 So we know that the first reaction is that the sulfur that is in within this coal is then converted to sulfur dioxide.

00:39 So we know that that process will look like this.

00:43 Sulfur in the coal that reacts with oxygen to form sulfur dioxide.

00:47 And we see that this equation is balanced on face.

00:51 And the second reaction that we are told is that the sulfur dioxide to prevent air pollution is treated with calcium oxide.

01:02 And this then forms calcium sulfate and if we look at this equation it's also balanced on face one calcium on both sides one sulfur and three oxygen but we can combine this into one chemical equation to make this process a lot easier so if we look at what cancels out we see that there's an so 2 on both the products and the reactants and so when we add these equations together we'll get sulfur plus c -a -o -2 yields c -a -s -o -3 so now that we have our basic basic chemical equation, we can then go from the initial amount of coal that we have, which is 6 .6 times 10 to 6 kilograms, and then convert that to c -a -o.

01:55 So, you know that this is our starting, number.

02:06 And so first let's convert this to grams by multiplying by 1 ,000...

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