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Chapter 3: Problem 69

The annual production of sulfur dioxide from burning coal and fossil fuels, auto exhaust, and other sources is about 26 million tons. The equation for the reaction is$$\mathrm{S}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g)$$How much sulfur (in tons), present in the original materials, would result in that quantity of \(\mathrm{SO}_{2} ?\)

Short Answer

Expert verified
Therefore, it will take about 13 million tons of sulfur to produce 26 million tons of sulfur dioxide.

Step by step solution

01

Understand the chemical equation

In the balanced equation \(S(s) + O_{2}(g) \rightarrow SO_{2}(g)\), one mole of sulfur reacts with one mole of oxygen to produce one mole of sulfur dioxide.
02

Convert known quantity to moles

It is known that the production of sulfur dioxide is 26 million tons per year. Using the molar mass of sulfur dioxide (approximately 64.066 g/mol) and the fact that 1 metric ton equals 1000000 g, the amount of sulfur dioxide in moles can be calculated using the formula \(Number of moles = mass (tons) * (1000000 \ g/1 ton) * (1 \ mole/64.066 g)\). Using this formula, the quantity of sulfur dioxide translates to approximately \(4.06*10^{8}\) moles.
03

Use stoichiometric ratio to find quantity of sulfur

Since stoichiometry of the given equation shows a 1:1 ratio between sulfur and sulfur dioxide, the amount (in moles) of the sulfur needed is equal to the amount of sulfur dioxide produced. Hence, the quantity of sulfur required is also \(4.06*10^{8}\) moles.
04

Convert moles of sulfur to tons

The molar mass of sulfur (approximately 32.066 g/mol) is used in conjunction with the calculated amount of sulfur (in moles) to find the sulfur's mass in grams. The formula used here is \(mass (g) = number of moles * molar mass (g/mole)\). The resulting number is then converted from grams to tons by dividing by 1000000. Using this method, the mass of sulfur that would result in the given quantity of sulfur dioxide is found to be approximately 13 million tons.

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Most popular questions from this chapter

A compound X contains 63.3 percent manganese (Mn) and 36.7 percent O by mass. When \(X\) is heated, oxygen gas is evolved and a new compound Y containing 72.0 percent \(\mathrm{Mn}\) and 28.0 percent \(\mathrm{O}\) is formed. (a) Determine the empirical formulas of X and Y. (b) Write a balanced equation for the conversion of \(\mathrm{X}\) to \(\mathrm{Y}\)

Ammonia and sulfuric acid react to form ammonium sulfate. (a) Write an equation for the reaction. (b) Determine the starting mass (in grams) of each reactant if \(20.3 \mathrm{~g}\) of ammonium sulfate is produced and \(5.89 \mathrm{~g}\) of sulfuric acid remains unreacted.

If we know the empirical formula of a compound, what additional information do we need to determine its molecular formula?

Nitroglycerin \(\left(\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{~N}_{3} \mathrm{O}_{9}\right)\) is a powerful explosive. Its decomposition may be represented by$$4 \mathrm{C}_{3} \mathrm{H}_{5} \mathrm{~N}_{3} \mathrm{O}_{9} \longrightarrow 6 \mathrm{~N}_{2}+12 \mathrm{CO}_{2}+10 \mathrm{H}_{2} \mathrm{O}+\mathrm{O}_{2} $$This reaction generates a large amount of heat and many gaseous products. It is the sudden formation of these gases, together with their rapid expansion, that produces the explosion. (a) What is the maximum amount of \(\mathrm{O}_{2}\) in grams that can be obtained from \(2.00 \times 10^{2} \mathrm{~g}\) of nitroglycerin? (b) Calculate the percent yield in this reaction if the amount of \(\mathrm{O}_{2}\) generated is found to be \(6.55 \mathrm{~g}\).

Potash is any potassium mineral that is used for its potassium content. Most of the potash produced in the United States goes into fertilizer. The major sources of potash are potassium chloride \((\mathrm{KCl})\) and potassium sulfate \(\left(\mathrm{K}_{2} \mathrm{SO}_{4}\right) .\) Potash production is often reported as the potassium oxide \(\left(\mathrm{K}_{2} \mathrm{O}\right)\) equivalent or the amount of \(\mathrm{K}_{2} \mathrm{O}\) that could be made from a given mineral. (a) If \(\mathrm{KCl}\) costs \(\$ 0.55\) per \(\mathrm{kg}\), for what price (dollar per \(\mathrm{kg}\) ) must \(\mathrm{K}_{2} \mathrm{SO}_{4}\) be sold to supply the same amount of potassium on a per dollar basis? (b) What mass (in kg) of \(\mathrm{K}_{2} \mathrm{O}\) contains the same number of moles of \(\mathrm{K}\) atoms as \(1.00 \mathrm{~kg}\) of KCl?
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