CHEMISTRY 101 – Calculating Percent by Mass and using it as a conversion factor

The mass percent of an element is that element’s percentage of the compounds total mass. We can calculate the mass percent of an element by dividing the mass of the element in one mole of the compound by the mass of one mole of the compound and multiplying times 100%. Let’s calculate the mass percent of chlorine in CCl2F2. According to our equation, we want the mass of chlorine in one mole of CCl2F2 divided by the mass of one mole of CCl2F2 times 100%. Let’s first calculate the mass of one mole of CCl2F2. We have one mole of carbon with a mass of 12.01 grams, plus two moles of chlorine with its mass of 35.45 grams, plus two moles of fluorine times in its mass of 19 grams. Adding these together we’ll get 120.91 grams of CCl2F2 in one mole of CCl2F2. Going back to our equation for percent chlorine by mass, we have two moles of chlorine in one mole of CCl2F2 and we use the molar mass in our denominator. Completing the calculation, we should get 58.64% chlorine by mass. We can also use mass percent as a conversion factor in dimensional analysis. Our practice problem reads: The typical coal plant burns approximately 1.46 times 10 to the 6 tons of coal per year. What is the mass of sulfur in kilograms produced in one year by one coal plant if the coal is approximately 1.68% sulfur by mass? We’ll start our dimensional analysis with tons of coal. From our hint, 1 ton of coal equals 1000 kg of coal. We can put tons of coal on the bottom in our conversion factor to cancel out our previous units of tons of coal. Then we can use percent sulfur by mass as a conversion factor to convert between mass of our compound coal and mass of the element sulfur. According to our problem, coal is 1.68% sulfur by mass, so for every 100 mass units, 1.68 of them will be sulfur. We can use the units of kilograms and convert directly from kilograms of coal to kilograms of sulfur. For every 100 kg of coal, we have 1.68 kg of sulfur. Our units of kilograms of coal cancel out and we’re left with just kilograms of sulfur. Completing this calculation, we should get 2.45 times 10 to the 7 kg of sulfur.

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