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Chapter 3: Problem 49

WEB DDT (dichlorodiphenyltrichloroethane) was the first chlorinated insecticide developed. It was used extensively in World War II to eradicate the mosquitoes that spread malaria. Its use was banned in the United States in 1978 because of environmental concerns. DDT is made up of carbon, hydrogen, and chlorine atoms. When a \(5.000-\mathrm{g}\) sample of DDT is burned in oxygen, \(8.692 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) and \(1.142 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) are obtained. A second five-gram sample yields \(2.571 \mathrm{~g}\) of \(\mathrm{HCl}\). What is the simplest formula for DDT?

Short Answer

Expert verified
Answer: The simplest formula for DDT is C₃H₂Cl.

Step by step solution

01

Calculate moles of carbon from the mass of CO2

We know that DDT produces CO2 when burned. We need to find out how many moles of carbon are in the 8.692g of CO2 produced. First, we need to find the molar mass of CO2, which is 12.01g/mol (C) + 2 x 16.00g/mol (O) = 44.01g/mol. Next, we will use the mass and molar mass of CO2 to find the moles of carbon: moles of \(\mathrm{CO}_{2} = \frac{8.692\,g\, \mathrm{CO}_{2}}{44.01\,g/mol} = 0.1974\,mol\, \mathrm{CO}_{2}\) Since there is one mole of carbon in one mole of CO2, we have: moles of C = 0.1974 mol
02

Calculate moles of hydrogen from the mass of H2O

Now, we need to find out how many moles of hydrogen are in the 1.142g of H2O produced. First, we need to find the molar mass of H2O, which is 2 x 1.008g/mol (H) + 16.00g/mol (O) = 18.016g/mol. Next, we will use the mass and molar mass of H2O to find the moles of hydrogen: moles of \(\mathrm{H}_{2}\mathrm{O} = \frac{1.142\,g\, \mathrm{H}_{2}\mathrm{O}}{18.016\,g/mol} = 0.0634\,mol\, \mathrm{H}_{2}\mathrm{O}\) Since there are two moles of hydrogen in one mole of H2O, we have: moles of H = 2 x 0.0634 mol = 0.1268 mol
03

Calculate moles of chlorine from the mass of HCl

A second five-gram sample yields 2.571g of HCl. We need to find out how many moles of chlorine are in the 2.571g of HCl. First, we need to find the molar mass of HCl, which is 1.008g/mol (H) + 35.45g/mol (Cl) = 36.458g/mol. Next, we will use the mass and molar mass of HCl to find the moles of chlorine: moles of \(\mathrm{HCl} = \frac{2.571\,g\, \mathrm{HCl}}{36.458\,g/mol} = 0.0705\,mol\, \mathrm{HCl}\) Since there is one mole of chlorine in one mole of HCl, we have: moles of Cl = 0.0705 mol
04

Determine the simplest mole ratio

Now that we have the moles of carbon, hydrogen, and chlorine, we can find the simplest whole number ratio of these elements in DDT. First, we will find the smallest number of moles among the three elements: smallest moles = min(0.1974, 0.1268, 0.0705) = 0.0705 Next, we will divide the moles of each element by the smallest number of moles to find the mole ratio: C: \(\frac{0.1974}{0.0705} = 2.80 \approx 3\) H: \(\frac{0.1268}{0.0705} = 1.80 \approx 2\) Cl: \(\frac{0.0705}{0.0705} = 1.00 \approx 1\) So the simplest formula for DDT is: \(C_3H_2Cl\)

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