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Chapter 3: Problem 78

Arrange the following substances in order of increasing mass percent of carbon. a. caffeine, \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{O}_{2}\) b. sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) c. ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\)

Short Answer

Expert verified
The substances arranged in increasing order of mass percent of carbon are Ethanol (c), Sucrose (b), and Caffeine (a).

Step by step solution

01

Calculate the molar mass of each substance

First, let's find the molar mass of each substance. The molar mass of an element can be found in the periodic table, which we can use to calculate the molar mass of the compounds. a. Caffeine, \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{O}_{2}\) Molar mass = \((8 \times \mathrm{C}) + (10 \times \mathrm{H}) + (4 \times \mathrm{N}) + (2 \times \mathrm{O})\) b. Sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) Molar mass = \((12 \times \mathrm{C}) + (22 \times \mathrm{H}) + (11 \times \mathrm{O})\) c. Ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) Molar mass = \((2 \times \mathrm{C}) + (6 \times \mathrm{H}) + \mathrm{O}\)
02

Calculate the mass of carbon in 1 mole of each substance

Now that we have the molar mass of each substance, we can calculate the mass of carbon in 1 mole of each substance. a. Caffeine Mass of carbon = (8 * molar mass of C) b. Sucrose Mass of carbon = (12 * molar mass of C) c. Ethanol Mass of carbon = (2 * molar mass of C)
03

Calculate the mass percent of carbon in each substance

Now that we have the mass of carbon in 1 mole of each substance, we can calculate the mass percent of carbon for each substance by dividing the mass of carbon in 1 mole of the substance by the molar mass of the substance and multiplying by 100. a. Caffeine Mass percent of carbon = \(\frac{(8 * \mathrm{C})}{\text{molar mass of caffeine}} \times 100\) b. Sucrose Mass percent of carbon = \(\frac{(12 * \mathrm{C})}{\text{molar mass of sucrose}} \times 100\) c. Ethanol Mass percent of carbon = \(\frac{(2 * \mathrm{C})}{\text{molar mass of ethanol}} \times 100\)
04

Arrange the substances in increasing order of mass percent of carbon

Now that we have calculated the mass percent of carbon for each substance, we can arrange them in increasing order. c. Ethanol b. Sucrose a. Caffeine Therefore, the substances arranged in increasing order of mass percent of carbon are Ethanol (c), Sucrose (b), and Caffeine (a).

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