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Chapter 3: Problem 25

Calculate the percentage by mass of the indicated element in the following compounds: (a) carbon in acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2},\) a gas used in welding; (b) hydrogen in ascorbic acid, \(\mathrm{HC}_{6} \mathrm{H}_{7} \mathrm{O}_{6},\) also known as vitamin C; (c) hydrogen in ammonium sulfate, \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\), a substance used as a nitrogen fertilizer; (d) platinum in \(\mathrm{PtCl}_{2}\left(\mathrm{NH}_{3}\right)_{2},\) a chemotherapy agent called cisplatin; (e) oxygen in the female sex hormone estradiol, \(\mathrm{C}_{18} \mathrm{H}_{24} \mathrm{O}_{2}\); (f) carbon in capsaicin, \(\mathrm{C}_{18} \mathrm{H}_{27} \mathrm{NO}_{3},\) the compound that gives the hot taste to chili peppers.

Short Answer

Expert verified
(a) Percentage by mass of carbon in acetylene: 92.2% (b) Percentage by mass of hydrogen in ascorbic acid: 4.6% (c) Percentage by mass of hydrogen in ammonium sulfate: 6.1% (d) Percentage by mass of platinum in cisplatin: 65.0% (e) Percentage by mass of oxygen in estradiol: 11.7% (f) Percentage by mass of carbon in capsaicin: 70.8%

Step by step solution

01

(a) Carbon in acetylene, C2H2

First, let's find the molar mass of the compound acetylene (C2H2). Use the atomic masses for carbon (C, 12.01 g/mol) and hydrogen (H, 1.01 g/mol): Molar mass of C2H2 = (2 × 12.01 g/mol) + (2 × 1.01 g/mol) = 24.02 g/mol + 2.02 g/mol = 26.04 g/mol Next, calculate the mass of the specified element (carbon) in the compound: Mass of carbon = 2 × 12.01 g/mol = 24.02 g/mol Now, calculate the percentage by mass of the carbon in the acetylene: Percentage by mass of carbon = (24.02 g/mol / 26.04 g/mol) × 100 = 92.2%
02

(b) Hydrogen in ascorbic acid, HC6H7O6

First, let's find the molar mass of the compound ascorbic acid (HC6H7O6). Use the atomic masses for carbon (C, 12.01 g/mol), hydrogen (H, 1.01 g/mol), and oxygen (O, 16.00 g/mol): Molar mass of HC6H7O6 = (1 × 1.01 g/mol) + (6 × 12.01 g/mol) + (7 × 1.01 g/mol) + (6 × 16.00 g/mol) = 1.01 g/mol + 72.06 g/mol + 7.07 g/mol + 96.00 g/mol = 176.14 g/mol Next, calculate the mass of the specified element (hydrogen) in the compound: Mass of hydrogen = (1 + 7) × 1.01 g/mol = 8.08 g/mol Now, calculate the percentage by mass of the hydrogen in the ascorbic acid: Percentage by mass of hydrogen = (8.08 g/mol / 176.14 g/mol) × 100 = 4.6%
03

(c) Hydrogen in ammonium sulfate, (NH4)2SO4

First, let's find the molar mass of the compound ammonium sulfate ((NH4)2SO4). Use the atomic masses for nitrogen (N, 14.01 g/mol), hydrogen (H, 1.01 g/mol), sulfur (S, 32.07 g/mol), and oxygen (O, 16.00 g/mol): Molar mass of (NH4)2SO4 = (2 × (1 × 14.01 g/mol + 4 × 1.01 g/mol)) + (1 × 32.07 g/mol) + (4 × 16.00 g/mol) = 2 × (14.01 g/mol + 4.04 g/mol) + 32.07 g/mol + 64.00 g/mol = 2 × 18.05 g/mol + 96.07 g/mol = 132.14 g/mol Next, calculate the mass of the specified element (hydrogen) in the compound: Mass of hydrogen = 2 × (4 × 1.01 g/mol) = 8.08 g/mol Now, calculate the percentage by mass of the hydrogen in the ammonium sulfate: Percentage by mass of hydrogen = (8.08 g/mol / 132.14 g/mol) × 100 = 6.1%
04

(d) Platinum in PtCl2(NH3)2, cisplatin

First, let's find the molar mass of the compound cisplatin (PtCl2(NH3)2). Use the atomic masses for platinum (Pt, 195.08 g/mol), chlorine (Cl, 35.45 g/mol), nitrogen (N, 14.01 g/mol), and hydrogen (H, 1.01 g/mol): Molar mass of PtCl2(NH3)2 = (1 × 195.08 g/mol) + (2 × 35.45 g/mol) + (2 × (1 × 14.01 g/mol + 3 × 1.01 g/mol)) = 195.08 g/mol + 70.90 g/mol + (2 × (14.01 g/mol + 3.03 g/mol)) = 195.08 g/mol + 70.90 g/mol + 2 × 17.05 g/mol = 300.18 g/mol Next, calculate the mass of the specified element (platinum) in the compound: Mass of platinum = 1 × 195.08 g/mol = 195.08 g/mol Now, calculate the percentage by mass of the platinum in the cisplatin: Percentage by mass of platinum = (195.08 g/mol / 300.18 g/mol) × 100 = 65.0%
05

(e) Oxygen in estradiol, C18H24O2

First, let's find the molar mass of the compound estradiol (C18H24O2). Use the atomic masses for carbon (C, 12.01 g/mol), hydrogen (H, 1.01 g/mol), and oxygen (O, 16.00 g/mol): Molar mass of C18H24O2 = (18 × 12.01 g/mol) + (24 × 1.01 g/mol) + (2 × 16.00 g/mol) = 216.18 g/mol + 24.24 g/mol + 32.00 g/mol = 272.42 g/mol Next, calculate the mass of the specified element (oxygen) in the compound: Mass of oxygen = 2 × 16.00 g/mol = 32.00 g/mol Now, calculate the percentage by mass of the oxygen in the estradiol: Percentage by mass of oxygen = (32.00 g/mol / 272.42 g/mol) × 100 = 11.7%
06

(f) Carbon in capsaicin, C18H27NO3

First, let's find the molar mass of the compound capsaicin (C18H27NO3). Use the atomic masses for carbon (C, 12.01 g/mol), hydrogen (H, 1.01 g/mol), nitrogen (N, 14.01 g/mol), and oxygen (O, 16.00 g/mol): Molar mass of C18H27NO3 = (18 × 12.01 g/mol) + (27 × 1.01 g/mol) + (1 × 14.01 g/mol) + (3 × 16.00 g/mol) = 216.18 g/mol + 27.27 g/mol + 14.01 g/mol + 48.00 g/mol = 305.46 g/mol Next, calculate the mass of the specified element (carbon) in the compound: Mass of carbon = 18 × 12.01 g/mol = 216.18 g/mol Now, calculate the percentage by mass of the carbon in the capsaicin: Percentage by mass of carbon = (216.18 g/mol / 305.46 g/mol) × 100 = 70.8%

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Most popular questions from this chapter

The reaction between potassium superoxide, \(\mathrm{KO}_{2}\), and \(\mathrm{CO}_{2}\), $$ 4 \mathrm{KO}_{2}+2 \mathrm{CO}_{2} \longrightarrow 2 \mathrm{~K}_{2} \mathrm{CO}_{3}+3 \mathrm{O}_{2} $$ is used as a source of \(\mathrm{O}_{2}\) and absorber of \(\mathrm{CO}_{2}\) in self-contained breathing equipment used by rescue workers. (a) How many moles of \(\mathrm{O}_{2}\) are produced when \(0.400 \mathrm{~mol}\) of \(\mathrm{KO}_{2}\) reacts in this fashion? (b) How many grams of \(\mathrm{KO}_{2}\) are needed to form \(7.50 \mathrm{~g}\) of \(\mathrm{O}_{2}\) ? (c) How many grams of \(\mathrm{CO}_{2}\) are used when \(7.50 \mathrm{~g}\) of \(\mathrm{O}_{2}\) are produced?

What is the molecular formula of each of the following compounds? (a) empirical formula \(\mathrm{CH}_{2}\), molar mass \(=84 \mathrm{~g} / \mathrm{mol}\) (b) empirical formula \(\mathrm{NH}_{2} \mathrm{Cl}\), molar mass \(=51.5 \mathrm{~g} / \mathrm{mol}\)

Hydrofluoric acid, \(\mathrm{HF}(a q),\) cannot be stored in glass bottles because compounds called silicates in the glass are attacked by the \(\mathrm{HF}(a q)\). Sodium silicate \(\left(\mathrm{Na}_{2} \mathrm{SiO}_{3}\right)\), for example, reacts as follows: $$ \begin{aligned} \mathrm{Na}_{2} \mathrm{SiO}_{3}(s)+8 \mathrm{HF}(a q) & \longrightarrow \\ \mathrm{H}_{2} \mathrm{SiF}_{6}(a q) &+2 \mathrm{NaF}(a q)+3 \mathrm{H}_{2} \mathrm{O}(l) \end{aligned} $$ (a) How many moles of HF are needed to react with 0.300 \(\mathrm{mol}\) of \(\mathrm{Na}_{2} \mathrm{SiO}_{3} ?\) (b) How many grams of NaF form when \(0.500 \mathrm{~mol}\) of HF reacts with excess \(\mathrm{Na}_{2} \mathrm{SiO}_{3} ?\) (c) How many grams of \(\mathrm{Na}_{2} \mathrm{SiO}_{3}\) can react with \(0.800 \mathrm{~g}\) of HF?

If Avogadro's number of pennies is divided equally among the 300 million men, women, and children in the United States, how many dollars would each receive? How does this compare with the gross domestic product (GDP) of the United States, which was \(\$ 14.4\) trillion in \(2008 ?\) (The GDP is the total market value of the nation's goods and services.)

Balance the following equations: (a) \(\mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)\) (b) \(\mathrm{N}_{2} \mathrm{O}_{5}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{HNO}_{3}(a q)\) (c) \(\mathrm{CH}_{4}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CCl}_{4}(l)+\mathrm{HCl}(g)\) (d) \(\mathrm{Al}_{4} \mathrm{C}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Al}(\mathrm{OH})_{3}(s)+\mathrm{CH}_{4}(g)\) (e) \(\mathrm{C}_{5} \mathrm{H}_{10} \mathrm{O}_{2}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) (f) \(\mathrm{Fe}(\mathrm{OH})_{3}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow\) \(\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\) (g) \(\mathrm{Mg}_{3} \mathrm{~N}_{2}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow\) \(\mathrm{MgSO}_{4}(a q)+\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}(a q)\)
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