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Chapter 3: Problem 29

(a) Write "true" or "false" for each statement. (a) A mole of horses contain a mole of horse legs. (b) A mole of water has a mass of 18.0 \(\mathrm{g} .\) (c) The mass of 1 molecule of water is 18.0 \(\mathrm{g}\) (d) A mole of NaCl (s) contains 2 moles of ions.

Short Answer

Expert verified
The short version of the answer is: (a) False (b) True (c) False (d) True

Step by step solution

01

Statement (a)

First, let's analyze statement (a): "A mole of horses contains a mole of horse legs." A mole is a unit of measurement used to represent a very large number of particles or entities, typically 6.022 x 10^23. In this case, the statement is suggesting that when there is a mole of horses, there would also be a mole of horse legs. Since a horse typically has 4 legs, a mole of horses would have 4 moles of horse legs. Therefore, the given statement is false.
02

Statement (b)

Now, let's analyze statement (b): "A mole of water has a mass of 18.0 g." To find the mass of a mole of a substance, we need to multiply its molar mass (the mass of one mole of a substance, in grams) by the number of moles. The molar mass of water \((H_2O)\) is 18.0 g/mol as it consists of two hydrogen atoms and one oxygen atom (1.0 g/mol + 1.0 g/mol + 16.0 g/mol). So, one mole of water would indeed have a mass of 18.0 g. Therefore, the given statement is true.
03

Statement (c)

Let's now examine statement (c): "The mass of 1 molecule of water is 18.0 g." As discussed earlier, the molar mass of water is 18.0 g/mol. The statement is asking about the mass of a single molecule of water, not a mole of water. To find the mass of a single molecule of water, we can divide the molar mass by Avogadro's number \((6.022 \times 10^23)\), so the mass of a single molecule of water is about 2.99 x 10^(-23) g. Therefore, the given statement is false.
04

Statement (d)

Finally, let's analyze statement (d): "A mole of NaCl (s) contains 2 moles of ions." Sodium chloride \((NaCl)\) is an ionic compound formed by sodium atoms \((Na^+)\) and chloride atoms \((Cl^-)\), which are bonded together as ions. When one mole of sodium chloride dissociates in solution, it produces one mole of sodium ions \((Na^+)\) and one mole of chloride ions \((Cl^-)\), resulting in a total of 2 moles of ions. Therefore, the given statement is true.

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Most popular questions from this chapter

What is the mass, in kilograms, of an Avogadro's number of people, if the average mass of a person is 160 \(\mathrm{lb}\) ? How does this compare with the mass of Earth, \(5.98 \times 10^{24} \mathrm{kg}\) ?

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

Write the balanced chemical equations for (a) the complete combustion of acetic acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right),\) the main ingredient in vinegar; (b) the decomposition of solid calcium hydroxide into solid calcium oxide (lime) and water vapor; (c) the combination reaction between nickel metal and chlorine gas.

Determine the empirical formulas of the compounds with the following compositions by mass: $$ \begin{array}{l}{\text { (a) } 55.3 \% \mathrm{K}, 14.6 \% \mathrm{P}, \text { and } 30.1 \% \mathrm{O}} \\ {\text { (b) } 24.5 \% \mathrm{Na}, 14.9 \% \mathrm{Si}, \text { and } 60.6 \% \mathrm{F}} \\ {\text { (c) } 62.1 \% \mathrm{C}, 5.21 \% \mathrm{H}, 12.1 \% \mathrm{N}, \text { and the remainder O }}\end{array} $$

(a) If an automobile travels 225 mi with a gas mileage of 20.5 mi/gal, how many kilograms of \(\mathrm{CO}_{2}\) are produced? Assume that the gasoline is composed of octane, \(\mathrm{C}_{8} \mathrm{H}_{18}(l),\) whose density is 0.692 \(\mathrm{g} / \mathrm{mL}\) . (b) Repeat the calculation for a truck that has a gas mileage of 5 \(\mathrm{mi} / \mathrm{gal} .\)
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