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Chapter 3: Problem 118

Which answer is correct? One mole of liquid bromine, \(\mathrm{Br}_{2},\) (a) has a mass of \(79.9 \mathrm{g} ;\) (b) contains \(6.022 \times 10^{23}\) Br atoms; (c) contains the same number of atoms as in \(12.01 \mathrm{g} \mathrm{H}_{2} \mathrm{O} ;\) (d) has twice the mass of 0.500 mole of gaseous \(\mathrm{Cl}_{2}\)

Short Answer

Expert verified
The correct statement is (c) One mole of liquid bromine, \(\mathrm{Br}_{2}\), contains the same number of atoms as in \(12.01 \mathrm{g}\) \(\mathrm{H}_{2} \mathrm{O}\).

Step by step solution

01

Validate Statement (a)

One mole of any element or compound is defined as its molar mass in grams. The molar mass of Bromine (\(\mathrm{Br}\)) is approximately 79.9 g/mol. However, liquid Bromine is \(\mathrm{Br}_{2}\), so its molar mass is \(79.9 \times 2 = 159.8 \mathrm{g/mol}\). Thus, one mole of liquid Bromine (\(\mathrm{Br}_{2}\)) does not have a mass of 79.9g. Hence statement (a) is incorrect.
02

Validate Statement (b)

Avogadro's number (\(6.022 \times 10^{23}\)) states the number of atoms in exactly one mole of any substance. However, a mole of liquid Bromine is \(\mathrm{Br}_{2}\), which implies that each molecule consists of two Br atoms. Therefore, one mole of liquid Bromine (\(\mathrm{Br}_{2}\)) contains \(2 \times 6.022 \times 10^{23}\) Br atoms. Consequently, statement (b) is incorrect.
03

Validate Statement (c)

This statement calls for an understanding of Avogadro's Law, which dictates that equal volumes of all gases at the same temperature and pressure contain an equal number of molecules. While the substances may differ, the number of molecules in a mole of any substance remains the same, that number being Avogadro's number (\(6.022 \times 10^{23}\)). Thus, one mole of \(\mathrm{Br}_{2}\) (Bromine) contains the same number of molecules as one mole of \(\mathrm{H}_{2} \mathrm{O}\) (Water). This makes statement (c) correct.
04

Validate Statement (d)

We again refer to the molar mass for this verification. The molar mass of Chlorine (\(\mathrm{Cl}\)) is approximately 35.45 g/mol, which makes the molar mass of gaseous Chlorine (\(\mathrm{Cl}_{2}\)) about \(35.45 \times 2 = 70.9 \mathrm{g/mol}\). Therefore, 0.500 mole of gaseous Chlorine (\(\mathrm{Cl}_{2}\)) would have a mass of \(0.500 \times 70.9 = 35.45 \mathrm{g}\), which is not half the mass of one mole of liquid Bromine (\(159.8 \mathrm{g}\)). Thus, statement (d) is incorrect.

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Most popular questions from this chapter

The insecticide dieldrin contains carbon, hydrogen, oxygen, and chlorine. When burned in an excess of oxygen, a 1.510 g sample yields \(2.094 \mathrm{g} \mathrm{CO}_{2}\) and \(0.286 \mathrm{g} \mathrm{H}_{2} \mathrm{O} .\) The compound has a molecular mass of 381 u and has half as many chlorine atoms as carbon atoms. What is the molecular formula of dieldrin?

Name these compounds: (a) \(\operatorname{SrO} ;\) (b) \(\mathrm{ZnS} ;\) (c) \(\mathrm{K}_{2} \mathrm{CrO}_{4}\) (d) \(\mathrm{Cs}_{2} \mathrm{SO}_{4} ;(\mathrm{e}) \mathrm{Cr}_{2} \mathrm{O}_{3} ;(\mathrm{f}) \mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3} ;(\mathrm{g}) \mathrm{Mg}\left(\mathrm{HCO}_{3}\right)_{2}\) (h) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4} ; \quad\) (i) \(\quad \mathrm{Ca}\left(\mathrm{HSO}_{3}\right)_{2} ; \quad(\mathrm{j}) \quad \mathrm{Cu}(\mathrm{OH})_{2}\) (k) \(\mathrm{HNO}_{3} ;\) (1) \(\mathrm{KClO}_{4} ;\) (m) \(\mathrm{HBrO}_{3} ;\) (n) \(\mathrm{H}_{3} \mathrm{PO}_{3}\).

The greatest number of \(\mathrm{N}\) atoms is found in (a) \(50.0 \mathrm{g}\) \(\mathrm{N}_{2} \mathrm{O} ;\) (b) \(17.0 \mathrm{g} \mathrm{NH}_{3} ;\) (c) \(150 \mathrm{mL}\) of liquid pyridine, \(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{N}(d=0.983 \mathrm{g} / \mathrm{mL}) ;\) (d) \(1.0 \mathrm{mol} \mathrm{N}_{2}\)

Explain which of the following statement(s) is (are) correct concerning glucose (blood sugar), \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) (a) The percentages, by mass, of \(\mathrm{C}\) and \(\mathrm{O}\) are the same as in CO. (b) The ratio of \(\mathrm{C}: \mathrm{H}: \mathrm{O}\) atoms is the same as in dihydroxyacetone, \(\left(\mathrm{CH}_{2} \mathrm{OH}\right)_{2} \mathrm{CO}\) (c) The proportions, by mass, of \(C\) and \(O\) are equal. (d) The highest percentage, by mass, is that of H.

The compound \(\mathrm{C}_{7} \mathrm{H}_{7} \mathrm{NO}_{2}\) contains (a) 17 atoms per mole; (b) equal percents by mass of \(\mathrm{C}\) and \(\mathrm{H} ;\) (c) about twice the percent by mass of \(\mathrm{O}\) as of \(\mathrm{N} ;\) (d) about twice the percent by mass of \(\mathrm{N}\) as of \(\mathrm{H}\).
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