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Chapter 2: Problem 65

Without doing detailed calculations, determine which of the following samples has the greatest number of atoms: (a) a cube of iron with a length of \(10.0 \mathrm{cm}\) \(\left(d=7.86 \mathrm{g} / \mathrm{cm}^{3}\right)\) (b) \(1.00 \mathrm{kg}\) of hydrogen contained in a \(10,000 \mathrm{L}\) balloon (c) a mound of sulfur weighing \(20.0 \mathrm{kg}\) (d) a 76 lb sample of liquid mercury \((d=13.5 \mathrm{g} / \mathrm{mL})\)

Short Answer

Expert verified
The sample of hydrogen has the greatest number of atoms.

Step by step solution

01

Cube of Iron

Calculate the mass of the cube of iron using its volume and density. Given that the length, height, and width of the cube are each equal to \(10.0 cm\), its volume is \(1000 cm^3\). Then, given that density is defined as mass divided by volume, the iron's mass is its volume times its density \(d=7.86 g/cm^3\). Therefore, the iron cube's mass is \(7860 g\). Using the molar mass of iron (\(55.85 g/mol\)), we can then calculate the number of moles in the cube, and then the number of atoms using Avogadro's constant (\(6.022 \times 10^{23} atoms/mol\)).
02

Hydrogen Balloon

The mass of hydrogen is given directly as \(1.00 kg\), which is equivalent to \(1000 g\). We can then use this mass and the molar mass of hydrogen (\(1.01 g/mol\)) to calculate the number of moles and then the number of atoms, as in Step 1.
03

Sulfur Mound

The mass of the mound of sulfur is given directly as \(20.0 kg\), which is equivalent to \(20000 g\). We can then use this mass and the molar mass of sulfur (\(32.07 g/mol\)) to calculate the number of moles, and then the number of atoms as in the previous steps.
04

Mercury Sample

First, convert the weight of the mercury sample from pounds to grams (\(1 lb = 454 g\)), obtaining roughly \(34504 g\). Then, using the molar mass of mercury (\(200.59 g/mol\)), calculate the number of moles, and then the number of atoms as in previous steps.
05

Comparison

Now compare the four calculated numbers of atoms. The sample with the greatest number has the greatest quantity of atoms.

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Most popular questions from this chapter

Determine the only possible \(2+\) ion for which the following two conditions are both satisfied: \(\bullet\) The net ionic charge is one-tenth the nuclear charge. \(\bullet\) The number of neutrons is four more than the number of electrons.

A particular silver solder (used in the electronics industry to join electrical components) is to have the atom ratio of \(5.00 \mathrm{Ag} / 4.00 \mathrm{Cu} / 1.00 \mathrm{Zn}\). What masses of the three metals must be melted together to prepare \(1.00 \mathrm{kg}\) of the solder?

Which statement is probably true concerning the masses of individual chlorine atoms: All have, some have, or none has a mass of 35.4527 u? Explain.

In one experiment, 2.18 g sodium was allowed to react with \(16.12 \mathrm{g}\) chlorine. All the sodium was used up, and 5.54 g sodium chloride (salt) was produced. In a second experiment, 2.10 g chlorine was allowed to react with \(10.00 \mathrm{g}\) sodium. All the chlorine was used up, and 3.46 g sodium chloride was produced.Show that these results are consistent with the law of constant composition.

Refer to the periodic table inside the front cover and identify (a) the element that is in group 14 and the fourth period (b) one element similar to and one unlike sulfur (c) the alkali metal in the fifth period (d) the halogen element in the sixth period
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