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Chapter 3: Problem 32

Without doing any detailed calculations (but using a periodic table to give atomic weights), rank the following samples in order of increasing numbers of atoms: \(0.2 \mathrm{~mol} \mathrm{PCl}_{5}\), molecules, $80 \mathrm{~g} \mathrm{Fe}_{2} \mathrm{O}_{3}, 3.0 \times 10^{23}$ CO molecules.

Short Answer

Expert verified
The order of increasing number of atoms in the given samples is as follows: \(3.0 \times 10^{23}\) CO molecules < 0.2 mol PCl5 < 80 g Fe2O3.

Step by step solution

01

Convert moles to atoms for PCl5

To find the number of atoms in 0.2 mol of PCl5, we'll first calculate the number of molecules and then multiply it by the total atoms in one PCl5 molecule. We know that the number of molecules in 1 mole is \(6.022 \times 10^{23}\) molecules (Avogadro's number). Number of PCl5 molecules = \(0.2 \mathrm{~mol} \times 6.022 \times 10^{23} \mathrm{~molecules/mol}\) There are 6 atoms in 1 PCl5 molecule (1 P and 5 Cl), so we'll multiply the number of molecules by 6 to find the total number of atoms. Number of atoms in PCl5 = \(0.2 \mathrm{~mol} \times 6.022 \times 10^{23} \mathrm{~atoms/mol} \times 6\)
02

Convert grams to atoms for Fe2O3

To find the number of atoms in 80 g of Fe2O3, first, we need to convert grams to moles and then multiply it by the Avogadro's number and total atoms in one Fe2O3 molecule. The molar mass of Fe2O3 is \(2 \times 55.85 + 3 \times 16 = 159.7\) g/mol. Number of moles of Fe2O3 = \(80 \mathrm{~g} \div 159.7 \mathrm{~g/mol}\) Next, we'll calculate the number of molecules and then multiply it by the total atoms in one Fe2O3 molecule (5 atoms: 2 Fe and 3 O). Number of atoms in Fe2O3 = \((80 \mathrm{~g} \div 159.7 \mathrm{~g/mol}) \times 6.022 \times 10^{23} \mathrm{~atoms/mol} \times 5\)
03

Find atoms in CO molecules

The number of CO molecules is already provided, so we just need to multiply it by the total atoms in one CO molecule (2 atoms: 1 C and 1 O). Number of atoms in CO molecules = \(3.0 \times 10^{23} \mathrm{~molecules} \times 2\)
04

Compare and Rank

Now we compare the total number of atoms in each sample and rank them accordingly: 1. Number of atoms in PCl5: \(0.2 \mathrm{~mol} \times 6.022 \times 10^{23} \mathrm{~atoms/mol} \times 6\) 2. Number of atoms in Fe2O3: \((80 \mathrm{~g} \div 159.7 \mathrm{~g/mol}) \times 6.022 \times 10^{23} \mathrm{~atoms/mol} \times 5\) 3. Number of atoms in CO molecules: \(3.0 \times 10^{23} \mathrm{~molecules} \times 2\) When comparing these values, we find that the order of increasing number of atoms is: \(3.0 \times 10^{23}\) CO molecules < 0.2 mol PCl5 < 80 g Fe2O3

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Most popular questions from this chapter

A method used by the U.S. Environmental Protection Agency (EPA) for determining the concentration of ozone in air is to pass the air sample through a "bubbler" containing sodium iodide, which removes the ozone according to the following equation: $\mathrm{O}_{3}(g)+2 \mathrm{NaI}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow$ $$ \mathrm{O}_{2}(g)+\mathrm{I}_{2}(s)+2 \mathrm{NaOH}(a q) $$ (a) How many moles of sodium iodide are needed to remove $5.95 \times 10^{-6} \mathrm{~mol}\( of \)\mathrm{O}_{3} ?(\mathbf{b})$ How many grams of sodium iodide are needed to remove \(1.3 \mathrm{mg}\) of \(\mathrm{O}_{3}\) ?

Aluminum sulfide reacts with water to form aluminum hydroxide and hydrogen sulfide. (a) Write the balanced chemical equation for this reaction. (b) How many grams of aluminum hydroxide are obtained from \(14.2 \mathrm{~g}\) of aluminum sulfide?

Balance the following equations: (a) $\mathrm{CaS}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{HS})_{2}(a q)+\mathrm{Ca}(\mathrm{OH})_{2}(a q)$ (b) $\mathrm{NH}_{3}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{H}_{2} \mathrm{O}(g)$ (c) $\mathrm{FeCl}_{3}(s)+\mathrm{Na}_{2} \mathrm{CO}_{3}(a q) \longrightarrow \mathrm{Fe}_{2}\left(\mathrm{CO}_{3}\right)_{3}(s)+\mathrm{NaCl}(a q)$ (d) $\mathrm{FeS}_{2}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{SO}_{2}(g)$

Cinnamaldehyde is a compound that is responsible for the characteristic aroma of cinnamon. It contains \(81.79 \% \mathrm{C}\), \(6.10 \% \mathrm{H},\) and the remaining is oxygen. Its molar mass is \(132 \mathrm{~g} / \mathrm{mol} .\) Determine its molecular formula.

Boron nitride, \(\mathrm{BN}\), is an electrical insulator with remarkable thermal and chemical stability. Its density is $2.1 \mathrm{~g} / \mathrm{cm}^{3}\(. It can be made by reacting boric acid, \)\mathrm{H}_{3} \mathrm{BO}_{3}$, with ammonia. The other product of the reaction is water. (a) Write a balanced chemical equation for the synthesis of BN. (b) If you made \(225 \mathrm{~g}\) of boric acid react with \(150 \mathrm{~g}\) ammonia, what mass of BN could you make? (c) Which reactant, if any, would be left over, and how many moles of leftover reactant would remain? (d) One application of \(\mathrm{BN}\) is as thin film for electrical insulation. If you take the mass of BN from part (a) and make a \(0.4 \mathrm{~mm}\) thin film from it, what area, in \(\mathrm{cm}^{2}\), would it cover?
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