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Chapter 9: Problem 52

Consider a sample containing \(12.011 \mathrm{~g}\) of naturally occurring carbon. (a) How many carbon atoms are in this sample? (b) How many dozens of carbon atoms are in this sample? (c) How many moles of carbon atoms are in this sample?

Short Answer

Expert verified
(a) The sample contains approximately \(6.0225 \times 10^{23}\) carbon atoms. (b) The sample contains approximately \(5.01875 \times 10^{22}\) dozens of carbon atoms. (c) The sample contains approximately \(1.000083\) moles of carbon atoms.

Step by step solution

01

Determine the molar mass of carbon atoms

The molar mass of an element can be found on the periodic table. For carbon, the molar mass is approximately \(12.01 \mathrm{~g/mol}\). We will use this value to convert between grams of carbon and moles of carbon atoms.
02

Calculate the number of moles of carbon atoms in the sample

To find the number of moles of carbon atoms in the sample, we will use the molar mass of carbon to convert from grams of carbon to moles of carbon atoms: number of moles of Carbon = \(\frac{mass}{molar~mass}\) number of moles of Carbon = \(\frac{12.011\mathrm{~g}}{12.01 \mathrm{~g/mol}} = 1.000083\mathrm{~mol}\)
03

Calculate the number of carbon atoms in the sample

To calculate the number of carbon atoms, we will multiply the number of moles with Avogadro's number (\(6.022 \times 10^{23}\) atoms per mole): number of carbon atoms = \(number~of~moles \times Avogadro's~number\) number of carbon atoms = \(1.000083\mathrm{~mol} \times (6.022 \times 10^{23}\mathrm{~atoms/mol}) = 6.0225 \times 10^{23}\mathrm{~atoms}\) (a) The sample contains approximately \(6.0225 \times 10^{23}\) carbon atoms.
04

Calculate the number of dozens of carbon atoms in the sample

To find the number of dozens of carbon atoms, simply divide the number of carbon atoms by 12 (since a dozen contains 12 items): number of dozens of carbon atoms = \(\frac{number~of~carbon~atoms}{12}\) number of dozens of carbon atoms = \(\frac{6.0225 \times 10^{23}\mathrm{~atoms}}{12} = 5.01875 \times 10^{22}\mathrm{~dozens}\) (b) The sample contains approximately \(5.01875 \times 10^{22}\) dozens of carbon atoms.
05

State the number of moles of carbon atoms in the sample

We already found the number of moles of carbon atoms in the sample in Step 2. (c) The sample contains approximately \(1.000083\) moles of carbon atoms.

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Most popular questions from this chapter

Chlorine \(\left(\mathrm{Cl}_{2}\right)\) and fluorine \(\left(\mathrm{F}_{2}\right)\) react to form \(\mathrm{ClF}_{3}\). A reaction vessel contains \(10.00 \mathrm{~g} \mathrm{Cl}_{2}\) and \(10.00 \mathrm{~g} \mathrm{~F}_{2}\). (Hint: Refer to Problem 9.82.) (a) Write a balanced chemical equation for this reaction. (b) Which reactant is limiting? (c) What is the theoretical yield for this reaction in grams? (d) How many grams of excess reactant are left over at the end of the reaction? (e) When this reaction is actually performed, \(12.50 \mathrm{~g}\) of \(\mathrm{ClF}_{3}\) is recovered. What is the percent yield of the reaction?

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Consider the following unbalanced chemical equation: \(\mathrm{H}_{2}+\mathrm{N}_{2} \rightarrow \mathrm{NH}_{3}\) (a) To run this reaction in a balanced fashion, how much nitrogen is required if you start with \(10.0 \mathrm{~g}\) of \(\mathrm{H}_{2} ?\) (b) How many grams of ammonia \(\left(\mathrm{NH}_{3}\right)\) will you produce if you run the reaction with the masses calculated in part (a)? (c) How many molecules of ammonia will you produce?

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