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Chapter 3: Problem 44

A diamond contains \(5.0 \times 10^{21}\) atoms of carbon. What amount (moles) of carbon and what mass (grams) of carbon are in this diamond?

Short Answer

Expert verified
There are 0.00830 moles of carbon and 99.7 grams of carbon in this diamond.

Step by step solution

01

Convert atoms of carbon to moles of carbon

To convert the given number of carbon atoms to moles, we will use Avogadro's number. To do this, divide the number of carbon atoms by Avogadro's number: Moles of carbon = \(\frac{5.0 \times 10^{21}}{(6.022 \times 10^{23})}\)
02

Calculate the moles of carbon

Now, proceed to calculate the moles of carbon: Moles of carbon = \(\frac{5.0 \times 10^{21}}{(6.022 \times 10^{23})} = 0.00830 \ mol\)
03

Convert moles of carbon to grams of carbon

Now, we will convert the moles of carbon we calculated in the previous step to grams. To do this, use the molar mass of carbon (12.01 g/mol): Mass of carbon (grams) = Moles of carbon 脳 Molar mass of carbon Mass of carbon (grams) = 0.00830 mol 脳 12.01 g/mol
04

Calculate the mass of carbon (grams)

Finally, calculate the mass of carbon (grams): Mass of carbon (grams) = 0.00830 mol 脳 12.01 g/mol = 99.7 g So, there are 0.00830 moles of carbon and 99.7 grams of carbon in this diamond.

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Most popular questions from this chapter

Zinc and magnesium metal each react with hydrochloric acid to make chloride salts of the respective metals, and hydrogen gas. A \(10.00-\mathrm{g}\) mixture of zinc and magnesium produces \(0.5171 \mathrm{~g}\) of hydrogen gas upon being mixed with an excess of hydrochloric acid. Determine the percent magnesium by mass in the original mixture.

Vitamin \(\mathrm{B}_{12}\), cyanocobalamin, is essential for human nutrition. It is concentrated in animal tissue but not in higher plants. Although nutritional requirements for the vitamin are quite low. people who abstain completely from animal products may develop a deficiency anemia. Cyanocobalamin is the form used in vitamin supplements. It contains \(4.34 \%\) cobalt by mass. Calculate the molar mass of cyanocobalamin, assuming that there is one atom of cobalt in every molecule of cyanocobalamin.

Cumene is a compound containing only carbon and hydrogen that is used in the production of acetone and phenol in the chemical industry. Combustion of \(47.6 \mathrm{mg}\) cumene produces some \(\mathrm{CO}_{2}\) and \(42.8 \mathrm{mg}\) water. The molar mass of cumene is between 115 and \(125 \mathrm{~g} / \mathrm{mol}\). Determine the empirical and molecular formulas.

Maleic acid is an organic compound composed of \(41.39 \% \mathrm{C}\), \(3.47 \% \mathrm{H}\), and the rest oxygen. If \(0.129 \mathrm{~mol}\) of maleic acid has a mass of \(15.0 \mathrm{~g}\), what are the empirical and molecular formulas of maleic acid?

DDT, an insecticide harmful to fish, birds, and humans, is produced by the following reaction: $$ 2 \mathrm{C}_{6} \mathrm{H}_{3} \mathrm{Cl}+\mathrm{C}_{2} \mathrm{HOCl}_{3} \longrightarrow \mathrm{C}_{14} \mathrm{H}_{4} \mathrm{Cl}_{5}+\mathrm{H}_{2} \mathrm{O} $$ \(\begin{array}{ll}\text { orobenzenc chloral } & \mathrm{D}\end{array}\) In a government lab, \(1142 \mathrm{~g}\) of chlorobenzene is reacted with \(485 \mathrm{~g}\) of chloral. a. What mass of DDT is formed? b. Which reactant is limiting? Which is in excess? c. What mass of the excess reactant is left over? d. If the actual yield of DDT is \(200.0 \mathrm{~g}\), what is the percent yield?
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