Chapter 9

Suppose you have \(0.5\) mole of gold, Au, atoms. (a) How many gold atoms do you have? (b) What is the mass in grams of this much gold?

Suppose you have \(0.10\) mole of uranium, \(U\), atoms. (a) How many uranium atoms do you have? (b) What is the mass in grams of this much uranium?

Suppose you have \(120.11 \mathrm{~g}\) of carbon atoms. (a) How many moles of carbon atoms do you have? (b) How many carbon atoms do you have?

If you have 1 mole of propane, \(\mathrm{C}_{3} \mathrm{H}_{8}\), a gas used in outdoor grills and industrial torches: (a) How many propane molecules do you have? (b) How many hydrogen atoms do you have? (c) What is the mass in grams of 1 mole of propane? Answer: (a) Having 1 mole of propane molecules means you have \(6.022 \times 10^{23}\) propane molecules. (That is the meaning of 1 mole.) (b) You know that 1 mole of propane contains 8 moles of hydrogen atoms. (That is what the subscript 8 in the formula \(\mathrm{C}_{3} \mathrm{H}_{8}\) tells you.) You also know there are \(6.022 \times 10^{23} \mathrm{H}\) atoms per mole of them, which means you have:

What is the mass in grams of 2 moles of propane?

How many moles of carbon atoms are there in 2 moles of propane?

Propane reacts with oxygen to produce \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\), as shown in the balanced equation: $$ \mathrm{C}_{3} \mathrm{H}_{8}+5 \mathrm{O}_{2} \rightarrow 3 \mathrm{CO}_{2}+4 \mathrm{H}_{2} \mathrm{O} $$ Write this reaction in words using the word mole(s) four times.

Suppose you have \(100.0 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\). (a) How many moles of \(\mathrm{H}_{2} \mathrm{O}\) molecules do you have? (b) How many \(\mathrm{H}_{2} \mathrm{O}\) molecules do you have? Answer: (a) \(100.0 \mathrm{~g} \mathrm{H}_{2} \mathrm{O} \times \frac{1 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}}{18.015 \mathrm{~g} \mathrm{H}_{2} \mathrm{O}}=5.551 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}\) or \(\frac{100.0 \mathrm{~g} \mathrm{H}_{2} \mathrm{O}}{18.015 \mathrm{~g} \mathrm{H}_{2} \mathrm{O} / \mathrm{mol}}=5.551 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}\) (b) \(5.551 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O} \times \frac{6.022 \times 10^{23} \mathrm{molecules} \mathrm{H}_{2} \mathrm{O}}{1 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}}=3.343 \times 10^{24} \mathrm{molecules} \mathrm{H}_{2} \mathrm{O}\)

Suppose you have \(5.000 \times 10^{24}\) molecules of methane, \(\mathrm{CH}_{4}\). (a) How many moles of methane do you have? (b) How many grams of methane do you have?

(a) Express the balanced chemical equation $$ \mathrm{CH}_{4}+2 \mathrm{O}_{2} \rightarrow 2 \mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2} $$ in words, using the word mole(s) wherever appropriate. (b) To produce 1 mole of \(\mathrm{CO}_{2}\) from this reaction, how many grams of \(\mathrm{CH}_{4}\) and \(\mathrm{O}_{2}\) must you combine? (c) What is the theoretical yield in grams of \(\mathrm{H}_{2} \mathrm{O}\) for this reaction? (d) If you recover \(30.0 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\), what is the percent yield? Answer: (a) One mole of methane molecules and 2 moles of oxygen molecules react to give 2 moles of water molecules and 1 mole of carbon dioxide molecules. (b) The molar mass of methane is \((12.011 \mathrm{~g} / \mathrm{mol} \mathrm{C})+(4 \times 1.0079 \mathrm{~g} / \mathrm{mol} \mathrm{H})=\) \(=16.043 \mathrm{~g} / \mathrm{mol} \mathrm{CH}_{4}\). This is the mass of \(1 \mathrm{~mole}\) of methane, which is what the reaction calls for. The molar mass of oxygen, \(\mathrm{O}_{2}\), is \((2 \times 15.999 \mathrm{~g} / \mathrm{mol} \mathrm{O})=31.998 \mathrm{~g} / \mathrm{mol}\). This is the mass of 1 mole of \(\mathrm{O}_{2}\). Because the reaction calls for 2 moles, we multiply by 2 to get \(63.996 \mathrm{~g}\) of \(\mathrm{O}_{2}\) needed. (c) The most we can hope to form is 2 moles of water. The molar mass of water is \((2 \times 1.0079 \mathrm{~g} / \mathrm{mol} \mathrm{H})+(15.999 \mathrm{~g} / \mathrm{mol} \mathrm{O})=18.015 \mathrm{~g} / \mathrm{mol} \mathrm{H}_{2} \mathrm{O} .\) This is the mass of 1 mole of water. So the theoretical yield is just twice this, which is \(36.030 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\). (d) \% yield \(=(30.0 \mathrm{~g} / 36.030 \mathrm{~g}) \times 100=83.3 \%\)

(a) Balance this unbalanced equation by inspection: $$ \mathrm{C}_{6} \mathrm{H}_{6}+\mathrm{H}_{2} \longrightarrow \mathrm{C}_{6} \mathrm{H}_{12} $$ Benzene Hydrogen Cyclohexane (b) Express this reaction in words, using the word mole(s) wherever appropriate. (c) To produce 1 mole of \(\mathrm{C}_{6} \mathrm{H}_{12}\) from this reaction, how many grams of \(\mathrm{C}_{6} \mathrm{H}_{6}\) and \(\mathrm{H}_{2}\) must you combine? (d) What is the theoretical yield in grams of \(\mathrm{C}_{6} \mathrm{H}_{12} ?\) (e) Suppose you recover \(24.0 \mathrm{~g}\) of \(\mathrm{C}_{6} \mathrm{H}_{1}\). What is the percent vield?

(a) Balance this unbalanced equation by inspection: $$ \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}+\mathrm{O}_{2} \longrightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O} $$ Glucose (b) Express this reaction in words, using the word mole(s) wherever appropriate. (c) To produce 6 moles of \(\mathrm{H}_{2} \mathrm{O}\) from this reaction, how many grams of glucose and \(\mathrm{O}_{2}\) must you combine? (d) What is the theoretical yield in grams of \(\mathrm{CO}_{2} ?\) (e) Suppose you recover \(196.0 \mathrm{~g}\) of \(\mathrm{CO}_{2}\). What is the percent yield?

How many grams of oxygen does it take to burn \(10.0 \mathrm{~g}\) of glucose? Answer:

How many aluminum atoms are there in \(10.0 \mathrm{~g}\) of aluminum oxide, \(\mathrm{Al}_{2} \mathrm{O}_{3} ?\)

How many molecules of water are there in \(10.0 \mathrm{~g}\) of water?

In the burning of propane, $$ \mathrm{C}_{3} \mathrm{H}_{8}+5 \mathrm{O}_{2} \rightarrow 3 \mathrm{CO}_{2}+4 \mathrm{H}_{2} \mathrm{O} $$ suppose \(10.0 \mathrm{~g}\) of propane is combined with \(10.0 \mathrm{~g}\) of oxygen. What is the theoretical yield of \(\mathrm{CO}_{2}\), in grams? Answer: Before we begin, we'll calculate the molar masses of everything because we'll probably need them: \(\mathrm{C}_{3} \mathrm{H}_{8}=44.096 \mathrm{~g} / \mathrm{mol} \quad \mathrm{O}_{2}=31.998 \mathrm{~g} / \mathrm{mol}\) \(\mathrm{CO}_{2}=44.009 \mathrm{~g} / \mathrm{mol} \quad \mathrm{H}_{2} \mathrm{O}=18.015 \mathrm{~g} / \mathrm{mol}\)

(a) What mass of oxygen is necessary to burn \(100.0 \mathrm{~g}\) of propane in a balanced fashion? (b) What is the theoretical yield of water, in grams?

Chemical treatment of zinc sulfide, \(\mathrm{ZnS}\), with oxygen, \(\mathrm{O}_{2}\), gives zinc oxide, \(\mathrm{ZnO}\), and sulfur dioxide gas, \(\mathrm{SO}_{2}\). (a) Write a balanced equation for the reaction. (b) If \(10.0 \mathrm{~g}\) of \(\mathrm{Zn} \mathrm{S}\) is combined with \(10.0 \mathrm{~g}\) of \(\mathrm{O}_{2}\), what is the theoretical yield of each product, in grams? (c) How much of the excess reactant is left over, in grams? (d) Suppose only \(7.50 \mathrm{~g}\) of \(\mathrm{Zn} \mathrm{O}\) is recovered. What is the percent yield of \(\mathrm{ZnO}\) ?

A compound is known to contain carbon and hydrogen. It might also contain oxygen. A sample of the compound is burned. The results of the combustion analysis are \(74.9 \% \mathrm{C}\) and \(25.1 \% \mathrm{H}\). (a) What is the chemical formula for this compound? (b) Write the balanced combustion reaction (reaction with \(\mathrm{O}_{2}\) ) for this compound. Answer (not worked out on purpose-you do it): (a) \(\mathrm{CH}_{4}\) (b) \(\mathrm{CH}_{4}+2 \mathrm{O}_{2} \rightarrow 2 \mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2}\)

A compound is known to contain carbon and hydrogen and might also contain oxygen. A sample is burned yielding \(54.6 \% \mathrm{C}\) and \(9.16 \% \mathrm{H}\). (a) What is the empirical formula of the compound? (b) The molar mass of the compound is \(132.159 \mathrm{~g} / \mathrm{mol}\). What is the molecular formula? (c) Write the balanced combustion reaction (reaction with \(\mathrm{O}_{2}\) ) for the compound. Answer (not worked out on purpose-you do it): (a) \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}\) (b) \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{3}\) (c) To balance the equation, look at \(\mathrm{C}\) and \(\mathrm{H}\) first. Then balance the elemental substance \(\left(\mathrm{O}_{2}\right)\) last: We make \(\mathrm{O}_{2}\) provide \(15 \mathrm{O}\) atoms by multiplying it by \(7.5\) (that is, \(\left.\frac{15}{2}\right)\) : This is a perfectly correct balanced equation, but if you prefer the balancing coefficients to be whole mumbers, you can multiply all of them by some number that makes them whole (in this case, 2): $$ 2 \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{3}+15 \mathrm{O}_{2} \rightarrow 12 \mathrm{CO}_{2}+12 \mathrm{H}_{2} \mathrm{O} $$

A compound is known to contain carbon and hydrogen and might also contain oxygen. A sample is burned yielding \(85.62 \% \mathrm{C}\) and \(14.37 \% \mathrm{H}\). (Be careful here. Remember, there is always a little inaccuracy associated with measured numbers). (a) What is the empirical formula for the compound? (b) The molar mass is \(28.054 \mathrm{~g} / \mathrm{mol}\). What is the molecular formula? (c) Write the balanced combustion reaction.

What is the mass percent of each element in hydrogen peroxide, \(\mathrm{H}_{2} \mathrm{O}_{2} ?\)

What is the mass percent of each element in trinitrotoluene (TNT), \(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{~N}_{3} \mathrm{O}_{6}\) ?

A compound is found to have the following elemental mass percents: \(\mathrm{Cl}=89.09 \%\), \(\mathrm{C}=10.06 \%, \mathrm{H}=0.84 \% .\) The molar mass of the compound is \(119.378 \mathrm{~g} / \mathrm{mol} .\) What are the empirical and molecular formulas?

A compound is known to contain \(\mathrm{C}\) and \(\mathrm{H}\), and might also contain \(\mathrm{O} .\) It is analyzed for \(C\) and \(H\) only, yielding the mass percents \(C=54.53 \%\) and \(H=9.15 \%\). The molar mass of the compound is \(88.106 \mathrm{~g} / \mathrm{mol}\). What are the empirical and molecular formulas?

How is the concept of " 1 mole" similar to the concept of " 1 dozen"?

When is it allowed to insert the word mole into a chemical equation when translating the equation into words?

Consider bicycles where each wheel has 24 spokes. (a) How many bicycles are there in 1 mole of bicycles? (b) How many tires are there in 1 mole of bicycles? (c) How many spokes are there in 1 mole of bicycles? (d) How many bicycles would you need to have a total of 1 mole of spokes.

How many \(\mathrm{O}_{2}\) molecules are there in 1 mole of \(\mathrm{O}_{2}\) molecules? How many \(\mathrm{O}\) atoms are there in 1 mole of \(\mathrm{O}_{2}\) molecules?

How many pennies are there in \(2.5\) moles of pennies? How many dollars does this equal? Answer both questions by using conversion factors, and show which units cancel.

How many years are there in 1 mole of seconds? Use conversion factors, and show which units cancel.

Translate the following balanced equation into words, first without using the word moles, then again with the word moles: \(2 \mathrm{SO}_{2}+\mathrm{O}_{2} \rightarrow 2 \mathrm{SO}_{3}\)

Sometimes using the word moles when translating a chemical equation into words can be very helpful. For example, consider the following correctly balanced equation. What difficulty do you run into when you try to translate it into words without using the word moles? How does using the word moles solve the difficulty? \(\mathrm{C}_{2} \mathrm{H}_{2}+\frac{5}{2} \mathrm{O}_{2} \rightarrow 2 \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O}\)

In words, what is the mass of 1 mole of atoms of any element?

In words, what is the mass of 1 mole of any molecule?

How do you calculate the molar mass of a compound?

How many atoms of the \({ }_{6}^{12} \mathrm{C}\) isotope are there in exactly \(12 \mathrm{~g}\) of the isotope?

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?

If you have 1 mole of glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) : (a) How many moles of carbon atoms do you have? (b) How many moles of hydrogen atoms do you have? (c) How many oxygen atoms do you have? (Note that we are not asking for moles here.)

Consider the ammonia \(\left(\mathrm{NH}_{3}\right)\) molecule. (a) If you have 1 mole of ammonia, how many moles of \(\mathrm{H}\) atoms do you have? (b) If you have 2 moles of ammonia, how many moles of \(\mathrm{H}\) atoms do you have? (c) If you have 2 moles of ammonia, how many N atoms do you have? (We are not asking for moles here.)

What do we mean by the theoretical yield of a reaction?

What do we mean by the actual yield of a reaction?

Why is the actual yield of a reaction often not equal to the theoretical yield?

What do we mean by the percent yield of a reaction?

A student runs a reaction to prepare \(40.0 \mathrm{~g}\) of aspirin and yet recovers only \(15.5 \mathrm{~g}\). What is the percent yield?

Consider the unbalanced chemical equation \(\mathrm{NO}+\mathrm{O}_{2} \rightarrow \mathrm{NO}_{2}\) (a) Balance the equation. (b) Translate the equation into words using the word mole(s) wherever you can. (c) To produce 2 moles of \(\mathrm{NO}_{2}\) by the reaction you just wrote, how many grams of \(\mathrm{NO}\) and \(\mathrm{O}_{2}\) must you combine? (d) What is the theoretical yield in grams of \(\mathrm{NO}_{2}\) ? (e) You carry out the reaction and recover \(22.5 \mathrm{~g}\) of \(\mathrm{NO}_{2}\). What is the percent yield?

Consider the unbalanced chemical equation \(\mathrm{HCl}+\mathrm{Zn} \rightarrow \mathrm{H}_{2}+\mathrm{ZnCl}_{2}\) (a) Balance the equation. (b) Translate the equation into words using the word mole \((s)\) wherever you can. (c) To produce 1 mole of \(\mathrm{H}_{2}\) from the reaction you just wrote, how many grams of \(\mathrm{HCl}\) and Zn must you combine? (d) What is the theoretical yield in grams of \(\mathrm{H}_{2}\) ? (e) You recover \(2.00 \mathrm{~g}\) of \(\mathrm{H}_{2}\) after carrying out the reaction. What is the percent yield?

Consider the unbalanced chemical equation \(\mathrm{Na}+\mathrm{Cl}_{2} \rightarrow \mathrm{NaCl}\) (a) Balance the equation. (b) Translate the equation into words using the word mole(s) wherever you can. (c) To produce 1 mole of \(\mathrm{NaCl}\) from the reaction, how many grams of \(\mathrm{Na}\) and \(\mathrm{Cl}_{2}\) must you combine? (d) What is the theoretical yield in grams of \(\mathrm{NaCl}\) from the reaction you ran in part (c)? (e) You carry out the reaction and recover \(45.50 \mathrm{~g}\) of \(\mathrm{NaCl}\). What is the percent yield?

The formula \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) is a source of many conversion factors. (a) Write at least three of them. (b) Suppose you have a sample of \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\), and it contains a total of 72,000 hydrogen atoms. How many carbon atoms does this sample contain? (c) Suppose you have a sample of \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\), and it contains a total of 72,000 hydrogen atoms. What is the mass in grams of the entire sample?

The balanced chemical equation \(2 \mathrm{AgBr} \rightarrow\) \(2 \mathrm{Ag}+\mathrm{Br}_{2}\) and the formulas of the substances in it are a source of many conversion factors. Write all that are possible using the word mole(s).