Chapter 3

Automotive air bags inflate when sodium azide, \(\mathrm{NaN}_{3}\) , rapidly decomposes to its component elements: $$ 2 \mathrm{NaN}_{3}(s) \longrightarrow 2 \mathrm{Na}(s)+3 \mathrm{N}_{2}(g) $$ (a) How many moles of \(\mathrm{N}_{2}\) are produced by the decomposition of 1.50 \(\mathrm{mol}\) of \(\mathrm{NaN}_{3} ?\) (b) How many grams of NaN \(_{3}\) are required to form 10.0 \(\mathrm{g}\) of nitrogen gas? (c) How many grams of NaN \(_{3}\) are required to produce 10.0 \(\mathrm{ft}^{3}\) of nitrogen gas, about the size of an automotive air bag, if the gas has a density of 1.25 \(\mathrm{g} / \mathrm{L} ?\)

The complete combustion of octane, \(\mathrm{C}_{8} \mathrm{H}_{18},\) a component of gasoline, proceeds as follows: $$ 2 \mathrm{C}_{8} \mathrm{H}_{18}(I)+25 \mathrm{O}_{2}(g) \longrightarrow 16 \mathrm{CO}_{2}(g)+18 \mathrm{H}_{2} \mathrm{O}(g) $$ (a) How many moles of \(\mathrm{O}_{2}\) are needed to burn 1.50 \(\mathrm{mol}\) of \(\mathrm{C}_{8} \mathrm{H}_{18}\) ? (b) How many grams of \(\mathrm{O}_{2}\) are needed to burn 10.0 \(\mathrm{g}\) of \(\mathrm{C}_{8} \mathrm{H}_{18}\) ? (c) Octane has a density of 0.692 \(\mathrm{g} / \mathrm{mL}\) at \(20^{\circ} \mathrm{C} .\) How many grams of \(\mathrm{O}_{2}\) are required to burn 15.0 \(\mathrm{gal}\) of \(\mathrm{C}_{8} \mathrm{H}_{18}\) (the capacity of an average fuel tank)? (d) How many grams of \(\mathrm{CO}_{2}\) are produced when 15.0 gal of \(\mathrm{C}_{8} \mathrm{H}_{18}\) are combusted?

A piece of aluminum foil 1.00 \(\mathrm{cm}^{2}\) and 0.550 -mm thick is allowed to react with bromine to form aluminum bromide. (a) How many moles of aluminum were used? (The density of aluminum is 2.699 \(\mathrm{g} / \mathrm{cm}^{3} .\) ) (b) How many grams of aluminum bromide form, assuming the aluminum reacts completely?

The combustion of one mole of liquid ethanol, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) , produces 1367 \(\mathrm{kJ}\) of heat. Calculate how much heat is produced when 235.0 \(\mathrm{g}\) of ethanol are combusted.

(a) Define the terms limiting reactant and excess reactant. (b) Why are the amounts of products formed in a reaction determined only by the amount of the limiting reactant? (c) Why should you base your choice of which compound is the limiting reactant on its number of initial moles, not on its initial mass in grams?

Define the terms theoretical yield, actual yield, and percent yield. (b) Why is the actual yield in a reaction almost always less than the theoretical yield?(c) Can a reaction ever have 110\(\%\) actual yield?

Sodium hydroxide reacts with carbon dioxide as follows: $$ 2 \mathrm{NaOH}(s)+\mathrm{CO}_{2}(g) \longrightarrow \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l) $$ Which is the limiting reactant when 1.85 mol \(\mathrm{NaOH}\) and 1.00 \(\mathrm{mol} \mathrm{CO}_{2}\) are allowed to react? How many moles of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) can be produced? How many moles of the excess reactant remain after the completion of the reaction?

Aluminum hydroxide reacts with sulfuric acid as follows: $$ 2 \mathrm{Al}(\mathrm{OH})_{3}(s)+3 \mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}(a q)+6 \mathrm{H}_{2} \mathrm{O}(l) $$ Which is the limiting reactant when 0.500 mol \(\mathrm{Al}(\mathrm{OH})_{3}\) and 0.500 \(\mathrm{mol} \mathrm{H}_{2} \mathrm{SO}_{4}\) are allowed to react? How many moles of \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) can form under these conditions? How many moles of the excess reactant remain after the completion of the reaction?

The fizz produced when an Alka-Seltzer tablet is dissolved in water is due to the reaction between sodium bicarbonate \(\left(\mathrm{NaHCO}_{3}\right)\) and citric acid \(\left(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\right) :\) $$ \begin{aligned} 3 \mathrm{NaHCO}_{3}(a q)+\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(a q) & \longrightarrow \\ & 3 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(a q) \end{aligned} $$ In a certain experiment 1.00 g of sodium bicarbonate and 1.00 g of citric acid are allowed to react. (a) Which is the limiting reactant? (b) How many grams of carbon dioxide form? (c) How many grams of the excess reactant remain after the limiting reactant is completely consumed?

One of the steps in the commercial process for converting ammonia to nitric acid is the conversion of \(\mathrm{NH}_{3}\) to \(\mathrm{NO} :\) $$ 4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) $$ In a certain experiment, 2.00 \(\mathrm{g}\) of \(\mathrm{NH}_{3}\) reacts with 2.50 \(\mathrm{g}\) of \(\mathrm{O}_{2} .\) (a) Which is the limiting reactant? (b) How many grams of \(\mathrm{NO}\) and \(\mathrm{H}_{2} \mathrm{O}\) form? (c) How many grams of the excess reactant remain after the limiting reactant is completely consumed? (d) Show that your calculations in parts (b) and (c) are consistent with the law of conservation of mass.

Solutions of sodium carbonate and silver nitrate react to form solid silver carbonate and a solution of sodium nitrate. A solution containing 3.50 \(\mathrm{g}\) of sodium carbonate is mixed with one containing 5.00 \(\mathrm{g}\) of silver nitrate. How many grams of sodium carbonate, silver nitrate, silver carbonate, and sodium nitrate are present after the reaction is complete?

Solutions of sulfuric acid and lead(II) acetate react to form solid lead(II) sulfate and a solution of acetic acid. If 5.00 g of sulfuric acid and 5.00 g of lead(II) acetate are mixed, calculate the number of grams of sulfuric acid, lead(II) acetate, lead(II) sulfate, and acetic acid present in the mixture after the reaction is complete.

When benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) reacts with bromine \(\left(\mathrm{Br}_{2}\right),\) bromobenzene \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Br}\right)\) is obtained: $$ \mathrm{C}_{6} \mathrm{H}_{6}+\mathrm{Br}_{2} \longrightarrow \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Br}+\mathrm{HBr} $$ (a) When 30.0 g of benzene reacts with 65.0 g of bromine, what is the theoretical yield of bromobenzene? (b) If the actual yield of bromobenzene is \(42.3 \mathrm{g},\) what is the percentage yield?

When ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)\) reacts with chlorine \(\left(\mathrm{Cl}_{2}\right),\) the main product is \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\) , but other products containing \(\mathrm{Cl},\) such as \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2},\) are also obtained in small quantities. The formation of these other products reduces the yield of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\) (a) Calculate the theoretical yield of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\) when 125 \(\mathrm{g}\) of \(\mathrm{C}_{2} \mathrm{H}_{6}\) reacts with 255 \(\mathrm{g}\) of \(\mathrm{Cl}_{2},\) assuming that \(\mathrm{C}_{2} \mathrm{H}_{6}\) and \(\mathrm{Cl}_{2}\) react only to form \(\mathrm{C}_{2} \mathrm{H}_{2} \mathrm{Cl}\) and \(\mathrm{HCl} .(\mathbf{b})\) Calculate the percent yield of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\) if the reaction produces 206 \(\mathrm{g}\) of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\)

Hydrogen sulfide is an impurity in natural gas that must be removed. One common removal method is called the Claus process, which relies on the reaction: $$ 8 \mathrm{H}_{2} \mathrm{S}(g)+4 \mathrm{O}_{2}(g) \longrightarrow \mathrm{S}_{8}(l)+8 \mathrm{H}_{2} \mathrm{O}(g) $$ Under optimal conditions the Claus process gives 98\(\%\) yield of \(S_{8}\) from \(\mathrm{H}_{2}\) . If you started with 30.0 g of \(\mathrm{H}_{2} \mathrm{S}\) and 50.0 \(\mathrm{g}\) of \(\mathrm{O}_{2},\) how many grams of \(\mathrm{S}_{8}\) would be produced, assuming 98\(\%\) yield?

Write the balanced chemical equations for (a) the complete combustion of acetic acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right),\) the main ingredient in vinegar; (b) the decomposition of solid calcium hydroxide into solid calcium oxide (lime) and water vapor; (c) the combination reaction between nickel metal and chlorine gas.

If \(1.5 \mathrm{mol} \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}, 1.5 \mathrm{mol} \mathrm{C}_{3} \mathrm{H}_{8},\) and 1.5 \(\mathrm{mol} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COCH}_{3}\) are completely combusted in oxygen, which produces the largest number of moles of \(\mathrm{H}_{2} \mathrm{O} ?\) Which produces the least? Explain.

(a) The molecular formula of acetylsalicylic acid (aspirin), one of the most common pain relievers, is \(\mathrm{CgH}_{8} \mathrm{O}_{4} .\) How many moles of \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\) are in a \(0.500-\mathrm{g}\) tablet of aspirin? Assume the tablet is composed entirely of aspirin. (b) How many molecules of \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\) are in this tablet? (c) How many carbon atoms are in the tablet?

Very small semiconductor crystals, composed of approximately 1000 to \(10,000\) atoms, are called quantum dots. Quantum dots made of the semiconductor Case are now being used in electronic reader and tablet displays because they emit light efficiently and in multiple colors, depending on dot size. The density of CdSe is 5.82 \(\mathrm{g} / \mathrm{cm}^{3} .\) (a) What is the mass of one 2.5 -nm CdSe quantum dot? (b) CdSe quantum dots that are 2.5 \(\mathrm{nm}\) in diameter emit blue light upon stimulation. Assuming that the dot is a perfect sphere and that the empty space in the dot can be neglected, calculate how many Cd atoms are in one quantum dot of this size. (c) What is the mass of one 6.5-nm CdSe quantum dot? (d) CdSe quantum dots that are 6.5 \(\mathrm{nm}\) in diameter emit red light upon stimulation. Assuming that the dot is a perfect sphere, calculate how many Cd atoms are in one quantum dot of this size. (e) If you wanted to make one 6.5 -nm dot from multiple \(2.5-\)nm dots, how many 2.5 -nm dots would you need, and how many CdSe formula units would be left over, if any?

(a) One molecule of the antibiotic penicillin G has a mass of \(5.342 \times 10^{-21} \mathrm{g} .\) What is the molar mass of penicillin G? (b) Hemoglobin, the oxygen-carrying protein in red blood cells, has four iron atoms per molecule and contains 0.340\(\%\) iron by mass. Calculate the molar mass of hemoglobin.

Serotonin is a compound that conducts nerve impulses in the brain. It contains \(68.2 \% \mathrm{C}, 6.86 \% \mathrm{H}, 15.9 \% \mathrm{N},\) and 9.08\(\% \mathrm{O}\) . Its molar mass is 176 \(\mathrm{g} / \mathrm{mol} .\) Determine its molecular formula.

The koala dines exclusively on eucalyptus leaves. Its digestive system detoxifies the eucalyptus oil, a poison to other animals. The chief constituent in eucalyptus oil is a substance called eucalyptol, which contains \(77.87 \% \mathrm{C}, 11.76 \% \mathrm{H},\) and the remainder O. (a) What is the empirical formula for this substance? (b) A mass spectrum of eucalyptol shows a peak at about 154 amu. What is the molecular formula of the substance?

Vanillin, the dominant flavoring in vanilla, contains \(\mathrm{C}, \mathrm{H}\) , and \(\mathrm{O} .\) When 1.05 \(\mathrm{g}\) of this substance is completely combusted, 2.43 \(\mathrm{g}\) of \(\mathrm{CO}_{2}\) and 0.50 \(\mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O}\) are produced. What is the empirical formula of vanillin?

An organic compound was found to contain only \(\mathrm{C}, \mathrm{H},\) and Cl. When a \(1.50-\mathrm{g}\) sample of the compound was completely combusted in air, 3.52 \(\mathrm{g}\) of \(\mathrm{CO}_{2}\) was formed. In a separate experiment, the chlorine in a \(1.00-\mathrm{g}\) sample of the compound was converted to 1.27 g of AgCl. Determine the empirical formula of the compound.

A compound, \(\mathrm{KBrO}_{x},\) where \(x\) is unknown, is analyzed and found to contain 52.92\(\%\) Br. What is the value of \(x ?\)

An element \(X\) forms an iodide \(\left(\mathrm{XI}_{3}\right)\) and a chloride \(\left(\mathrm{XCl}_{3}\right) .\) The iodide is quantitatively converted to the chloride when it is heated in a stream of chlorine: $$ 2 \mathrm{XI}_{3}+3 \mathrm{Cl}_{2} \longrightarrow 2 \mathrm{XCl}_{3}+3 \mathrm{I}_{2} $$ If 0.5000 \(\mathrm{g}\) of \(\mathrm{XI}_{3}\) is treated with chlorine, 0.2360 \(\mathrm{g}\) of \(\mathrm{XCl}_{3}\) is obtained. (a) Calculate the atomic weight of the element X. (b) Identify the element X.

A chemical plant uses electrical energy to decompose aqueous solutions of NaCl to give \(\mathrm{Cl}_{2}, \mathrm{H}_{2},\) and \(\mathrm{NaOH} :\) $$ 2 \mathrm{NaCl}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{NaOH}(a q)+\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) $$ If the plant produces \(1.5 \times 10^{6} \mathrm{kg}\left(1500\) metric tons) of \(\mathrm{Cl}_{2}\right.\) daily, estimate the quantities of \(\mathrm{H}_{2}\) and \(\mathrm{NaOH}\) produced.

When hydrocarbons are burned in a limited amount of air, both CO and \(\mathrm{CO}_{2}\) form. When 0.450 g of a particular hydrocarbon was burned in air, 0.467 \(\mathrm{g}\) of \(\mathrm{CO}, 0.733 \mathrm{g}\) of \(\mathrm{CO}_{2},\) and 0.450 \(\mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O}\) were formed. (a) What is the empirical formula of the compound? (b) How many grams of O \(_{2}\) were used in the reaction? (c) How many grams would have been required for complete combustion?

A mixture of \(\mathrm{N}_{2}(g)\) and \(\mathrm{H}_{2}(g)\) reacts in a closed container to form ammonia, \(\mathrm{NH}_{3}(g) .\) The reaction ceases before either reactant has been totally consumed. At this stage \(3.0 \mathrm{mol} \mathrm{N}_{2}, 3.0 \mathrm{mol} \mathrm{H}_{2},\) and 3.0 \(\mathrm{mol} \mathrm{NH}_{3}\) are present. How many moles of \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) were present originally?

A mixture containing \(\mathrm{KClO}_{3}, \mathrm{K}_{2} \mathrm{CO}_{3}, \mathrm{KHCO}_{3},\) and \(\mathrm{KCl}\) was heated, producing \(\mathrm{CO}_{2}, \mathrm{O}_{2},\) and \(\mathrm{H}_{2} \mathrm{O}\) gases according to the following equations: $$ \begin{array}{l}{2 \mathrm{KClO}_{3}(s) \longrightarrow 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g)} \\ {2 \mathrm{KHCO}_{3}(s) \longrightarrow \mathrm{K}_{2} \mathrm{O}(s)+\mathrm{H}_{2} \mathrm{O}(g)+2 \mathrm{CO}_{2}(g)} \\\ {\mathrm{K}_{2} \mathrm{CO}_{3}(s) \longrightarrow \mathrm{K}_{2} \mathrm{O}(s)+\mathrm{CO}_{2}(g)}\end{array} $$ The KCl does not react under the conditions of the reaction. If 100.0 g of the mixture produces 1.80 \(\mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O}, 13.20 \mathrm{g}\) of \(\mathrm{CO}_{2}\) and 4.00 \(\mathrm{g}\) of \(\mathrm{O}_{2},\) what was the composition of the original mixture? (Assume complete decomposition of the mixture.)

When a mixture of 10.0 g of acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) and 10.0 \(\mathrm{g}\) of oxygen \(\left(\mathrm{O}_{2}\right)\) is ignited, the resulting combustion reaction produces \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) . (a) Write the balanced chemical equation for this reaction. (b) Which is the limiting reactant? (c) How many grams of \(\mathrm{C}_{2} \mathrm{H}_{2}, \mathrm{O}_{2}, \mathrm{CO}_{2},\) and \(\mathrm{H}_{2} \mathrm{O}\) are present after the reaction is complete?

The semiconductor gallium arsenide, GaAs, is used in high-speed integrated circuits, light-emitting diodes, and solar cells. Its density is 5.32 \(\mathrm{g} / \mathrm{m}^{3} .\) It can be made by reacting trimethylgallium, \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{Ga},\) with arsine gas, \(\mathrm{AsH}_{3}\) . The other product of the reaction is methane, \(\mathrm{CH}_{4}\) . (a) If you reacted 450.0 g of trimethylgallium with 300.0 \(\mathrm{g}\) of arsine, what mass of GaAs could you make? (b) Which reactant, if any, would be left over, and how many moles of the leftover reactant would remain? (c) One application of GaAs uses it as a thin film. If you take the mass of GaAs from part (a) and make a 40 -nm thin film from it, what area, in \(\mathrm{cm}^{2},\) would it cover? Recall that \(1 \mathrm{nm}=1 \times 10^{-9} \mathrm{m} .\)

Paclitaxel, \(\mathrm{C}_{47} \mathrm{H}_{51} \mathrm{NO}_{14},\) is an anticancer compound that is difficult to make in the lab. One reported synthesis requires 11 steps, and the final yield of paclitaxel is only 5\(\% .\) Assuming all steps have equivalent yields, what is the average percent yield for each step in the synthesis?

Consider a sample of calcium carbonate in the form of a cube measuring 2.005 in. on each edge. If the sample has a density of 2.71 \(\mathrm{g} / \mathrm{cm}^{3}\) , how many oxygen atoms does it contain?

(a) If an automobile travels 225 mi with a gas mileage of 20.5 mi/gal, how many kilograms of \(\mathrm{CO}_{2}\) are produced? Assume that the gasoline is composed of octane, \(\mathrm{C}_{8} \mathrm{H}_{18}(l),\) whose density is 0.692 \(\mathrm{g} / \mathrm{mL}\) . (b) Repeat the calculation for a truck that has a gas mileage of 5 \(\mathrm{mi} / \mathrm{gal} .\)

Introduced the idea of structural isomerism, with 1 -propanol and 2 -propanol as examples. Determine which of these properties would distinguish these two substances: (a) boiling point, (b) combustion analysis results, (c) molecular weight, (d) density at a given temperature and pressure. You can check on the properties of these two compounds in Wolfram Alpha (http://www. wolframalpha.com/) or the CRC Handbook of Chemistry and Physics.

Hydrogen cyanide, HCN, is a poisonous gas. The lethal dose is approximately 300 \(\mathrm{mg}\) HCN per kilogram of air when inhaled. (a) Calculate the amount of HCN that gives the lethal dose in a small laboratory room measuring \(12 \times 15 \times 8.0 \mathrm{ft}\) . The density of air at \(26^{\circ} \mathrm{C}\) is 0.00118 \(\mathrm{g} / \mathrm{cm}^{3} .\) (b) If the HCN is formed by reaction of \(\mathrm{NaCN}\) with an acid such as \(\mathrm{H}_{2} \mathrm{SO}_{4}\) what mass of NaCN gives the lethal dose in the room? $$ 2 \mathrm{NaCN}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{Na}_{2} \mathrm{SO}_{4}(a q)+2 \mathrm{HCN}(g) $$ (c) HCN forms when synthetic fibers containing Orlon or Acrilan burn. Acrilan has an empirical formula of \(\mathrm{CH}_{2} \mathrm{CHCN},\) so HCN is 50.9\(\%\) of the formula by mass. A rug measures \(12 \times 15 \mathrm{ft}\) and contains 30 oz of Acrilan fibers per square yard of carpet. If the rug burns, will a lethal dose of HCN be generated in the room? Assume that the yield of HCN from the fibers is 20\(\%\) and that the carpet is 50\(\%\) consumed.

The source of oxygen that drives the internal combustion engine in an automobile is air. Air is a mixture of gases, principally \(\mathrm{N}_{2}(\sim 79 \%)\) and \(\mathrm{O}_{2}(\sim 20 \%) .\) In the cylinder of an automobile engine, nitrogen can react with oxygen to produce nitric oxide gas, NO. As NO is emitted from the tailpipe of the car, it can react with more oxygen to produce nitrogen dioxide gas. (a) Write balanced chemical equations for both reactions. (b) Both nitric oxide and nitrogen dioxide are pollutants that can lead to acid rain and global warming; collectively, they are called "\({NO}_{x}\)" gases. In \(2009,\) the United States emitted an estimated 19 million tons of nitrogen dioxide into the atmosphere. How many grams of nitrogen dioxide is this? (c) The production of \(\mathrm{NO}_{x}\) gases is an unwanted side reaction of the main engine combustion process that turns octane, \(\mathrm{C}_{8} \mathrm{H}_{18},\) into \(\mathrm{CO}_{2}\) and water. If 85\(\%\) of the oxygen in an engine is used to combust octane and the remainder used to produce nitrogen dioxide, calculate how many grams of nitrogen dioxide would be produced during the combustion of 500 g of octane.

The thermite reaction, $$ \mathrm{Fe}_{2} \mathrm{O}_{3}+\mathrm{Al} \rightarrow \mathrm{Al}_{2} \mathrm{O}_{3}+\mathrm{Fe} $$ produces so much heat that the Fe product melts. This reaction is used industrially to weld metal parts under water, where a torch cannot be employed. It is also a favorite chemical demonstration in the lecture hall (on a small scale). (a) Balance the chemical equation for the thermite reaction, and include the proper states of matter. (b) Calculate how many grams of aluminum are needed to completely react with 500.0 g of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) in this reaction. (c) This reaction produces 852 kJ of heat per mole of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) reacted. How many grams of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) are needed to produce \(1.00 \times 10^{4} \mathrm{kJ}\) of heat? (d) If you performed the reverse reaction aluminum-oxide plus iron makes iron oxide plus aluminum-would that reaction have heat as a reactant or a product?

One of the most bizarre reactions in chemistry is called the Ugi reaction: $$ \begin{array}{l}{\mathrm{R}_{1} \mathrm{C}(=\mathrm{O}) \mathrm{R}_{2}+\mathrm{R}_{3}-\mathrm{NH}_{2}+\mathrm{R}_{4} \mathrm{COOH}+\mathrm{R}_{5} \mathrm{NC} \rightarrow} \\ {\mathrm{R}_{4} \mathrm{C}(=\mathrm{O}) \mathrm{N}\left(\mathrm{R}_{3}\right) \mathrm{C}\left(\mathrm{R}_{1} \mathrm{R}_{2}\right) \mathrm{C}=\mathrm{ONHR}_{5}+\mathrm{H}_{2} \mathrm{O}}\end{array} $$ (a) Write out the balanced chemical equation for the Ugi reaction, for the case where \(R=C H_{3} C H_{2} C H_{2} C H_{2} C H_{2} C H_{2}-\) (this is called the hexyl group) for all compounds. (b) What mass of the "hexyl Ugi product" would you form if 435.0 \(\mathrm{mg}\) of \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\) was the limiting reactant?