Stoichiometry of Formulas and Equations

Concentrated sulfuric acid (18.3 M) has a density of 1.84 g/mL. (a) How many moles of H₂SO₄ are in each milliliter of solution? (b) What is the mass % of H₂SO₄ in the solution?

The study of sulfur-nitrogen compounds is an active area of chemical research, made more so by the discovery in the early 1980s of one such compound that conducts electricity like a metal. The first sulfur-nitrogen compound was prepared in 1835 and serves today as a reactant for preparing many of the others. Mass spectrometry of the compound shows a molar mass of 184.27 g/mol, and analysis shows it to contain 2.288 g of S for every 1.000 g of N. What is its molecular formula?

Narceine is a narcotic in opium that crystallizes from solution as a hydrate that contains 10.8 mass % water and has a molar mass of 499.52 g/mol. Determine x in narceine.xH₂O.

In 1961, scientists agreed that the atomic mass unit (amu) would be defined as 1/12 the mass of an atom of ¹²C. Before then, it was defined as 1/16 the average mass of an atom of naturally occurring oxygen (a mixture of ¹⁶O, ¹⁷O, and ¹⁸O). The current atomic mass of oxygen is 15.9994 amu. (a) Did Avogadro’s number change after the definition of an amu changed and, if so, in what direction? (b) Did the definition of the mole change? (c) Did the mass of a mole of a substance change? (d) Before 1961, was Avogadro’s number 6.02×10²³ (when considered to three significant figures), as it is today?

The zirconium oxalate K2Zr(C2O4)3(H2C2O). H2O was synthesized by mixing 1.68 g of ZrOCl2 .8H2O with 5.20 g of H2C2O4.2H2O and an excess of aqueous KOH. After 2 months, 1.25 g of crystalline product was obtained, as well as aqueous KCl and water. Calculate the percent yield.

A student weighs a sample of carbon on a balance that is accurate to ±0.001 g. (a) How many atoms are in 0.001 g of C? (b) The carbon is used in the following reaction:
$P{b}_3{O}_4\left(s\right)+C\left(s\right)\to 3PbO\left(s\right)+CO\left(g\right)$

What mass difference in the lead(II) oxide would be caused by an error in the carbon mass of 0.001 g?

Calculate each of the following quantities: 

(a) Volume of 18.0 M sulfuric acid that must be added to water to prepare 2.00 L of a 0.429 M solution 

(b) Molarity of the solution obtained by diluting 80.6 mL of 0.225 M ammonium chloride to 0.250 L 

(c) Volume of water added to 0.130 L of 0.0372 M sodium hydroxide to obtain a 0.0100 M solution (assume the volumes are additive at these low concentrations)

(d) Mass of calcium nitrate in each milliliter of a solution prepared by diluting 64.0 mL of 0.745 M calcium nitrate to a final volume of 0.100 L

 The following circles represent a chemical reaction between AB2 and B2:

(a) Write a balanced equation for the reaction. (b) What is the limiting reactant? (c) How many moles of product can be made from 3.0 mol of B2 and 5.0 mol of AB2? (d) How many moles of excess reactant remain after the reaction in part (c)?

 A 0.652-g sample of a pure strontium halide reacts with excess sulfuric acid, and the solid strontium sulfate formed is separated, dried, and found to weigh 0.755 g. What is the formula of the original halide?

Is each of the following statements true or false? Correct any that are false: (a) Amole of one substance has the same number of atoms as a mole of any other substance. (b)The theoretical yield for a reaction is based on the balanced chemical equation. (c) A limiting-reactant problem is presented when the quantity of available material is given in moles for one of the reactants. (d)To prepare 1.00 L of 3.00 M NaCl, weigh 175.5 g of NaCl and dissolve it in 1.00 Lof distilled water. (e) The concentration of a solution is an intensive property, but the amount of solute in a solution is an extensive property

In each pair, choose the larger of the indicated quantities or state that the samples are equal: Mass: 6.02´10²³ atoms of ²³⁵U or 6.02´10²³ atoms of ²³⁸U

Box A represents one unit volume of solution A. Which box – B, C or D represents one unit volume after adding enough solvent to solution A to (a) triple its volume; (b) double its volume; (c)quadruple its volume?
 

For the reaction between solid tetraphosphorus trisulfide and oxygen gas to form solid tetraphosphorusdecaoxide and sulfur dioxide gas, write a balanced equation. Show the equation (see Table 3.5) in terms grams.

Solar winds composed of free protons, electrons, andparticles bombard Earth constantly, knocking gas molecules outof the atmosphere. In this way, Earth loses about 3.0 kg of matterper second. It is estimated that the atmosphere will be gone inabout 50 billion years. Use this estimate to calculate the amount (mol) of nitrogen,which makes up 75.5 mass % of the atmosphere.

Assuming that the volume are additive, what is the concentration of KBr in a solution prepared by mixing 0.200 L of 0.053 M KBr with 0.550 L of 0.078 M KBr?

Hydrogen gas has been suggested as a clean fuel because it produces only water vapour when it burns.Ifthe reaction has a 98.8% yield, what mass of hydrogen forms 105 kg of water?

Seawater is approximately 4.0% by mass dissolved ions. About 85% of the mass of the dissolved ions is from NaCl. 

(a) Find the mass % of NaCl in seawater. 

(b) Find the mass % of Na+ ions and of Cl- ions in seawater. 

(c) Find the molarity of NaCl in seawater at 150C (d of seawater at 150C = 1.025 g/mL).

Calculate each of the following quantities:Number of atoms in 0.0015 mol of fluorine gas

Elements X (green) and Y (purple) react according to the following equation: ${\mathbf{X}}_{\mathbf{2}}+\text{ 3}{\mathbf{Y}}_{\mathbf{2}}\to 2{\mathbf{XY}}_{\mathbf{3}}$. Which molecular scene represents the product of the reaction?

To 1.35 L of 0.325 M HCl, you add 3.57 L of a second HCl solution of unknown concentration. The resulting solution is 0.893 M HCl. Assuming the volumes are additive, calculate the molarity of the second HCl solution.

Nitrogen (N), phosphorous(P), and potassium (K) are main nutrients in plant fertilizers. By industry convention, the number on the label refer to the mass percentage of N, P₂O₅ and K₂O, in that order. Calculate the N/P/K ratio of a 30/10/10 fertilizer in terms of moles of each element, and express it as x/y/1.0

What mass % of ammonium sulfate, ammonium hydrogen phosphate, and potassium chloride would you use to prepare 10/10/10 plant fertilizer (see Problem 3.140)?

Methane and ethane are the two simplest hydrocarbons. What is the mass % C in a mixture that is 40.0% methane and 60.0% ethane by mass?

Ferrocene, synthesized in 1951, was the first organic iron compound with bonds. An understanding of the structure of ferrocene gave rise to new ideas about chemical bonding and led to the preparation of many useful compounds. In the combustion analysis of ferrocene, which contains only and a 0.9437-g sample produced 2.233 g of and 0.457 g of What is the empirical formula of ferrocene?

When carbon-containing compounds are burned in a limited amount of air, some CO(g)as well as CO₂(g)is produced. A gaseous product mixture is 35.0 mass % COand 65.0 mass % CO₂ What is the mass % in the mixture?

When 1.5173 g of an organic iron compound containing Fe, C, H, and O was burned in O₂, 2.838 g of CO₂ and 0.8122 g of H₂O were produced. In a separate experiment to determine the mass % of iron, 0.3355 g of the compound yielded 0.0758 g of Fe2O₃. What is the empirical formula of the compound?

Write a balanced equation for the reaction depicted below:

If each reactant molecule represents 1.25×10^-2 mol and the reaction yield is 87%, how many grams of Si-containing product form?

Citric acid (right) is concentrated in citrus fruits and plays a central metabolic role in nearly every animal and plant cell. (a) What are the molar mass and formula of citric acid? (b) How many moles of citric acid are in 1.50 qt of lemon juice (d = 1.09 g/mL) that is 6.82% citric acid by mass?

Various nitrogen oxides, as well as sulfur oxides, contribute to acidic rainfall through complex reaction sequences. Nitrogen and oxygen combine during high-temperature combustion of fuels in air to form nitrogen monoxide gas, which reacts with more oxygen to form nitrogen dioxide gas. In contact with water vapor, nitrogen dioxide forms aqueous nitric acid and more nitrogen monoxide. (a) Write balanced equations for these reactions. (b) Use the equations to write one overall balanced equation that does not include nitrogen monoxide and nitrogen dioxide. (c) How many metric tons (t) of nitric acid form when 1350 t of atmospheric nitrogen is consumed (1 t = 1000 kg)?

Alum [KAI(SO₄)₂ .xH₂O] is used in food preparation, dye fixation, and water purification. To prepare alum, aluminum is reacted with potassium hydroxide and the product with sulfuric acid. Upon cooling, alum crystallizes from the solution. (a) A 0.5404-g sample of alum is heated to drive off the waters of hydration, and the resulting KAI(SO₄)₂ weighs 0.2941 g. Determine the value of and the complete formula of alum. (b) When 0.7500 g of aluminum is used, 8.500 g of alum forms. What is the percent yield?

Nitrogen monoxide reacts with elemental oxygen to form nitrogen dioxide. The scene at right represents an initial mixture of reactants. If the reaction has a 66% yield, which of the scenes below (A, B, or C) best represents the final product mixture?

During studies of the reaction in Sample Problem

$\mathbf{2}{\mathit{N}}_{\mathbf{2}}{\mathit{H}}_{\mathbf{4}}\mathbf{\left(}\mathit{l}\mathbf{\right)}\mathbf{+}{\mathit{N}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{4}}\mathbf{\left(}\mathit{l}\mathbf{\right)}\mathbf{\to }\mathbf{3}{\mathit{N}}_{\mathbf{2}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{+}\mathbf{4}{\mathit{H}}_{\mathbf{2}}\mathit{O}\mathbf{\left(}\mathit{g}\mathbf{\right)}$

a chemical engineer measured a less-than-expected yield of N2 and discovered that the following side reaction occurs: 

${\mathit{N}}_{\mathbf{2}}{\mathit{H}}_{\mathbf{4}}\mathbf{\left(}\mathit{l}\mathbf{\right)}\mathbf{+}\mathbf{2}{\mathit{N}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{4}}\mathbf{\left(}\mathit{l}\mathbf{\right)}\mathbf{\to }\mathbf{6}\mathit{N}\mathit{O}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{+}\mathbf{2}{\mathit{H}}_{\mathbf{2}}\mathit{O}\mathbf{\left(}\mathit{g}\mathbf{\right)}$

In one experiment, 10.0 g of NO formed when 100.0 g of each reactant was used. What is the highest percent yield of N2 that can be expected?

Fluorine is so reactive that it forms compounds with materials inert to other treatments. (a) When 0.327 g of platinum is heated in fluorine, 0.519 g of a dark red, volatile solid forms. What is its empirical formula? (b) When 0.265 g of this red solid reacts with excess xenon gas, 0.378 g of an orange-yellow solid forms. What is the empirical formula of this compound, the first to contain a noble gas? (c) Fluorides of xenon can be formed by direct reaction of the elements at high pressure and temperature. Under conditions that produce only the tetra- and hexafluorides, 1.85×10^-4 mol of xenon reacted with 5.00×10^-4 mol of fluorine, and 9.00×10^-6 mol of xenon was found in excess. What are the mass percents of each xenon fluoride in the product mixture?

Hemoglobin is 6.0% heme (C₃₄H₃₂FeN₄O₄) by mass. To remove the heme, hemoglobin is treated with acetic acid and NaCl to form hemin (C₃₄H₃₂N₄O₄FeCl). At a crime scene, a blood sample contains 0.65 g of hemoglobin. (a) How many grams of heme are in the sample? (b) How many moles of heme? (c) How many grams of Fe? (d) How many grams of hemin could be formed for a forensic chemist to measure?

Manganese is a key component of extremely hard steel. The element occurs naturally in many oxides. A 542.3-g sample of a manganese oxide has an Mn/O ratio of 1.00/1.42 and consists of braunite (Mn₂O₃) and manganosite (MnO). (a) What masses of braunite and manganosite are in the ore? (b) What is the ratio Mn³⁺/Mn²⁺ in the ore?

Sulfur dioxide is a major industrial gas used primarily for the production of sulfuric acid, but also as a bleach and food preservative. One way to produce it is by roasting iron pyrite (iron disulfide, FeS₂) in oxygen, which yields the gas and solid iron(III) oxide. What mass of each of the other three substances is involved in producing 1.00 kg of sulfur dioxide?

The human body excretes nitrogen in the form of urea, NH₂CONH₂. The key biochemical step in urea formation is the reaction of water with arginine to produce urea and ornithine:

(a) What is the mass percent of nitrogen in urea, arginine, and ornithine? (b) How many grams of nitrogen can be excreted as urea when 135.2 g of ornithine is produced?

Aspirin (acetylsalicylic acid, C₉H₈O₄) is made by reacting salicylic acid (C₇H₆O₃) with acetic anhydride [(CH₃CO)₂O]:

${\mathit{C}}_{\mathbf{7}}{\mathit{H}}_{\mathbf{6}}{\mathit{O}}_{\mathbf{3}}\mathbf{\left(}\mathit{S}\mathbf{\right)}\mathbf{+}{\mathbf{\left(}\mathit{C}{\mathit{H}}_{\mathbf{3}}\mathit{C}\mathit{O}\mathbf{\right)}}_{\mathbf{2}}\mathit{O}\mathbf{\left(}\mathit{I}\mathbf{\right)}\mathbf{\to }{\mathit{C}}_{\mathbf{9}}{\mathit{H}}_{\mathbf{8}}{\mathit{O}}_{\mathbf{4}}\mathbf{\left(}\mathit{S}\mathbf{\right)}\mathbf{+}\mathit{C}{\mathit{H}}_{\mathbf{3}}\mathit{C}\mathit{O}\mathit{O}\mathit{H}\mathbf{\left(}\mathit{I}\mathbf{\right)}$

In one reaction, 3.077 g of salicylic acid and 5.50 mL of acetic anhydride react to form 3.281 g of aspirin. (a) Which is the limiting reactant (d of acetic anhydride = 1.080 g/mL)? (b) What is the percent yield of this reaction? (c) What is the percent atom economy of this reaction?

The rocket fuel hydrazine (N₂H₄) is made by the three-step Raschig process, which has the following overall equation: 

$\mathit{N}\mathit{a}\mathit{O}\mathit{C}\mathit{I}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{+}\mathbf{2}\mathit{N}{\mathit{H}}_{\mathbf{3}}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{\to }{\mathit{N}}_{\mathbf{2}}\mathit{H}\mathbf{4}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{+}\mathit{N}\mathit{a}\mathit{C}\mathit{I}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{+}{\mathit{H}}_{\mathbf{2}}\mathit{O}\mathbf{\left(}\mathit{I}\mathbf{\right)}$

What is the percent atom economy of this process?

Lead(II) chromate (PbCrO₄) is used as the yellow pigment in traffic lanes, but is banned from house paint because of the risk of lead poisoning. It is produced from chromite (FeCr₂O₄), an ore of chromium: 

$\mathbf{4}\mathit{F}\mathit{e}\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{4}}\mathbf{\left(}\mathit{S}\mathbf{\right)}\mathbf{+}\mathbf{8}{\mathit{K}}_{\mathbf{2}}\mathit{C}{\mathit{O}}_{\mathbf{3}}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{+}\mathbf{7}{\mathit{O}}_{\mathbf{2}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{\to }\mathbf{2}\mathit{F}{\mathit{e}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{3}}\mathbf{\left(}\mathit{s}\mathbf{\right)}\mathbf{+}\mathbf{8}{\mathit{K}}_{\mathbf{2}}\mathit{C}\mathit{r}{\mathit{O}}_{\mathbf{4}}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{+}\mathbf{8}\mathit{C}{\mathit{O}}_{\mathbf{2}}\mathbf{\left(}\mathit{g}\mathbf{\right)}$

Lead(II) ion then replaces the K⁺ ion. If a yellow paint is 0.511% PbCrO₄ by mass, how many grams of chromite are needed per kilogram of paint?

Ethanol (CH₃CH₂OH), the intoxicant in alcoholic beverages, is also used to make other organic compounds. In concentrated sulfuric acid, ethanol forms diethyl ether and water:

$\mathbf{2}\mathit{C}{\mathit{H}}_{\mathbf{3}}\mathit{C}{\mathit{H}}_{\mathbf{2}}\mathit{O}\mathit{H}\mathbf{\left(}\mathit{I}\mathbf{\right)}\mathbf{\to }\mathit{C}{\mathit{H}}_{\mathbf{3}}\mathit{C}{\mathit{H}}_{\mathbf{2}}\mathit{O}\mathit{C}{\mathit{H}}_{\mathbf{3}}\mathit{C}{\mathit{H}}_{\mathbf{2}}\mathbf{\left(}\mathit{I}\mathbf{\right)}\mathbf{+}{\mathit{H}}_{\mathbf{2}}\mathit{O}\mathbf{\left(}\mathit{g}\mathbf{\right)}$

In a side reaction, some ethanol forms ethylene and water:

$\mathit{C}{\mathit{H}}_{\mathbf{3}}\mathit{C}{\mathit{H}}_{\mathbf{2}}\mathit{O}\mathit{H}\mathbf{\left(}\mathit{I}\mathbf{\right)}\mathbf{\to }\mathit{C}{\mathit{H}}_{\mathbf{2}}\mathbf{=}\mathit{C}{\mathit{H}}_{\mathbf{2}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{+}{\mathit{H}}_{\mathbf{2}}\mathit{O}\mathbf{\left(}\mathit{g}\mathbf{\right)}$

(a) If 50.0 g of ethanol yields 35.9 g of diethyl ether, what is the percent yield of diethyl ether? (b) During the process, 45.0% of the ethanol that did not produce diethyl ether reacts by the side reaction. What mass of ethylene is produced?

When powdered zinc is heated with sulfur, a violent reaction occurs, and zinc sulfide forms:

$\mathit{Z}\mathit{n}\mathbf{\left(}\mathit{s}\mathbf{\right)}\mathbf{+}{\mathit{S}}_{\mathbf{8}}\mathbf{\left(}\mathit{s}\mathbf{\right)}\mathbf{\to }\mathit{Z}\mathit{n}\mathit{S}\mathbf{\left(}\mathit{s}\mathbf{\right)}\mathbf{\left[}\mathit{u}\mathit{n}\mathit{b}\mathit{a}\mathit{l}\mathit{a}\mathit{n}\mathit{c}\mathit{e}\mathit{d}\mathbf{\right]}$

Some of the reactants also combine with oxygen in air to form zinc oxide and sulfur dioxide. When 83.2 g of Zn reacts with 52.4 g of S₈, 104.4 g of ZnS forms. What is the percent yield of ZnS? (b) If all the remaining reactants combine with oxygen, how many grams of each of the two oxides form?

Cocaine (C₁₇H₂₁O₄N) is a natural substance found in coca leaves, which have been used for centuries as a local anesthetic and stimulant. Illegal cocaine arrives in the United States either as the pure compound or as the hydrochloride salt (C₁₇H₂₁O₄NHCl). At 25^oC, the salt is very soluble in water (2.50 kg/L), but cocaine is much less so (1.70 g/L). (a) What is the maximum amount (in g) of the salt that can dissolve in 50.0 mL of water? (b) If the solution in part (a) is treated with NaOH, the salt is converted to cocaine. How much additional water (in L) is needed to dissolve it?

High-temperature superconducting oxides hold great promise in the utility, transportation, and computer industries. (a) One superconductor is La_2-xSr_xCuO₄. Calculate the molar masses of this oxide when x = 0, x = 1, and x = 0.163. (b) Another common superconducting oxide is made by heating a mixture of barium carbonate, copper(II) oxide, and yttrium(III) oxide, followed by further heating in O2:

$$\begin{gathered} \mathbf{4}{\mathbf{BaCO}}_{\mathbf{3}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{6}\mathbf{CuO}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}{\mathbf{Y}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{\to }\mathbf{2}{\mathbf{YBa}}_{\mathbf{2}}{\mathbf{Cu}}_{\mathbf{3}}{\mathbf{O}}_{\mathbf{6}\mathbf{.}\mathbf{5}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{4}{\mathbf{CO}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)} \\ \mathbf{2}{\mathbf{Ba}}_{\mathbf{2}}{\mathbf{Cu}}_{\mathbf{3}}{\mathbf{O}}_{\mathbf{6}\mathbf{.}\mathbf{5}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{O}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\to }\mathbf{2}{\mathbf{YBa}}_{\mathbf{2}}{\mathbf{Cu}}_{\mathbf{3}}{\mathbf{O}}_{\mathbf{7}}\mathbf{\left(}\mathbf{s}\mathbf{\right)} \end{gathered}$$

When equal masses of the three reactants are heated, which reactant is limiting? (c) After the product in part (b) is removed, what is the mass percent of each reactant in the remaining solid mixture?