Stoichiometry of Formulas and Equations

An oxide of nitrogen contains 30.45 mass %. 

(a) What is the empirical formula of the oxide? 

(b) If the molar mass is $\mathbf{90}\mathbf{\pm }\mathbf{5}\mathbf{g}\mathbf{/}\mathbf{mol}\mathbf{,}$ what is the molecular formula?

A chloride of silicon contains 79.1 mass % Cl. 

(a) What is the empirical formula of the chloride?

(b) If the molar mass is 269 g/mol, what is the molecular formula?

Allyl sulfide gives garlic its characteristic odor.

Calculate 

1. The mass in grams of 2.63 mol of allyl sulfide;
2. The number of carbon atoms in 35.7g of allyl sulfide.

A sample of 0.600 mol of a metal M reacts completely with excess fluorine to form 46.8 g of $\mathit{M}{\mathit{F}}_{\mathbf{2}}$.
 (a) How many moles of F are in the sample of that forms?
 (b) How many grams of M are in this sample of $\mathit{M}{\mathit{F}}_{\mathbf{2}}$ 
(c) What element is represented by the symbol M?

A 0.370 mol sample of a metal oxide $\left(M_2{0}_3\right)$ weighs 55.4 g.
 (a) How many moles of O are in the sample?
 (b) How many grams of M are in the sample?
 (c) What element is represented by the symbol M?

Nicotine is a poisonous, addictive compound found in tobacco. A sample of nicotine contains 6.16 mmol of C, 8.56 mmol of H, and 1.23 mmol of N [1 mmol (1 millimole) =10^-3 mol]. What is the empirical formula?

Cortisol (m = 362.47 g/mol), one of the major steroid hormones, is a key factor in the synthesis of protein. Its profound effect on the reduction of inflammation explains its use in the treatment of rheumatoid arthritis. Cortisol is 69.6% C, 8.34% H, and 22.1% O by mass. What is its molecular formula?

Acetaminophen (below) is a popular nonaspirin, “over-thecounter” pain reliever. What is the mass % of each element in acetaminophen?

Write balanced equations for each of the following by inserting the correct coefficients in the blanks:  

1. $\mathbf{\_Cu}\left(s\right)\mathbf{+}{\mathbf{\_S}}_{\mathbf{8}}\left(s\right)\mathbf{\to }{\mathbf{\_Cu}}_{\mathbf{2}}\mathbf{S}\left(s\right)$
2. ${\mathbf{\_P}}_{\mathbf{4}}{\mathbf{O}}_{\mathbf{10}}\left(s\right)\mathbf{+}{\mathbf{\_H}}_{\mathbf{2}}\mathbf{O}\left(l\right)\mathbf{\to }{\mathbf{\_H}}_{\mathbf{3}}{\mathbf{PO}}_{\mathbf{4}}\left(l\right)$
3. ${\mathbf{\_B}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}\left(s\right)\mathbf{+}\mathbf{\_NaOH}\left(\mathrm{aq}\right)\mathbf{\to }{\mathbf{\_Na}}_{\mathbf{3}}{\mathbf{BO}}_{\mathbf{3}}\left(\mathrm{aq}\right)\mathbf{+}{\mathbf{\_H}}_{\mathbf{2}}\mathbf{O}\left(l\right)$
4. ${\mathbf{\_CH}}_{\mathbf{3}}{\mathbf{NH}}_{\mathbf{2}}\left(g\right)\mathbf{+}{\mathbf{\_O}}_{\mathbf{2}}\left(g\right)\mathbf{\to }{\mathbf{\_CO}}_{\mathbf{2}}\left(g\right)\mathbf{+}{\mathbf{\_H}}_{\mathbf{2}}\mathbf{O}\left(g\right)\mathbf{+}{\mathbf{\_N}}_{\mathbf{2}}\left(g\right)$
   

Write balanced equations for each of the following by inserting the correct coefficients in the blanks:

1. $\mathbf{\_Cu}{\left({\mathrm{NO}}_3\right)}_{\mathbf{2}}\left(\mathrm{aq}\right)\mathbf{+}\mathbf{\_KOH}\left(\mathrm{aq}\right)\mathbf{\to }\mathbf{\_Cu}{\left(\mathrm{OH}\right)}_{\mathbf{2}}\left(s\right)\mathbf{+}{\mathbf{\_KNO}}_{\mathbf{3}}\left(\mathrm{aq}\right)$
2. ${\mathbf{\_BCl}}_{\mathbf{3}}\left(g\right)\mathbf{+}{\mathbf{\_H}}_{\mathbf{2}}\mathbf{O}\left(l\right)\mathbf{\to }{\mathbf{\_H}}_{\mathbf{3}}{\mathbf{BO}}_{\mathbf{3}}\left(s\right)\mathbf{+}\mathbf{\_HCl}\left(g\right)$
   
3. ${\mathbf{\_CaSiO}}_{\mathbf{3}}\left(s\right)\mathbf{+}\mathbf{\_HF}\left(g\right)\mathbf{\to }{\mathbf{\_SiF}}_{\mathbf{4}}\left(g\right)\mathbf{+}{\mathbf{\_CaF}}_{\mathbf{2}}\left(s\right)\mathbf{+}{\mathbf{\_H}}_{\mathbf{2}}\mathbf{O}\left(l\right)$
   
4. $\mathit{\_}{\left(\mathrm{CN}\right)}_{\mathbf{2}}\left(g\right)\mathbf{+}\mathit{\_}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\left(l\right)\mathbf{\to }{\mathbf{\_H}}_{\mathbf{2}}{\mathbf{C}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{4}}\left(\mathrm{aq}\right)\mathbf{+}{\mathbf{\_NH}}_{\mathbf{3}}\left(g\right)$
   

Write balanced equations for each of the following by inserting the correct coefficients in the blanks:

1. ${\mathbf{\_SO}}_{\mathbf{2}}\left(g\right)\mathbf{+}{\mathbf{\_O}}_{\mathbf{2}}\left(g\right)\mathbf{\to }{\mathbf{\_SO}}_{\mathbf{3}}\left(g\right)$
   
2. ${\mathbf{\_Sc}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}\left(s\right)\mathbf{+}{\mathbf{\_H}}_{\mathbf{2}}\mathbf{O}\left(l\right)\mathbf{\to }\mathbf{\_Sc}{\left(\mathrm{OH}\right)}_{\mathbf{3}}\left(s\right)$
   
3. ${\mathbf{\_H}}_{\mathbf{3}}{\mathbf{PO}}_{\mathbf{4}}\left(\mathrm{aq}\right)\mathbf{+}\mathbf{\_NaOH}\left(\mathrm{aq}\right)\mathbf{\to }{\mathbf{\_Na}}_{\mathbf{2}}{\mathbf{HPO}}_{\mathbf{4}}\left(\mathrm{aq}\right)\mathbf{+}{\mathbf{\_H}}_{\mathbf{2}}\mathbf{O}\left(l\right)$
   
4. ${\mathbf{\_C}}_{\mathbf{6}}{\mathbf{H}}_{\mathbf{10}}{\mathbf{O}}_{\mathbf{2}}\left(s\right)\mathbf{+}{\mathbf{\_O}}_{\mathbf{2}}\left(g\right)\mathbf{\to }{\mathbf{\_CO}}_{\mathbf{2}}\left(g\right)\mathbf{+}{\mathbf{\_H}}_{\mathbf{2}}\mathbf{O}\left(g\right)$
   

Convert the following into balanced equations:When solutions of calcium chloride and sodium phosphate are mixed, solid calcium phosphate forms and sodium chloride remains in the solution. 

Convert the following into balanced equations:

When nitrogen dioxide is bubbled into water, a solution ofnitric acid forms and gaseous nitrogen monoxide is released.

Loss of atmospheric ozone has led to an ozone "hole" over Antartica. The process occurs in part by three consecutive reactions:

Chlorine monoxide forms ClOOCl  

The circle below represents a mixture of A2 and B2 before they react to form AB3.

How many molecules of product can form?

Percent yields are generally calculated from mass quantities. Would the result be the same if mole quantities were used instead? Why?

Reactants A and B form product C. Write a detailed Plan to find the mass of C when 25 g of A reacts with excess B.

Reactants D and E form product F. Write a detailed Plan to find the mass of F when 27 g of D reacts with 31 g of E.

Chlorine gas can be made in the laboratory by the reaction of hydrochloric acid and manganese(IV):

$\mathbf{4}\mathbf{HCl}\left(\mathrm{aq}\right)\mathbf{+}{\mathbf{MnO}}_{\mathbf{2}}\left(s\right)\mathbf{\to }{\mathbf{MnCl}}_{\mathbf{2}}\left(\mathrm{aq}\right)\mathbf{+}\mathbf{2}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\left(g\right)\mathbf{+}{\mathbf{Cl}}_{\mathbf{2}}\left(g\right)$ 

When 1.82 mol of $\mathbf{HCl}$ reacts with excess ${\mathbf{MnO}}_{\mathbf{2}}$ 

(a) How many moles of ${\mathbf{Cl}}_{\mathbf{2}}$ react?

(b) How many grams of ${\mathbf{Cl}}_{\mathbf{2}}$ form?

What three types of information does a balanced chemical equation provide? How?

How does a balanced chemical equation apply the law of conservation of mass?

The scenes below represent a chemical reaction between elements A (red) and B (green):

Which best represents the balanced equation for the reaction?

$$\begin{gathered} \mathbf{\left(}\mathbf{a}\mathbf{\right)}\mathbf{ }\mathbf{2}\mathbf{A}\mathbf{\to }{\mathbf{A}}_{\mathbf{2}}\mathbf{+}{\mathbf{B}}_{\mathbf{2}} \\ \mathbf{\left(}\mathbf{b}\mathbf{\right)}\mathbf{ }{\mathbf{A}}_{\mathbf{2}}\mathbf{+}{\mathbf{B}}_{\mathbf{2}}\mathbf{\to }\mathbf{2}\mathbf{AB} \\ \mathbf{\left(}\mathbf{c}\mathbf{\right)}\mathbf{ }{\mathbf{B}}_{\mathbf{2}}\mathbf{+}\mathbf{2}\mathbf{AB}\mathbf{\to }\mathbf{2}{\mathbf{B}}_{\mathbf{2}}\mathbf{+}{\mathbf{A}}_{\mathbf{2}} \\ \mathbf{\left(}\mathbf{d}\mathbf{\right)}\mathbf{ }\mathbf{4}{\mathbf{A}}_{\mathbf{2}}\mathbf{+}\mathbf{4}{\mathbf{B}}_{\mathbf{2}}\mathbf{\to }\mathbf{8}\mathbf{AB} \end{gathered}$$

Elemental phosphorus occurs as tetratomic molecules, ${\mathit{P}}_{\mathbf{4}}\mathbf{.}$ What mass of chlorine gas is needed to react completely with 455 g of phosphorus to form phosphorus pentachloride?

Calculate the mass of each product formed when 174 g of silver sulphide reacts with excess hydrochloric acid: 

$\mathit{A}{\mathit{g}}_{\mathbf{2}}\mathit{S}\left(s\right)\mathbf{+}\mathit{H}\mathit{C}\mathit{l}\left(aq\right)\mathbf{\to }\mathit{A}\mathit{g}\mathit{C}\mathit{l}\left(s\right)\mathbf{+}{\mathit{H}}_{\mathbf{2}}\mathit{S}\left(g\right)\left[unbalanced\right]$

Calculate the mass of each product formed when 43.82 g of diborane$\left(B_2{H}_6\right)$reacts with excess water:

${\mathit{B}}_{\mathbf{2}}{\mathit{H}}_{\mathbf{6}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}{\mathit{H}}_{\mathbf{2}}\mathit{O}\mathbf{\left(}\mathbf{I}\mathbf{\right)}\mathbf{\to }{\mathit{H}}_{\mathbf{3}}\mathit{B}{\mathit{O}}_{\mathbf{3}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}{\mathit{H}}_{\mathbf{2}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{\left[}\mathbf{unbalanced}\mathbf{\right]}$

Chromium(III) oxide reacts with hydrogen sulfide $\left(H_{2}S\right)$ gas to form chromium(III) sulfide and water: $\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{3}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{3}{\mathit{H}}_{\mathbf{2}}\mathit{S}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\to }\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{S}}_{\mathbf{3}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{3}{\mathit{H}}_{\mathbf{2}}\mathit{O}\mathbf{\left(}\mathbf{I}\mathbf{\right)}$

To produce 421 g of $\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{S}}_{\mathbf{3}}\mathbf{,}$

(a) How many moles of $\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{3}}$ are required?

(b) How many grams of $\mathit{X}{\mathit{r}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{3}}$ are required?

Potassium nitrate decomposes on heating, producing potassium oxide and gaseous nitrogen and oxygen: 

$\mathbf{4}\mathit{K}\mathit{N}{\mathit{O}}_{\mathbf{3}}\left(s\right)\mathbf{\to }\mathbf{2}{\mathit{K}}_{\mathbf{2}}\mathit{O}\left(s\right)\mathbf{+}\mathbf{2}{\mathit{N}}_{\mathbf{2}}\left(g\right)\mathbf{+}{\mathbf{50}}_{\mathbf{2}}\left(g\right)$

To produce 56.6 kg of oxygen, how many 

(a) Moles of $\mathit{K}\mathit{N}{\mathit{O}}_{\mathbf{3}}$ must be heated?

(b) Grams of $\mathit{K}\mathit{N}{\mathit{O}}_{\mathbf{3}}$ must be heated?

Bismuth oxide reacts with carbon to form bismuth metal: $\mathit{B}{\mathit{i}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{3}}\left(s\right)\mathbf{+}\mathbf{3}\mathit{C}\left(s\right)\mathbf{\to }\mathbf{2}\mathit{B}\mathit{i}\left(s\right)\mathbf{+}\mathbf{3}\mathit{C}{\mathit{O}}_{\mathbf{2}}\left(g\right)$

When 283 g of $\mathit{B}{\mathit{i}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{3}}$ reacts with excess carbon,

(a) How many moles of $\mathit{B}{\mathit{i}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{3}}$ react?

(b) How many moles of $\mathit{B}\mathit{i}$ form?

Elemental sulfur occurs as octatomic molecules, ${\mathit{S}}_{\mathbf{8}}$. What mass of fluorine gas is needed to react completely with 17.8 g of sulfur to form sulfur hexafluoride?

Solid iodine trichloride is prepared in two steps: first, a reaction between solid iodine and gaseous chlorine to form iodine monochloride; then, treatment with more chlorine. 

(a) Write a balanced equation for each step. 

(b) Write a balanced equation for the overall reaction. 

(c) How many grams of iodine are needed to prepare 2.45 kg of the final product?

Lead can be prepared from galena [lead(II) sulfide] by first roasting the galena in oxygen gas to form lead(II) oxide and sulfur dioxide. Heating the metal oxide with more galena forms the molten metal and more sulfur dioxide. (a) Write a balanced equation for each step. 

(b) Write an overall balanced equation for the process. 

(c) How many metric tons of sulfur dioxide form for every metric ton of lead obtained?

Many metals react with oxygen gas to form the metal oxide. For example, calcium reacts as follows: 

$\mathbf{2}\mathbf{Ca}\left(s\right)\mathbf{+}{\mathbf{O}}_{\mathbf{2}}\left(g\right)\mathbf{\to }\mathbf{2}\mathbf{CaO}\left(s\right)$

You wish to calculate the mass of calcium oxide that can be prepared from 4.20 g of  and 2.80 g of ${\mathbf{O}}_{\mathbf{2}}$

(a) How many moles of CaO can be produced from the given mass of Ca ?

(b) How many moles of CaO can be produced from the given mass of ${\mathbf{O}}_{\mathbf{2}}$

(c) Which is the limiting reactant? 

(d) How many grams of CaO can be produced?

Metal hydrides react with water to form hydrogen gas and the metal hydroxide. For example, ${\mathbf{SrH}}_{\mathbf{2}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{2}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{\left(}\mathbf{I}\mathbf{\right)}\mathbf{\to }\mathbf{Sr}{\mathbf{\left(}\mathbf{OH}\mathbf{\right)}}_{\mathbf{2}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{2}{\mathbf{H}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}$ 

You wish to calculate the mass of hydrogen gas that can be prepared from 5.70 g of ${\mathbf{SrH}}_{\mathbf{2}}$ and 4.75 g of ${\mathbf{H}}_{\mathbf{2}}\mathbf{O}$ 

(a) How many moles of ${\mathbf{H}}_{\mathbf{2}}$ can be produced from the given mass of ${\mathbf{SrH}}_{\mathbf{2}}$

(b) How many moles of ${\mathbf{H}}_{\mathbf{2}}$ can be produced from the given mass of ${\mathbf{H}}_{\mathbf{2}}\mathbf{O}$ 

(c) Which is the limiting reactant? 

(d) How many grams of  ${\mathbf{H}}_{\mathbf{2}}$ can be produced?

Calculate the maximum numbers of moles and grams of ${\mathbf{H}}_{\mathbf{2}}\mathbf{S}$ that can form when 158 g of aluminium sulfide reacts with 131 g of water:

${\mathbf{AI}}_{\mathbf{2}}{\mathbf{S}}_{\mathbf{3}}\mathbf{+}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{\to }\mathbf{AI}{\mathbf{\left(}\mathbf{OH}\mathbf{\right)}}_{\mathbf{3}}\mathbf{+}{\mathbf{H}}_{\mathbf{2}}\mathbf{S}\mathbf{\left[}\mathbf{unbalanced}\mathbf{\right]}$

What mass of the excess reactant remains?

When 0.100 mol of carbon is burned in a closed vessel with 8.00 g of oxygen, how many grams of carbon dioxide can form? Which reactant is in excess, and how many grams of it remain after the reaction?

A mixture of 0.0375 g of hydrogen and 0.0185 mol of oxygen in a closed container is sparked to initiate a reaction. How many grams of water can form? Which reactant is in excess, and how many grams of it remain after the reaction?

Calcium nitrate and ammonium fluoride react to form calcium fluoride, dinitrogen monoxide, and water vapor. What mass of each substance is present after 16.8 g of calcium nitrate and 17.50 g of ammonium fluoride react completely?

Two successive reactions,$\mathbf{A}\mathbf{\to }\mathbf{B}$ and $\mathbf{B}\mathbf{\to }\mathbf{C}$ have yields of 73% and 68%, respectively. What is the overall percent yield for conversion of A to C?

What is the percent yield of a reaction in which 45.5 g of tungsten (VI) oxide (WO₃) reacts with excess hydrogen gas to produce metallic tungsten and 9.60 mL of water (d = 1.00 g/mL)?

What is the percent yield of a reaction in which 200. g of phosphorus trichloride reacts with excess water to form 128 g of HCl and aqueous phosphorous acid  $\left(H_3{\mathrm{PO}}_3\right)$ ?

When 20.5 g of methane and 45.0 g of chlorine gas undergo a reaction that has a 75.0% yield, what mass of chloromethane  $\left({\mathrm{CH}}_3\mathrm{Cl}\right)$forms? Hydrogen chloride also forms.

When 56.6 g of calcium and 30.5 g of nitrogen gas undergo a reaction that has a 93.0% yield, what mass of calcium nitride forms?

Cyanogen, ${\left(\mathrm{CN}\right)}_{\mathbf{2}}$ has been observed in the atmosphere of Titan, Saturn’s largest moon, and in the gases of interstellar nebulas. On Earth, it is used as a welding gas and a fumigant. In its reaction with fluorine gas, carbon tetrafluoride and nitrogen trifluoride gases are produced. What mass of carbon tetrafluoride forms when 60.0 g of each reactant is used?

Calculate each of the following quantities: 

(a) Volume in milliliters of 2.26 M potassium hydroxide that contains 8.42 g of solute

(b) Number of Cu2+ ions in 52 L of 2.3 M copper(II) chloride

(c) Molarity of 275 mL of solution containing 135 mmol of glucose

Calculate each of the following quantities:

(a) Grams of solute in 185.8 mL of 0.267 M calcium acetate 

(b) Molarity of 500. mL of solution containing 21.1 g of potassium iodide 

(c) Moles of solute in 145.6 L of 0.850 M sodium cyanide

Are the following instructions for diluting a 10.0 M solution to a 1.00 M solution correct: “Take 100.0 mL of the 10.0 M solution and add 900.0 mL water”? Explain.

An intermediate step in the industrial production of nitric acid involves the reaction of ammonia with oxygen gas to form nitrogen monoxide and water. How many grams of nitrogen monoxide can form by the reaction of 485 g of ammonia with 792 g of oxygen?

Butane gas is compressed and used as a liquid fuel in disposable cigarette lighters and lightweight camping stoves. Suppose a lighter contains 5.50 mL of butane (d =0.579 g/mL). 

(a) How many grams of oxygen are needed to burn the butane completely? 

(b) How many moles of H₂O form when all the butane burns? 

(c) How many total molecules of gas form when the butane burns completely?`

Sodium borohydride $\mathbf{\left(}{\mathbf{NaBH}}_{\mathbf{4}}\mathbf{\right)}$  is used industrially in many organic syntheses. One way to prepare it is by reacting sodium hydride with gaseous diborane  $\left(B_2{H}_6\right)$ Assuming an 88.5% yield, how many grams of  ${\mathbf{NaBH}}_{\mathbf{4}}$ can be prepared by reacting 7.98 g of sodium hydride and 8.16 g of diborane?

A mathematical equation useful for dilution calculations is ${\mathbf{M}}_{\mathbf{dil}}\mathbf{ }\mathbf{\times }{\mathbf{V}}_{\mathbf{dil}}\mathbf{=}{\mathbf{M}}_{\mathbf{conc}}\mathbf{\times }{\mathbf{V}}_{\mathbf{conc}\mathbf{.}}$       

 (a) What does each symbol mean, and why does the equation work? 

(b) Given the volume and molarity of a CaCl₂ solution, how do you determine the number of moles and the mass of solute?