Stoichiometry of Formulas and Equations

Question. In the process of balancing the equation

$\mathbf{Al}\mathbf{+}{\mathbf{Cl}}_{\mathbf{2}}\mathbf{\to }{\mathbf{AlCl}}_{\mathbf{3}}$

Student I writes: $\mathbf{Al}\mathbf{+}{\mathbf{Cl}}_{\mathbf{2}}\mathbf{\to }{\mathbf{AlCl}}_{\mathbf{2}}$

Student II writes: $\mathbf{Al}\mathbf{+}{\mathbf{Cl}}_{\mathbf{2}}\mathbf{+}\mathbf{Cl}\mathbf{\to }{\mathbf{AlCl}}_{\mathbf{3}}$

Student III writes: $\mathbf{2}\mathbf{Al}\mathbf{+}\mathbf{3}{\mathbf{Cl}}_{\mathbf{2}}\mathbf{\to }\mathbf{2}{\mathbf{AlCl}}_{\mathbf{3}}$

Is the approach of Student I valid? Student II? Student III? Explain.

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

1. ${\mathbf{\_As}}_{\mathbf{4}}{\mathbf{S}}_{\mathbf{6}}\left(s\right)\mathbf{+}{\mathbf{\_O}}_{\mathbf{2}}\left(g\right)\mathbf{\to }{\mathbf{\_As}}_{\mathbf{4}}{\mathbf{O}}_{\mathbf{2}}\left(s\right)\mathbf{+}{\mathbf{\_SO}}_{\mathbf{2}}\left(g\right)$
   
2. ${\mathbf{\_Ca}}_{\mathbf{3}}{\left({\mathrm{PO}}_4\right)}_{\mathbf{2}}\left(s\right)\mathbf{+}{\mathbf{\_SiO}}_{\mathbf{2}}\left(s\right)\mathbf{+}\mathbf{\_C}\left(s\right)\mathbf{\to }{\mathbf{\_P}}_{\mathbf{4}}\left(g\right)\mathbf{+}{\mathbf{\_CaSiO}}_{\mathbf{3}}\left(l\right)\mathbf{+}\mathbf{\_CO}\left(g\right)$
3. $\mathbf{\_Fe}\left(s\right)\mathbf{+}{\mathbf{\_H}}_{\mathbf{2}}\mathbf{O}\left(g\right)\mathbf{\to }{\mathbf{\_Fe}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}\left(s\right)\mathbf{+}{\mathbf{\_H}}_{\mathbf{2}}\left(g\right)$
   
4. ${\mathbf{\_S}}_{\mathbf{2}}{\mathbf{Cl}}_{\mathbf{2}}\left(l\right)\mathbf{+}{\mathbf{\_NH}}_{\mathbf{3}}\left(g\right)\mathbf{\to }{\mathbf{\_S}}_{\mathbf{4}}{\mathbf{N}}_{\mathbf{4}}\left(s\right)\mathbf{+}{\mathbf{\_S}}_{\mathbf{8}}\left(s\right)\mathbf{+}{\mathbf{\_NH}}_{\mathbf{4}}\mathbf{Cl}\left(s\right)$
   

What does the term stoichiometrically equivalent ratio mean, and how it is applied in solving problem?

Hydrocarbon mixtures are used as fuels. A252-g gaseous mixture of CH4 and C3H8 burns in excess O2, and 748 g of CO2 gas is collected. What is the mass % of CH4 in the mixture?

Calculate each of the following quantities: (a) Molarity of the solution resulting from dissolving 46.0 g of silver nitrate in enough water to give a final volume of 335 mL (b) Volume in liters of 0.385 M manganese (II) sulfate that contains 63.0 g of solute (c) Volume in milliliters of 6.44×10^-2 M adenosine triphosphate (ATP) that contains 1.68 mmol of ATP.

Calculate each of the following quantities: (a) Molarity of a solution prepared by diluting 37.00 mL of 0.250 M potassium chloride to 150.00 mL (b) Molarity of a solution prepared by diluting 25.71 mL of 0.0706 M ammonium sulfate to 500.00 mL (c) Molarity of sodium ion in a solution made by mixing 3.58 mL of 0.348 M sodium chloride with 500. mL of 6.81×10^-2 M sodium sulfate (assume volumes are additive).

A sample of concentrated nitric acid has a density of 1.41 g/mL and contains 70.0% HNO₃ by mass. (a) What mass of HNO₃ is present per liter of solution? (b) What is the molarity of the solution?

How many milliliters of 0.383 M HCl are needed to react with 16.2 g of CaCO₃?

$\mathbf{2}\mathit{H}\mathit{C}\mathit{l}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{+}\mathit{C}\mathit{a}\mathit{C}{\mathit{O}}_{\mathbf{3}}\mathbf{\left(}\mathit{s}\mathbf{\right)}\mathbf{\to }\mathit{C}\mathit{a}\mathit{C}{\mathit{l}}_{\mathbf{2}}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{+}\mathit{C}{\mathit{O}}_{\mathbf{2}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{+}{\mathit{H}}_{\mathbf{2}}\mathit{O}\mathbf{\left(}\mathit{l}\mathbf{\right)}$

How many grams of solid barium sulfate form when 35.0 mL of 0.160 M barium chloride reacts with 58.0 mL of 0.065 M sodium sulfate? Aqueous sodium chloride forms also.

How many moles of excess reactant are present when 350 mL of 0.210 M sulfuric acid reacts with 0.500 L of 0.196 M sodium hydroxide to form water and aqueous sodium sulfate?

Ordinary household bleach is an aqueous solution of sodium hypochlorite. What is the molarity of a bleach solution that contains 20.5 g of sodium hypochlorite in a total volume of 375 mL?

Muriatic acid, an industrial grade of concentrated HCl, is used to clean masonry and cement. Its concentration is 11.7 M. (a) Write instructions for diluting the concentrated acid to make 3.0 gallons of 3.5 M acid for routine use (1 gal = 4 qt; 1 qt = 0.946 L). (b) How many milliliters of the muriatic acid solution contain 9.66 g of HCl?

A sample of impure magnesium was analyzed by allowing it to react with excess HCl solution: 

$\mathit{M}\mathit{g}\mathbf{\left(}\mathit{s}\mathbf{\right)}\mathbf{+}\mathbf{2}\mathit{H}\mathit{C}\mathit{l}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{\to }\mathit{M}\mathit{g}\mathit{C}{\mathit{l}}_{\mathbf{2}}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{+}{\mathit{H}}_{\mathbf{2}}\mathbf{\left(}\mathit{g}\mathbf{\right)}$

After 1.32 g of the impure metal was treated with 0.100 L of 0.750 M HCl, 0.0125 mol of HCl remained. Assuming the impurities do not react, what is the mass % of Mg in the sample?

One of the compounds used to increase the octane rating of gasoline is toluene (right). Suppose 20.0 mL of toluene (d 0.867 g/mL) is consumed when a sample of gasoline burns in air. (a) How many grams of oxygen are needed for complete combustion of the toluene? (b) How many total moles of gaseous products form? (c) How many molecules of water vapor form?

How many grams of NaH₂PO₄ are needed to react with 43.74 mL of 0.285 M NaOH?

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

3.16 Calculate each of the following quantities:

(a) Mass in grams of 8.35 mol of copper(I) carbonate

(b) Mass in grams of${\text{4.04×10}}^{\text{20}}$ molecules of dinitrogen pentaoxide

(c) Number of moles and formula units in 78.9 g of sodium perchlorate

(d) Number of sodium ions, perchlorate ions, Cl atoms, and O atoms in the mass of the compound in part (c).

3.17 Calculate each of the following quantities:

(a) Mass in grams of 8.42 mol of chromium(III) sulfate decahydrate

(b) Mass in grams of molecules of dichlorineheptaoxide

(c) Number of moles and formula units in 6.2 g of lithium sulfate

(d) Number of lithium ions, sulfate ions, S atoms, and O atoms in the mass of compound in part (c)

Calculate each of the following:

a). Mass % of H in ammonium bicarbonate

b). Mass % of O in sodium dihydrogen phosphate heptahydrate

^{Question: Calculate each of the following:}

^{a. Mass % of I in strontium periodate}

^{b. Mass % of Mn in potassium permanganate}

The atomic mass of $\mathbf{CI}$ is 35.45 amu, and the atomic mass of $\mathbf{AI}$  is 26.98 amu. What are the masses in grams of 3 mol of  $\mathbf{AI}$ atoms and of 2 mol of  $\mathbf{CI}$ atoms?

(a) How many moles of C atoms are in 1 mol of sucrose $\mathbf{\left(}{\mathbf{C}}_{\mathbf{12}}{\mathbf{H}}_{\mathbf{22}}{\mathbf{O}}_{\mathbf{11}}\mathbf{\right)}\mathbf{?}$ (b) How many C atoms are in 2 mol of sucrose?

3.3 why might the expression "1 mol of chlorine" be confusing? What change would remove any uncertainty? For what other elements might a similar confusion exist? Why?

3.4 How is the molecular mass of a compound the same as the molar mass, and how is it different?

3.5 What advantage is there to using a counting unit (the mole) in chemistry rather than a mass unit?

3.6 You need to calculate the number of ${\mathbf{P}}_{\mathbf{4}}$ molecules that can form from 2.5 g of ${\mathbf{Ca}}_{\mathbf{3}}{\left({\mathrm{PO}}_4\right)}_{\mathbf{2}}$ Explain how you would proceed. (That is, write a solution "Plan," without actually doing any calculations.)

3.7 Each of the following balances weighs the indicated numbers of atoms of two elements:

Which element-left, right, or neither,
 (a) Has the higher molar mass?
 (b) Has more atoms per gram?
 (c) Has fewer atoms per gram?
 (d) Has more atoms per mole?

3.8 Calculate the molar mass of each of the following:

                   (a) ${}^{\mathbf{Sr}{\left(\mathrm{OH}\right)}_{\mathbf{2}}}$       (b) ${}^{{\mathbf{N}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}}$        (c) ${}^{{\mathbf{NaCIO}}_{\mathbf{3}}}$       (d)  ${}^{{\mathbf{Cr}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}}$

Calculate the molar mass of each of the following:

(a) ${\left({\mathrm{NH}}_4\right)}_{\mathbf{3}}\mathbf{ }{\mathbf{PO}}_{\mathbf{4}}$      (b)  ${\mathbf{CH}}_{\mathbf{2}}{\mathbf{CI}}_{\mathbf{2}}$      (c)  ${\mathbf{CuSO}}_{\mathbf{4}}\mathbf{.}\mathbf{5}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}$      (d)  ${\mathbf{BrF}}_{\mathbf{3}}$

3.10 Calculate the molar mass of each of the following:

(a)  $\mathbf{SnO}$      (b)  ${\mathbf{BaF}}_{\mathbf{2}}$       (c)   ${\mathbf{AI}}_{\mathbf{2}}{\left({\mathrm{SO}}_4\right)}_{\mathbf{3}}$      (d)   ${\mathbf{MnCI}}_{\mathbf{2}}$

Each of the following balances weighs the indicated numbers of atoms of two elements:

Which element-left, right, or neither,
 (a) Has the higher molar mass?
 (b) Has more atoms per gram?
 (c) Has fewer atoms per gram?
 (d) Has more atoms per mole?

Calculate each of the following quantities:
 (a) Mass in grams of 0.68 mol of  ${\mathbf{KMnO}}_{\mathbf{4}}$
 (b) Moles of O atoms in 8.18 g of $\mathbf{Ba}{\left({\mathrm{NO}}_3\right)}_{\mathbf{2}}$ 
 (c) Number of O atoms in $\mathbf{7}\mathbf{.}\mathbf{3}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{g}$ of ${\mathbf{CaSO}}_{\mathbf{4}\mathbf{ }}\mathbf{2}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}$

3.13 Calculate each of the following quantities:
(a) Mass in kilograms of $\mathbf{4}\mathbf{.}\mathbf{6}\mathbf{\times }{\mathbf{10}}^{\mathbf{21}}$molecules of ${\mathbf{NO}}_{\mathbf{2}}$
(b) Moles of Cl atoms in 0.0615 g of ${\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{4}}{\mathbf{Cl}}_{\mathbf{2}}$
(c) Number of ions in 5.82 g of ${\mathbf{SrH}}_{\mathbf{2}}$

3.14 Calculate each of the following quantities:
 (a) Mass in grams of $\mathbf{6}\mathbf{.}\mathbf{44}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}$mol of ${\mathbf{MnSO}}_{\mathbf{4}}$
 (b) Moles of compounds in 15.8 kg of $\mathbf{Fe}{\left({\mathrm{ClO}}_4\right)}_{\mathbf{3}}$
 (c) Number of N atoms in 92.6 mg of ${\mathbf{NH}}_{\mathbf{4}}{\mathbf{NO}}_{\mathbf{2}}$

3.15 Calculate each of the following quantities:
 (a) Total number of ions in 38.1 g of ${\mathbf{SrF}}_{\mathbf{2}}$
 (b) Mass in kilograms of 3.58 mol of ${\mathbf{CuCl}}_{\mathbf{2}\mathbf{ }}\mathbf{2}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}$
 (c) Mass in milligrams of $\mathbf{2}\mathbf{.}\mathbf{88}\mathbf{\times }{\mathbf{10}}^{\mathbf{22}}$formula unit $\mathbf{Bi}{\mathbf{\left(}{\mathbf{NO}}_{\mathbf{3}}\mathbf{\right)}}_{\mathbf{3}}$$\mathbf{5}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}$.

Calculate each of the following:

1. Mass fraction of C in cesium acetate
2. Mass fraction of O in uranyl sulfate trihydrate $\mathit{U}{\mathit{O}}_{\mathbf{2}}^{\mathbf{2}\mathbf{+}}$

Calculate each of the following:

1. Mass fraction of Cl in calcium chlorate
2. Mass fraction of P in tetraphosphorous hexaoxide

Oxygen is required for the metabolic combustion of foods. Calculate the number of atoms in 38.0 g of oxygen gas, the amount absorbed from the lungs at rest in about 15 min.

Cisplatin(right) or platinol, is used in the treatment of certain cancers. 

Calculate

1. The moles of compound in 285.3 g of cisplatin;
2. The number of hydrogen atoms in 0.98 mol of cisplatin.

Menthol (m = 156.3 g/mol), a strong-smelling substance used in cough drops, is a compound of carbon, hydrogen, and oxygen. When 0.1595 g of menthol was subjected to combustion analysis, it produced 0.449 g of CO2 and 0.184 g of H2O. What is menthol’s molecular formula?

Iron reacts slowly with oxygen and water to form a compound commonly called rust. For 45.2 kg of rust, Calculate

1. The moles of compound
2. The moles of ${\mathbf{Fe}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}$
3. The grams of iron

Propane is widely used in liquid from as a fuel for barbecue grills and camp stoves. For 85.5g of propane, calculate

1. The moles of the compound;
2. The grams of carbon.

The effectiveness of a nitrogen fertilizer is determined mainly by its mass % N. Rank the following fertilizer, most effective first: potassium nitrate; ammonium nitrate; ammonium sulfate; urea,$\mathbf{CO}\left({\mathrm{NH}}_2\right)\mathbf{.}$

The mineral galena is composed of lead(II) sulfide and has an average density of $\mathbf{7}\mathbf{.46}\mathbf{g}\mathbf{/}{\mathbf{cm}}^{\mathbf{3}}$.

1. How many moles of lead(II) sulfide are in $\mathbf{1}\mathbf{.00}{\mathbf{ft}}^{\mathbf{3}}$ of galena?
2. How many lead atoms are in $\mathbf{1}\mathbf{.00}{\mathbf{dm}}^{\mathbf{3}}$ of galena?

Hemoglobin, a protein in red blood cells, carries ${\mathbf{O}}_{\mathbf{2}}$ from the lungs to the body’s cells. Iron(as ferrous ion, ${\mathbf{Fe}}^{\mathbf{2}\mathbf{+}}$) makes up 0.33 mass % of hemoglobin. If the molar mass of hemoglobin is 6.8 g/mol, how many ${\mathbf{Fe}}^{\mathbf{2}\mathbf{+}}$ ions are in one molecule? 

List three ways compositional data may be given in a problem that involves finding an empirical formula.

What is the empirical formula and empirical formula mass for each of the following compounds?

a) ${\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{4}}$

b) ${\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{6}}{\mathbf{O}}_{\mathbf{2}}$

c) ${\mathbf{N}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{5}}$

d) ${\mathbf{Ba}}_{\mathbf{3}}{\mathbf{\left(}{\mathbf{PO}}_{\mathbf{4}}\mathbf{\right)}}_{\mathbf{2}}$

e) ${\mathbf{Te}}_{\mathbf{4}}{\mathbf{I}}_{\mathbf{16}}$

What is the molecular formula for each of the following compounds?

a) Empirical formula ${\mathbf{CH}}_{\mathbf{2}}\left(M_w=42.08g/\mathrm{mol}\right)$

b) Empirical formula ${\mathbf{NH}}_{\mathbf{2}}\left(M_w=32.05g/\mathrm{mol}\right)$

c) Empirical formula ${\mathbf{NO}}_{\mathbf{2}}\left(M_w=92.02g/\mathrm{mol}\right)$

d) Empirical formula$\mathbf{CHN}\left(M_w=135.14g/\mathrm{mol}\right)$

Find the empirical formula of the following compounds:

(a)  0.063 mol of chlorine atoms combined with 0.22 mol of oxygen atoms

(b)  2.45 g of silicon combined with 12.4 g of chlorine

(c)  27.3 mass % carbon and 72.7 mass % oxygen

What is the molecular formula for each of the following compounds?

a) Empirical formula $\mathbf{CH}\mathbf{(}{\mathbf{M}}_{\mathbf{w}}\mathbf{=}\mathbf{78}\mathbf{.11}\mathbf{g}\mathbf{/}\mathbf{mol}\mathbf{)}$

b) Empirical formula ${\mathbf{C}}_{\mathbf{3}}{\mathbf{H}}_{\mathbf{6}}{\mathbf{O}}_{\mathbf{2}}\mathbf{(}{\mathbf{M}}_{\mathbf{w}}\mathbf{=}\mathbf{74}\mathbf{.08}\mathbf{g}\mathbf{/}\mathbf{mol}\mathbf{)}$

c) Empirical formula $\mathbf{HgCl}\mathbf{(}{\mathbf{M}}_{\mathbf{w}}\mathbf{=}\mathbf{472}\mathbf{.10}\mathbf{g}\mathbf{/}\mathbf{mol}\mathbf{)}$

d) Empirical formula${\mathbf{C}}_{\mathbf{7}}{\mathbf{H}}_{\mathbf{4}}{\mathbf{O}}_{\mathbf{2}}\mathbf{(}{\mathbf{M}}_{\mathbf{w}}\mathbf{=}\mathbf{240}\mathbf{.20}\mathbf{g}\mathbf{/}\mathbf{mol}\mathbf{)}$

Find the empirical formula of the following compounds:

(a) 0.039 mol of iron atoms combined with 0.052 mol of oxygen atoms

(b) 0.903 g of phosphorus combined with 6.99 g of bromine

(c) A hydrocarbon with 79.9 mass % carbon