1. Sample Problem 7.1 Number of Atoms in Balanced Chemical Equations
Indicate the number of each type of atom in the following balanced chemical equation:
Fe2S3(s) + 6HCl(aq) → 2FeCl3(aq) + 3H2S(g)
Solution
The total number of atoms in each formula is obtained by multiplying the coefficient by each subscript in a chemical formula.

2. Sample Problem 7.1 Number of Atoms in Balanced Chemical Equations
Continued
Study Check 7.1
When ethane, C2H6, burns in oxygen, the products are carbon dioxide and water. The balanced chemical equation is written as Δ
2C2H6(g) + 7O2(g) → 4CO2(g) + 6H2O(g)
Calculate the number of each type of atom in the reactants and in the products.
Answer
In both the reactants and products, there are 4 C atoms, 12 H atoms, and 14 O atoms.

3. Sample Problem 7.2 Balancing a Chemical Equation
The chemical reaction of methane, CH4, and oxygen gas, O2, produces carbon dioxide (CO2) and water (H2O). Write a balanced chemical equation for this reaction.
Solution
Step 1 Write an equation using the correct formulas for the reactants and products. Δ
CH4(g) + O2(g) → CO2(g) + H2O(g)

4. Sample Problem 7.2 Balancing a Chemical Equation
Continued
Step 2 Count the atoms of each element in the reactants and products. When we compare the atoms on the reactant side and the atoms on the product side, we see that there are more H atoms in the reactants and more O atoms in the products.
Step 3 Use coefficients to balance each element. We will start by balancing the H atoms in CH4 because it has the most atoms. By placing a coefficient of 2 in front of the formula for H2O, a total of 4 H atoms in the products is obtained. Only use coefficients to balance an equation. Do not change any of the subscripts: This would alter the chemical formula of a reactant or product.

5. Sample Problem 7.2 Balancing a Chemical Equation
Continued
We can balance the O atoms on the reactant side by placing a coefficient of 2 in front of the formula O2. There are now 4 O atoms in both the reactants and products.
Step 4 Check the final equation to confirm it is balanced. In the final equation, the numbers of atoms of C, H, and O are the same in both the reactants and the products. The equation is balanced.

6. Sample Problem 7.2 Balancing a Chemical Equation
Continued
In a balanced chemical equation, the coefficients must be the lowest possible whole numbers. Suppose you had obtained the following for the balanced equation:
Although there are equal numbers of atoms on both sides of the equation, this is not written correctly. To obtain coefficients that are the lowest whole numbers, we divide all the coefficients by 2.
Study Check 7.2
Balance the following chemical equation:
Al(s) + Cl2(g) → AlCl3(s)
Answer
2Al(s) + 3Cl2(g) → 2AlCl3(s)

7. Sample Problem 7.3 Balancing Chemical Equations with Polyatomic Ions
Balance the following chemical equation:
Na3PO4(aq) + MgCl2(aq)2 → Mg3(PO4)2(s) + NaCl(aq)
Solution
Step 1 Write an equation using the correct formulas for the reactants and products.
Na3PO4(aq) + MgCl2(aq) → Mg3(PO4)2(s) + NaCl(aq) Unbalanced
Step 2 Count the atoms of each element in the reactants and products. When we compare the number of ions in the reactants and products, we find that the equation is not balanced. In this equation, we can balance the phosphate ion as a group of atoms because it appears on both sides of the equation.

8. Sample Problem 7.3 Balancing Chemical Equations with Polyatomic Ions
Continued
Na3PO4(aq) + MgCl2(aq) → Mg3(PO4)2(s) + NaCl(aq)
Step 3 Use coefficients to balance each element. We begin with the formula that has the highest subscript values, which in this equation is Mg3(PO4)2. The subscript 3 in Mg3(PO4)2 is used as a coefficient for MgCl2 to balance magnesium. The subscript 2 in Mg3(PO4)2 is used as a coefficient for Na3PO4 to balance the phosphate ion.
2Na3PO4(aq) + 3MgCl2(aq) → Mg3(PO4)2(s) + NaCl(aq)

9. Sample Problem 7.3 Balancing Chemical Equations with Polyatomic Ions
Continued
In the reactants and products, we see that the sodium and chloride ions are not yet balanced. A coefficient of 6 is placed in front of the NaCl to balance the equation.
2Na3PO4(aq) + 3MgCl2(aq) → Mg3(PO4)2(s) + 6NaCl(aq)
Step 4 Check the final equation to confirm it is balanced. A check of the total number of ions confirms the equation is balanced. A coefficient of 1 is understood and not usually written.
2Na3PO4(aq) + 3MgCl2(aq) → Mg3(PO4)2(s) + 6NaCl(aq) Balanced

10. Sample Problem 7.3 Balancing Chemical Equations with Polyatomic Ions
Continued
Study Check 7.3
Balance the following chemical equation:
Pb(NO3)2(aq) + AlBr3(aq) → PbBr2(s) + Al(NO3)3(aq)
Answer
3Pb(NO3)2(aq) + 2AlBr3(aq) → 3PbBr2(s) + 2Al(NO3)3(aq)

11. Sample Problem 7.4 Identifying Reactions and Predicting Products
Classify each of the following as a combination, decomposition, single replacement,
double replacement, or combustion reaction:
a. 2Fe2O3(s)+ 3C(s) → 3CO2(g) + 4Fe(s) Δ
b. 2KClO3(s) → 2KCl(s) + 3O2(g)
c. C2H4(g) + 3O2(g) → 2CO2(g) + 2H2O(g) + energy
Solution
a. In this single replacement reaction, a C atom replaces Fe in Fe2O3 to form the compound CO2 and Fe atoms.
b. When one reactant breaks down to produce two products, the reaction is decomposition.
c. The reaction of a carbon compound with oxygen to produce carbon dioxide, water, and energy makes this a combustion reaction.
Study Check 7.4
Nitrogen gas (N2) and oxygen gas (O2) react to form nitrogen dioxide gas. Write the balanced chemical equation using the correct chemical formulas of the reactants and product, and identify the reaction type.
Answer
N2(g) + 2O2(g) → 2NO2(g) combination

12. Sample Problem 7.5 Calculating the Number of Molecules
How many molecules are present in 1.75 moles of carbon dioxide, CO2?
The solid form of carbon dioxide is known as “dry ice.”
Solution
Step 1 State the given and needed quantities.
Step 2 Write a plan to convert moles to atoms or molecules.

13. Sample Problem 7.5 Calculating the Number of Molecules
Continued
Step 3 Use Avogadro’s number to write conversion factors.
Step 4 Set up the problem to calculate the number of particles.
Study Check 7.5
How many moles of water, H2O, contain 2.60 × 1023 molecules of water?
Answer
0.432 mole of H2O

14. Sample Problem 7.6 Calculating the Moles of an Element in a Compound
Propyl acetate, C5H10O2, gives the odor and taste to pears. How many moles of C are present in 1.50 moles of propyl acetate?
Solution
Step 1 State the given and needed quantities.
Step 2 Write a plan to convert moles of compound to moles of an element.
Step 3 Write equalities and conversion factors using subscripts.

15. Sample Problem 7.6 Calculating the Moles of an Element in a Compound
Continued
Step 4 Set up the problem to calculate the moles of an element.
Study Check 7.6
How many moles of propyl acetate, C5H10O2, contain mole of O?
Answer
0.240 mole of propyl acetate

16. Sample Problem 7.7 Calculating the Molar Mass for a Compound
Calculate the molar mass for lithium carbonate, Li2CO3, used to treat bipolar disorder.
Solution
Step 1 Obtain the molar mass of each element.
Step 2 Multiply each molar mass by the number of moles (subscript) in the formula.
Grams from 2 moles of Li:
Grams from 1 mole of C:

17. Sample Problem 7.7 Calculating the Molar Mass for a Compound
Continued
Grams from 3 moles of O:
Step 3 Calculate the molar mass by adding the masses of the elements.
2 moles of Li = g of Li
1 mole of C = g of C
3 moles of O = g of O
Molar mass of Li2CO3 = g
Study Check 7.7
Calculate the molar mass for salicylic acid, C7H6O3, used to treat skin conditions such as acne, psoriasis, and dandruff.
Answer g

18. Sample Problem 7.8 Converting Moles of an Element to Grams
Silver metal is used in the manufacture of tableware, mirrors, jewelry, and dental alloys. If the design for a piece of jewelry requires mole of silver, how many grams of silver are needed?
Solution
Step 1 State the given and needed quantities.
Step 2 Write a plan to convert moles to grams.
Step 3 Determine the molar mass and write conversion factors.

19. Sample Problem 7.8 Converting Moles of an Element to Grams
Continued
Step 4 Set up the problem to convert moles to grams. Calculate the grams of silver using the molar mass factor that cancels mole Ag.
Study Check 7.8
A dentist orders gold to prepare dental crowns and fillings. Calculate the number of grams of gold (Au) present in mole of gold.
Answer
24.4 g of Au

20. Sample Problem 7.9 Converting the Mass of a Compound to Moles
A box of salt contains 737 g of NaCl. How many moles of NaCl are present?
Solution
Step 1 State the given and needed quantities.
Step 2 Write a plan to convert grams to moles.
Step 3 Determine the molar mass and write conversion factors.
(1 × 22.99) + (1 × 35.45) = g/mole

21. Sample Problem 7.9 Converting the Mass of a Compound to Moles
Continued
Step 4 Set up the problem to convert grams to moles.
Study Check 7.9
One tablet of an antacid contains 680. mg of CaCO3. How many moles of CaCO3 are present?
Answer
mole of CaCO3

22. Sample Problem 7.10 Calculating Moles of a Reactant
In the chemical reaction of iron and sulfur, how many moles of sulfur are needed to react with 1.42 moles of iron?
2Fe(s) + 3S(s) → Fe2S3(s)
Solution
Step 1 State the given and needed quantities (moles).
Step 2 Write a plan to convert the given to the needed quantity (moles).
Step 3 Use coefficients to write mole–mole factors.

23. Sample Problem 7.10 Calculating Moles of a Reactant
Continued
Step 4 Set up the problem to give the needed quantity (moles).
Study Check 7.10
Using the equation in Sample Problem 7.10, calculate the number of moles of iron needed to react with 2.75 moles of sulfur.
Answer
1.83 moles of iron

24. Sample Problem 7.11 Mass of Product
When acetylene, C2H2, burns in oxygen, high temperatures are produced that are used for welding metals. Δ
2C2H2(g) + 5O2(g) → 4CO2(g) + 2H2O(g)
How many grams of CO2 are produced when 54.6 g of C2H2 is burned?
Solution
Step 1 State the given and needed quantities (grams).
Step 2 Write a plan to convert the given to the needed quantity (grams).

25. Sample Problem 7.11 Mass of Product
Continued
Step 3 Use coefficients to write mole–mole factors; write molar mass factors if needed.
Step 4 Set up the problem to give the needed quantity (grams).

26. Sample Problem 7.11 Mass of Product
Continued
Study Check 7.11
Using the equation in Sample Problem 7.11, calculate the grams of CO2 that can be produced when 25.0 g of O2 reacts.
Answer
27.5 g of CO2

27. Sample Problem 7.12 Moles of Product from Limiting Reactant
The chemical reaction of carbon monoxide and hydrogen is used to produce methanol, CH3OH.
CO(g) + 2H2(g) → CH3OH(g)
If 3.00 moles of CO and 5.00 moles of H2 are the initial reactants, what is the limiting reactant and how many moles of methanol can be produced?
Solution
Step 1 State the given and needed moles.
Step 2 Write a plan to convert the moles of each reactant to moles of product.

28. Sample Problem 7.12 Moles of Product from Limiting Reactant
Continued
Step 3 Write the mole–mole factors from the equation.
Step 4 Calculate the number of moles of product from each reactant and select the smaller number of moles as the amount of product from the limiting reactant.
Moles of CH3OH (product) from CO:

29. Sample Problem 7.12 Moles of Product from Limiting Reactant
Continued
Moles of CH3OH (product) from H2:
The smaller amount, 2.50 moles of CH3OH, is the maximum amount of methanol that can be produced from the limiting reactant, H2, when it is completely consumed.
Study Check 7.12
If the initial mixture of reactants for Sample Problem 7.12 contains 4.00 moles of CO and 4.00 moles of H2, what is the limiting reactant and how many moles of methanol can be produced?
Answer
H2 is the limiting reactant; 2.00 moles of methanol can be produced.

30. Sample Problem 7.13 Mass of Product from a Limiting Reactant
When silicon dioxide (sand) and carbon are heated, the products are silicon carbide, SiC, and carbon monoxide. Silicon carbide is a ceramic material that tolerates extreme temperatures and is used as an abrasive and in the brake discs of sports cars. How many grams of CO are formed from 70.0 g of SiO2 and 50.0 g of C?
Heat
SiO2(s) + 3C(s) → SiC(s) + 2CO(g)
Solution
Step 1 State the given and needed grams.
Step 2 Write a plan to convert the grams of each reactant to grams of product.

31. Sample Problem 7.13 Mass of Product from a Limiting Reactant
Continued
Step 3 Write the molar mass factors and mole–mole factors from the equation.
Molar mass factors:
Mole–mole factors:

32. Sample Problem 7.13 Mass of Product from a Limiting Reactant
Continued
Step 4 Calculate the number of grams of product from each reactant and select the smaller number of grams as the amount of product from the limiting reactant.
Grams of CO (product) from SiO2:
Grams of CO (product) from C:
The smaller amount, 65.3 g of CO, is the most CO that can be produced.

33. Sample Problem 7.13 Mass of Product from a Limiting Reactant
Continued
Study Check 7.13
Hydrogen sulfide burns with oxygen to give sulfur dioxide and water. How many grams of sulfur dioxide are formed from the reaction of 8.52 g of H2S and 9.60 g of O2? Δ
2H2S(g) + 3O2(g) → 2SO2(g) + 2H2O(g)
Answer
12.8 g of SO2

34. Sample Problem 7.14 Calculating Percent Yield
On a space shuttle, LiOH is used to absorb exhaled CO2 from breathing air to form LiHCO3.
LiOH(s) + CO2(g) → LiHCO3(s)
What is the percent yield of LiHCO3 for the reaction if 50.0 g of LiOH gives 72.8 g of LiHCO3?
Solution
Step 1 State the given and needed quantities.
Step 2 Write a plan to calculate the theoretical yield and the percent yield.
Calculation of theoretical yield:

35. Sample Problem 7.14 Calculating Percent Yield
Continued
Calculation of percent yield:
Step 3 Write the molar mass factors and the mole–mole factor from the balanced equation.
Molar mass factors:
Mole–mole factors:

36. Sample Problem 7.14 Calculating Percent Yield
Continued
Step 4 Calculate the percent yield by dividing the actual yield 1given2 by the theoretical yield and multiplying the result by 100%.
Calculation of theoretical yield:
Calculation of percent yield:
A percent yield of 51.3% means that 72.8 g of the theoretical amount of 142 g of LiHCO3 was actually produced by the reaction.
Study Check 7.14
For the reaction in Sample Problem 7.14, what is the percent yield of LiHCO3 if 8.00 g of CO2 produces 10.5 g of LiHCO3?
Answer
84.7%

37. Sample Problem 7.15 Calculating Heat in a Reaction
How much heat, in kilojoules, is released when nitrogen and hydrogen react to form 50.0 g of ammonia?
N2(g) + 3H2(g) → 2NH3(g) ΔH = –92.2 kJ
Solution
Step 1 State the given and needed quantities.
Step 2 Write a plan using the heat of reaction and any molar mass needed.
Step 3 Write the conversion factors including heat of reaction.

38. Sample Problem 7.15 Calculating Heat in a Reaction
Continued
Step 4 Set up the problem to calculate the heat.
Study Check 7.15
Mercury(II) oxide decomposes to mercury and oxygen.
2HgO(s) → 2Hg(l) + O2(g) ΔH = +182 kJ
a. Is the reaction exothermic or endothermic?
b. How many kilojoules are needed to react 25.0 g of mercury(II) oxide?
Answer
a. endothermic b kJ