Mass RelationshipsBy

Doba Jackson, Ph.D.

Balancing Chemical Equations

A balanced chemical equation shows that the law of conservation of mass is adhered to.

In a balanced chemical equation, the numbers and kinds of atoms on both sides of the reaction arrow are identical.

2NaCl(s)2Na(s) + Cl2(g)

right side:

2 Na2 Cl

left side:

2 Na2 Cl

Chemical Symbols on a Different Level

2H2O(l)2H2(g) + O2(g)

2 molecules of hydrogen gas react with 1 molecule of oxygen gas to yield 2 molecules of liquid water.

microscopic:

Chemical Symbols on a Different Level

2H2O(l)2H2(g) + O2(g)

0.56 kg of hydrogen gas react with 4.44 kg of oxygen gas to yield 5.00 kg of liquid water.

macroscopic:

2 molecules of hydrogen gas react with 1 molecule of oxygen gas to yield 2 molecules of liquid water.

microscopic:

Chemical Arithmetic: Stoichiometry

How many grams of each reactant is needed and how many grams of the product are expected?

2(12.0 amu) + 4(1.0 amu) = 28.0 amuC2H4:

Chemical Arithmetic: Stoichiometry

HCl: 1.0 amu + 35.5 amu = 36.5 amu

Molecular Mass: Sum of atomic masses of all atoms in a molecule.

Formula Mass: Sum of atomic masses of all atoms in a formula unit of any compound, molecular or ionic.

1 mole = 28.0 gC2H4:

6.022 x 1023 molecules = 28.0 g

Chemical Arithmetic: Stoichiometry

One mole of any substance is equivalent to its molecular or formula mass.

1 mole = 36.5 g

6.022 x 1023 molecules = 36.5 g

HCl:

Chemical Arithmetic: Stoichiometry

How many moles of chlorine gas, Cl2, are in 25.0 g?

25.0 g Cl2

70.9 g Cl2

1 mol Cl2x = 0.353 mol Cl2

Chemical Arithmetic: Stoichiometry

How many grams of sodium hypochlorite, NaOCl, are in 0.705 mol?

0.705 mol NaOCl

1 mol NaOCl

74.5 g NaOClx = 52.5 g NaOCl

Na = 22.99 amuO = 15.99 amuCl = 35.45 amu

Chemical Arithmetic: Stoichiometry

Stoichiometry: The relative proportions in which elements form compounds or in which substances react.

aA + bB cC + dD

Moles ofA

Grams ofA

Moles ofB

Grams ofB

Mole Ratio Between A

and B (Coefficients)

Molar Mass of B

Molar Mass of A

Chemical Arithmetic: Stoichiometry

How many grams of NaOH are needed to react with 25.0 g Cl2?

2NaOH(aq) + Cl2(g) NaOCl(aq) + NaCl(aq) + H2O(l)

Aqueous solutions of sodium hypochlorite (NaOCl), best known as household bleach, are prepared by reaction of sodium hydroxide with chlorine gas:

Moles ofCl2

Grams ofCl2

Moles ofNaOH

Grams ofNaOH

Mole Ratio Molar MassMolar Mass

Chemical Arithmetic: Stoichiometry

How many grams of NaOH are needed to react with 25.0 g Cl2?

2NaOH(aq) + Cl2(g) NaOCl(aq) + NaCl(aq) + H2O(l)

Aqueous solutions of sodium hypochlorite (NaOCl), best known as household bleach, are prepared by reaction of sodium hydroxide with chlorine gas:

1 mol NaOH

40.0 g NaOH25.0 g Cl2

70.9 g Cl2

1 mol Cl2

1 mol Cl2

2 mol NaOH

= 28.2 g NaOH

xx x

Yields of Chemical Reactions

The amount actually formed in a reaction.

The amount predicted by calculations.

Actual Yield:

Theoretical Yield:

Actual yield of product

Theoretical yield of productx 100%Percent Yield =

Reactions with Limiting Amounts of Reactants

Limiting Reactant: The reactant that is present in limiting amount. The extent to which a chemical reaction takes place depends on the limiting reactant.

Excess Reactant: Any of the other reactants still present after determination of the limiting reactant.

C2H4O(aq) + H2O(l) C2H6O2(l)

Reactions with Limiting Amounts of Reactants

At a high temperature, ethylene oxide reacts with water to form ethylene glycol, which is an automobile antifreeze and a starting material in the preparation of polyester polymers:

C2H4O(aq) + H2O(l) C2H6O2(l)

Problem: Reactions with Limiting Amounts of Reactants

Li2O(s) + H2O(g) 2LiOH(s)

Lithium oxide is used aboard the space shuttle to remove water from the air supply according to the equation:

If 80.0 g of water are to be removed and 65.0 g of Li2O are available, which reactant is limiting? How many grams of excess reactant remain? How many grams of LiOH are produced?

Reactions with Limiting Amounts of Reactants

Li2O(s) + H2O(g) 2LiOH(s)

Which reactant is limiting?

65.0 g Li2O

1 mol Li2O

1 mol H2O

29.9 g Li2O

1 mol Li2O

= 4.44 moles H2O80.0 g H2O

18.0 g H2O

1 mol H2O

= 2.17 moles H2O

Amount of H2O given:

Amount of H2O that will react with 65.0 g Li2O:

Li2O is limiting

x

x

x

Reactions with Limiting Amounts of Reactants

Li2O(s) + H2O(g) 2LiOH(s)

80.0 g H2O - 39.1 g H2O = 40.9 g H2O

2.17 mol H2O

1 mol H2O

18.0 g H2O= 39.1 g H2O (consumed)

How many grams of excess H2O remain?

remaininginitial consumed

x

Reactions with Limiting Amounts of Reactants

Li2O(s) + H2O(g) 2LiOH(s)

2.17 mol H2O

1 mol LiOH

23.9 g LiOH= 104 g LiOH

How many grams of LiOH are produced?

1 mol H2O

2 mol LiOHxx

Concentrations of Reactants in Solution: Molarity

Molarity (M): The number of moles of a substance dissolved in each liter of solution. In practice, a solution of known molarity is prepared by weighing an appropriate amount of solute, placing it in a container called a volumetric flask, and adding enough solvent until an accurately calibrated final volume is reached.

Solution: A homogeneous mixture.

Solute: The dissolved substance in a solution.

Solvent: The major component in a solution.

Concentrations of Reactants in Solution: Molarity

Molarity converts between mole of solute and liters of solution:

Molarity =Moles of solute

Liters of solution

L

molor 1.00 M

1.00 L

1.00 mol= 1.00

1.00 mol of sodium chloride placed in enough water to make 1.00 L of solution would have a concentration equal to:

Concentrations of Reactants in Solution: Molarity

Molar mass C6H12O6 = 180.0 g/mol

How many grams of solute would you use to prepare 1.50 L of 0.250 M glucose, C6H12O6?

1 mol

0.275 mol 180.0 g= 49.5 g

1 L

1.50 L 0.250 mol= 0.275 mol

x

x

Diluting Concentrated Solutions

dilute solutionconcentrated solution + solvent

Since the number of moles of solute remains constant, all that changes is the volume of solution by adding more solvent.

Mi x Vi = Mf x Vf

finalinitial

Diluting Concentrated Solutions

Add 6.94 mL 18.0 M sulfuric acid to enough water to make 250.0 mL of 0.500 M solution.

Mi = 18.0 M Mf = 0.500 M

Vi = ? mL Vf = 250.0 mL

= 6.94 mL18.0 M

250.0 mLVi =

Vf 0.500 M=

Sulfuric acid is normally purchased at a concentration of 18.0 M. How would you prepare 250.0 mL of 0.500 M aqueous H2SO4?

xMi

Mfx

Solution Stoichiometry

aA + bB cC + dD

Moles ofA

Volume ofSolution of A

Moles ofB

Volume ofSolution of B

Mole Ratio Between A

and B (Coefficients)

Molar Mass of B

Molarity of A

Solution Stoichiometry

H2SO4(aq) + 2NaOH(aq) Na2SO4(aq) + 2H2O(l)

What volume of 0.250 M H2SO4 is needed to react with 50.0 mL of 0.100 M NaOH?

Moles ofH2SO4

Volume ofSolution of H2SO4

Moles ofNaOH

Volume ofSolution of NaOH

Mole Ratio Between H2SO4

and NaOH

Molarity of NaOH

Molarity of H2SO4

Solution Stoichiometry

H2SO4(aq) + 2NaOH(aq) Na2SO4(aq) + 2H2O(l)

2 mol NaOH

1 mol H2SO4

0.250 mol H2SO4

1 L solution

1 L

0.100 mol

1 L

1000 mL

= 0.00500 mol NaOH

Volume of H2SO4 needed:

1000 mL

1 L

10.0 mL solution (0.250 M H2SO4)

0.00500 mol NaOH

50.0 mL NaOH

Moles of NaOH available:

x

x

x

x x

Titration

How can you tell when the reaction is complete?

HCl(aq) + NaOH(aq) NaCl(aq) + 2H2O(l)

Titration: A procedure for determining the concentration of a solution by allowing a carefully measured volume to react with a solution of another substance (the standard solution) whose concentration is known.

Once the reaction is complete you can calculate the concentration of the unknown solution.

Titration

unknown concentration solutionErlenmeyerflask

buret standard solution(known concentration)

An indicator is added which changes color once the reaction is complete

Titration

HCl(aq) + NaOH(aq) NaCl(aq) + 2H2O(l)

48.6 mL of a 0.100 M NaOH solution is needed to react with 20.0 mL of an unknown HCl concentration. What is the concentration of the HCl solution?

Moles ofNaOH

Volume ofSolution of NaOH

Moles ofHCl

Volume ofSolution of HCl

Mole Ratio Between NaOH

and HCl

Molarity of HCl

Molarity of NaOH

Titration

HCl(aq) + NaOH(aq) NaCl(aq) + 2H2O(l)

20.0 mL solution

0.00486 mol HCl= 0.243 M HCl

Concentration of HCl solution:

Moles of NaOH available:

1 L

0.100 mol= 0.00486 mol NaOH

48.6 mL NaOH

1000 mL

1 L

Moles of HCl reacted:

1 mol NaOH

1 mol HCl= 0.00486 mol HCl

0.00486 mol NaOH

1 L

1000 mL

x

x

x

x

Problem: What is the molecular mass of table sugar (sucrose, C12H22O11), and what is its molar mass in g/mol?

Problem: How many moles of sucrose are in a tablespoon of

sugar containing 2.85 g?

Problem: How many grams are in 0.0626 mol of NaHCO3, the main ingredient of Alka-Seltzer tablets?

Problem: Aqueous solutions of sodium hypochlorite (NaOCl, household bleach) are prepared by reaction of sodium hydroxide with chlorine. How many grams of NaOH are needed to react with 25.0 g of Cl2?

Problem: Cisplatin, an anticancer agent used for the treatment of solid tumors, is prepared by the reaction of ammonia with potassium tetrachloroplatinate. Assume that 10.0 g of K2PtCl4 and 10.0 g of NH3 are allowed to react.   

(a) Which reactant is limiting, and which is in excess?(b) How many grams of the excess reactant are consumed, and how many grams remain?(c) How many grams of cisplatin are formed?