Chemical Formulas

Methane

CH4

MOLECULAR FORMULAS: representation of molecules in terms of their constituent atoms -– H2, H2O

DIATOMIC - two atoms; example: H2, N2, CO (carbon monoxide)

TRIATOMIC - three atoms; example: CO2 (carbon dioxide), O3(ozone)

POLYATOMIC - more than three atoms; examples: NH3 (ammonia), CH4 (methane), C2H6O2 (ethylene glycol)

What limits the “boundary” of a molecule?

Atoms in molecules are held together by strong interactions called CHEMICAL BONDS

Interactions between neutral atoms in a molecule (e.g. H2, H2O) is called a COVALENT bond, forming covalent compounds

Interactions between charged elements (IONS) result in a different kind of chemical bond, called an IONIC BOND

Compounds formed via interactions between ionic (charged) elements are called ionic compounds.

In a crystal of NaCl a Na+ ion interacts with the neighboring Cl- ion, hence a NaCl “molecule” does not exist.

However, if one counted the number of sodium ions and the number of Cl- ions in a given volume we would find that the ratio of Na+ : Cl- is 1:1.

A crystal of sodium chloride is electrically neutral and its CHEMICAL FORMULA can be expressed as NaCl.

Chemical formulas indicate the constituent elements in a compound (covalent or ionic)

The term molecular formula refers specifically to covalent compounds.

How are chemical formulas determined?

ELEMENTAL ANALYSIS

Determination of the relative amounts of the elements in a compound

Determines the EMPIRICAL FORMULA which is the simplest possible formula and indicates the relative amounts of constituent elements

For example, the molecular formula of hydrogen peroxide is H2O2; its empirical formula is HO.

The empirical and the chemical formula can be the same, for example, H2O.

For ionic compounds, the empirical formula is the same as the chemical formula (NaCl)

Problem

An oxide of nitrogen is analyzed and found to contain 25.9% N and 74.1% O. What is the empirical formula of the compound?

In 100.0 g of compound:

# moles of N = 25.9 g N / (14.01 g/mol) = 1.85 mol

# moles of O = 74.1 g O / (16.00 g/mol) = 4.63 mol

Ratio of O: N :: 2.5:1

Must be whole numbers – N2O5

Combustion Analysis - elemental analysis of organic compounds.

Organic compounds contain predominantly C and H.

Minor elements include O, N, S, Cl, P, etc.

In combustion analysis the organic compound is burnt in the presence of oxygen (O2) to form carbon dioxide (CO2), water (H2O) and other gases (nitrogen (N2), sulfur dioxide (SO2))

A sample of a compound that is known to contain only carbon, hydrogen, and oxygen is combusted, and the CO2 and H2O produced are trapped and weighed. The original sample weighed 8.38 g and yielded 16.0 g CO2 and 9.5 g H2O. What is the empirical formula?

Need to determine the number of moles of C and H in the compound, and then determine the mass of O in the compound.

Moles of C =

(16.0 g CO2 / 44.0 g/mol CO2) x (1 mol C/1 mol CO2)

= 0.364 mol C

Moles of H =

(9.80 g H2O / 18.0 g/mol H2O) x (2 mol H / 1 mol H2O)

= 1.09 mol H

Mass of C in compound = 0.364 mol C x 12.0 g/mol C

= 4.37 g C

Mass of H in compound = 1.09 mol H x 1.01 g/ mol H

= 1.10 g H

Mass of O in compound = 8.38 g - 4.37 g - 1.10 g = 2.91 g O

Moles of O in compound = (2.91 g O / 16.0 g/mol O)

= 0.182 mol O

Mole ratio of C : H : O is 0.364 : 1.09 : 0.182 or 2:6:1

Hence empirical formula is C2H6O

Determining Chemical Formulas

The empirical formula tells you the simplest ratio of the individual elements in the compound.

For an ionic compound this information is enough.

For a molecular compound this may not be enough since the empirical formula may not be the molecular formula.

Knowledge of the MOLAR MASS of the compound and its empirical formula, allows the molecular formula to be determined.

Elemental analysis of a sugar shows that it consists of 40.0% carbon (C), 6.7% hydrogen (H), 53.3% oxygen (O). The molar mass of the compound was found to be 180.0 g/mol. What is the molecular formula of the compound?

moles of C in 100.0 g of compound = (mass of C g)/(atomic mass g/mol) = 40.0/12.01 = 3.33 mol C in 100.0 g of compound

moles of H in 100.0 g of compound = (mass of H g)/(atomic mass g/mol)= 6.7/1.01 = 6.7 mol H in 100.0 g of compound

moles of O in 100.0 g of compound = (mass of O g)/(atomic mass g/mol)= 53.3/16.00 = 3.33 mol O in 100.0 g of compound

Ratio of C:H:O :: 1:2:1; hence empirical formula is CH2O

Molar mass of empirical formula = 12.01 + 2(1.01) + 16.00 = 30.0 g/mol

Ratio of molar mass of compound : molar mass of empirical formula

180.0/30.0 = 6.0

molecular formula is (CH2O) 6 or C6H12O6

Chemical Reactions & Equations

In a chemical reaction elements and/or compounds collide, interact and react to form new compounds.

The compounds that come together are called the REACTANTS and the new compounds formed are the PRODUCTS.

An important aspect of a chemical reaction is that MASS IS ALWAYS CONSERVED - i.e. the total mass of the reactants must equal the total mass of the products.

To ensure that mass is conserved, we have to keep track of the number of atoms of each element in the reactants and number of atoms of each element in the products

Writing Chemical Equations

reactantsH2 + O2 H2O

products

Mass has not been conserved - equation is not BALANCED

Need to make sure that the number of atoms of a given element is the same on either side.

H2 + O2 H2O

H is balanced, but O is not.

To balance O, multiply H2O by 2

H2 + O2 2 H2O

Now O is balanced but not H (4 H’s on right, 2 on left)

Multiply H2 by 2

2H2 + O2 2 H2O

Now the equation is balanced.

However, for a complete chemical equation the state of all reactants and products must be included

2H2 + O2 2 H2O

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

g - gas; l - liquid; s- solid

aq - denotes a solution of a solute in water (solvent)

Note: the subscripts in the molecular formula must never be changed in balancing equations. Changing the subscript corresponds to a different molecular formula, hence a different molecule, with completely different properties

“Rules” to balance chemical equations

Consider the reaction of methane, CH4, burning in air to produce CO2 and H2O (combustion reaction)

CH4 + O2 CO2 + H2O

It is usually best to first balance those elements that occur in the fewest chemical formulas on each side of the equation.

So in this example balance C and H first

C is already balanced. However 4 H’s on the left and 2 on the right

Hence,

CH4 + O2 CO2 + 2H2O

Now balance O

CH4 + 2O2 CO2 + 2H2O

Now specify the state of each reactant and product

CH4(g) + 2O2(g) CO2(g) + 2H2O(g)

Ag2S(s) + KCN(aq) + O2(g) + H2O(l)

KAg(CN)2(aq) + S(s) + KOH(aq)

Sometimes it is hard to balance a chemical reaction by “inspection”

Can the use algebraic expressions to balance equations

a Ag2S(s) + b KCN(aq) + c O2(g) + d H2O(l)

1 KAg(CN)2(aq) + e S(s) + f KOH(aq)

Element Reactant Product

Ag 2 a 1

S a e

K b 1 + f

C b 2

N b 2

O 2c + d f

H 2d f

2 a = 1 ; a = 0.5

b = 2

a = e ; e = 0.5

b = 1 + f; f = 1

2d = f; d = 0.5

2c + d = f; c = 0.25

Divide all by 0.25

a = 2; b = 8; c = 1; d = 2; e = 2; f = 4

Hence

2 Ag2S(s) + 8 KCN(aq) + O2(g) + 2 H2O(l)

4 KAg(CN)2(aq) + 2 S(s) + 4 KOH(aq)

Chemical Stoichiometry

Reactants are consumed and products are formed in definite proportions.

These proportions are given by the coefficients in the balanced equations for chemical reactions

The calculation of the quantities of reactants and products is called STOICHIOMETRY.

Stoichiometry is the use of chemical equations to calculate quantities of substances that take part in chemical reactions.

To do a stoichiometric calculation, the chemical equation for the calculation must be balanced.

Equations are read in terms of moles of reactants and product

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

2 moles of H2 (g) reacts with 1 mole of O2 (g) to form 2 moles of H2O(g)

Or:

2No molecules of H2 (g) + No molecules of O2 (g) 2No molecules of H2O(g)

Problem

Consider the reaction of 100 g of H2(g) with sufficient O2 (g) to produce the stoichiometric quantity of H2O(g). (stoichiometric quantities are the exact amounts of reactants and products predicted by balanced equations). Calculate the mass of H2O formed.

Need a balanced equation for this reaction

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

(mass of H2) = (100.g H2)/(2.02 g/mol) = 49.5 mol H2

(molar mass of H2)

To find the mass of water formed, need to find the number of moles of H2 that reacted:

2 moles of H2 reacts with 1 mole of O2 to form 2 moles of H2O

=> 49.5 moles of H2 will form 49.5 moles of H2O

Hence, the mass of H2O(g) formed

=(49.5 moles H2O) x (18.02 g/mol) = 892 g H2O

Problem: Diethyl ether (C4H10O) combusts in air, reacting with O2 to form H2O and CO2. How many grams of CO2 would be produced if 350.0 mL of diethyl ether were combusted in an unlimited amount of oxygen? The density of diethyl ether is 0.713 g/mL.

First write a balanced equation

?C4H10O(l) + ?O2(g) ?H2O(l) + ?CO2(g)

Then convert the volume of diethyl ether to mass

Next, determine the number of moles of diethyl ether reacted

Determine the number of moles of CO2 formed based on the stoichiometry of the reaction

Finally determine the mass of CO2 produced

Answer: 592 g CO2

For reactions occurring in solution, instead of using moles as a unit of quantity, define moles/liter = MOLARITY

Molarity is defined as the number of moles of a solute per liter of solution.

Note: the solute can be a solid, liquid, or gas dissolved in a solvent.

Problem

For the reaction:

2 PbO2(s) + 4 HNO3(aq) 2 PbNO3(aq) + 2 H2O (l) + O2(g)

What volume of 7.91M solution of nitric acid, HNO3, is just sufficient to react with 15.9 g of lead dioxide, PbO2?

Answer: 0.0168 L

Volume Relationship of Gases in Chemical Reactions

Gay Lussac’s law of combining volumes – states that the volumes of gaseous reactants and products stand in ratios of simple integers, as long as those volumes are measured at the SAME temperature and pressure.

These integers are the same as the integers used to balance the chemical equation.

A balanced chemical equation therefore provides a relationship between the volumes of gases reacting.

Problem:

Gaseous H2 and N2 react according to the equation

3H2 (g) + N2 (g) 2 NH3(g)

If in a given reaction 5.00 L of NH3 are formed, what volume of H2 reacted, assuming that the temperature and pressure before and after the reaction are the same.

From the balanced reaction above, assuming the same temperature and pressure before and after the reaction, 2 volumes of NH3 are formed from 3 volumes of H2

Hence, 5.00 L of NH3 are formed from (3/2)x5.00 L = 7.5 L of H2

If everything went perfectly in the reaction : Fe(s) + S (s) FeS (s)

55.8 g (1 mole) of iron will react with 32.1 g (1 mole) of S to form 87.9 g (1 mole) of FeS.

If stoichiometric amounts of reactants were used, and assuming that there are no competing factors to limit the amount of products being formed, then a stoichiometric amount of product is formed

Limiting Reactants and Product Yields

If we were to mix reactants together in non-stoichiometric amounts then what determines the amount of product formed?

The reactant which is first used up determines the amount of product formed.

This reactants is called the LIMITING REACTANT.

The other reactants are in EXCESS when the reaction stops.

If additional amounts of the limiting reactant is added the reaction starts again.

Problem:

Calcium carbonate CaCO3(s) is decomposed by HCl(aq) to give CaCl2 (aq), CO2(g) and H2O(l). If 10.0g of CaCO3 are treated with 10.0 g of HCl, how many grams of CO2 are generated?

First write a balanced equation for the reaction:

CaCO3 (s) + 2HCl(aq) CaCl2(aq) + H2O(l) + CO2(g)

1 mole of CaCO3 reacts with 2 moles of HCl to form 1 mole of CO2

Moles of CaCO3 = (10.0 g)/(100.0g/mol) = 0.100 mole CaCO3

Moles of HCl = (10.0 g)/(36.5 g/mol) = 0.274 mol HCl

Hence 0.1 mole of CaCO3 reacts with 0.2 moles of HCl. Since the amount of HCl present is greater that 0.2, HCl is in excess and CaCO3 is the limiting reactant.

Hence, 0.1 mole of CO2 formed.

Mass of CO2 formed = 0.1 mol x 44.01 g/mol = 4.40 g CO2

Product Yields

In the previous calculation 4.40 g is the amount of CO2 we would expect to be formed

4.40 g CO2 is the CALCULATED or the THEORETICAL PRODUCT YIELD.

This assumes that the reaction goes to completion, and that there are no competing factors that may reduce the amount of CO2 formed.

The measured amount of product formed is called the ACTUAL YIELD which is often smaller than the theoretical yield.

(theoretical yield)

Percentage Yield = (actual yield) x 100 %

The larger the % yield the more cost effective is the process and hence a more likely candidate for industrial scale processes

(other factors are also important: the nature of the by-products - are they environmentally safe -, the cost of the starting materials, etc.)

Problem:

The principle step in the recovery of elemental iron (Fe) from iron oxide (FeO) is a process known as reduction. In this reaction hydrogen (H2) at elevated temperatures is used as the reducing agent. Calculate the percent yield of Fe if 1.00 g of H2 reacts with 30.0 g of FeO and produces 19.5 g of Fe. The reaction between FeO and H2 is:

FeO(s) + H2 (g) Fe(s) + H2O(g)

First we need to determine the limiting reactant

Moles of H2 in reaction mixture = 1.00 g / (2.02g/mol) = 0.500 mol

Moles of FeO reaction mixture = 30.0 g / (71.85 g/mol) = 0.418 mol

From the stoichiometry of the equation FeO and H2 react in a 1:1 ratio.

Hence, FeO is the limiting reactant

The number of moles of Fe that should be formed = 0.418 moles

Mass of Fe that should be formed

= 0.418 mole x 55.85g.mol = 23.3 g of Fe.

The actual yield of FeO is 19.5 g

23.3

% yield = (19.5)x100 = 83.7%

Ideally for an industrial process, the % yield should be large.

Performing stoichiometric calculations, determining % yields, are important in analyzing the “success” of a chemical reaction.

Sometime, a reaction performed on a lab-scale may have good product yields but when the reaction is scaled up to an industrial process, the yield may be lower.