chemical equations the mathematics of chemical formulas

Chemical Equations

The Mathematics of Chemical Formulas

Chemical EquationA chemical equationchemical equation represents changes in bonding and energy that occur during a chemical reaction. Qualitative and quantitative changes are recorded in a chemical equation.

Chemical EquationA number, called a coefficientcoefficient, is placed before formulas to indicate the ratios of moles (or molecules) involved in the reaction.

Chemical EquationThe coefficient 1 is not written, but is understood. Equations are always balanced to conform to the laws of conservation of mass and charge.

Chemical EquationFor example, the equation

2H2 + O2 2H2O + heat

gives the following information:a. hydrogen + oxygen waterb. 4 atoms + 2 atoms 6 atomsc. 2 molecules + 1 molecule 2 moleculesd. 2 moles + 1 mole 2 molese. energy is liberated (energy changes

need not always be noted).

Chemical EquationNotice that the law of conservation of mass is observed, as there are 6 atoms in both the reactants and in the product. It is not necessary, however, to have the same number of moles or molecules in reactants and products.

Chemical EquationIn a chemical equation, it is often helpful to indicate the phase of the reactants and products, using the following symbols: (s) solid, (l) liquid, (g) gas, (aq) aqueous solution.

Chemical EquationExample Balance the following equation using only whole-number coefficients

SiO2 + C SiC + CO

(NH4)3PO4 + Ba(NO3)2 Ba3(PO4)2 + NH4NO3

Concept of The MoleA gram atomic massgram atomic mass of an element is that quantity of an element whose mass in grams is numerically equal to its atomic mass.

Concept of the MoleFor example, the atomic mass of carbon is 12.01115. Therefore, 12.01115 grams of carbon is one gram atomic mass of carbon.

Concept of the MoleA gram atomic mass of ANY element contains the same number of atoms. This number, 6.02x1023, is called Avogadro’s Avogadro’s numbernumber.

The MoleA mole is defined as Avogadro’s number of particles. One mole is 6.02 x 1023 particles, which can be atoms, molecules, ions, electrons, or any other kind.

The MoleThe mole is a pure number, that is, without any associated units, and is designated by the symbol N.

The MoleA mole of O2 molecules (oxygen gas), is 6.02 x 1023 molecules, or N molecules. However, this quantity of gas contains 2 moles of oxygen atoms.

RelationshipsA gram atomic mass of an element contains N atoms. One mole of an element is also N atoms. Therefore one mole of an element is the same quantity as one gram atomic mass of that element.

RelationshipsThe mass of one mole in grams is numerically the same as the atomic mass of the element. Thus one mole of carbon has a mass of 12.01115 grams.

Molecular (Formula) MassThe molecular (formula) massmolecular (formula) mass of a compound is the sum of the atomic masses of all the atoms in one molecule (or one formula unit) of the compound.

Molecular (Formula) MassThe term formula massformula mass is preferred for ionic compounds and network solids, which do not have discrete molecules.

Molecular (Formula) MassExample What is the molecular (formula) mass of Na2CO3?

Gram Molecular (Formula) Mass

A gram molecular (formula) gram molecular (formula) massmass of a compound is that quantity of a compound whose mass in grams equals its molecular (formula) mass. As in the case of gram atomic mass, a gram molecular mass of a compound is equal to one mole.


Example What is the mass in grams of one mole of water, H2O?


Example What is the mass in grams of one mole of water, H2O?

One hydrogen has a mass of 1.007 g, so 2 x 1.007 = 2.014 g

One oxygen has a mass of 16.00 g Total mass is: 2.014 + 16.00 = 18.0 g

Finding Number of MolesIn the case of a liquid or a solid, the number of moles in a given quantity can be found by dividing the mass of the sample in grams by its molecular mass.

Stoichiometry

StoichiometryStoichiometry is the study of the quantitative relationships that are implied by chemical formulas and chemical equations.

StoichiometryUsing stiochiometric methods, we can determine the proportions in which elements combine to form substances.

StoichiometryWe are concerned with two basic kinds of chemical problems – those involving formulas and those involving equations. In solving these problems, the mole concept and mole relationships are often useful.

Problems Involving Formulas

1. Determining percentage percentage compositioncomposition The percentage composition of a compound is its composition in terms of the percentage of each component present with respect to the whole.


Ionic solids often include definite amounts of water of hydrationwater of hydration as part of their crystal structures. Water will then appear as part of the empirical formula.


Examples What is the percentage composition, by mass, of the elements in sodium sulfate, Na2SO4?

What is the percentage of water, by mass, in sodium carbonate crystals, Na2CO3 • 10H2O?


Empirical formulas An empirical formula represents the simplest ratio in which atoms combine to form a compound.


The molecular formula of ethane is C2H6. The simplestsimplest ratio of carbon to hydrogen atoms in this compound is 1:3. Therefore, the empirical formula of ethane is CH3.


Note that the molecular formula is always a simple multiple of the empirical formula.


If you know the mass ratio of the elements in a compound, you can determine its empirical formula. For example, suppose you know that in a compound composed of carbon and hydrogen, the mass ratio of carbon to hydrogen is approximately 4:1.


Recall that 1 gram-atom of carbon has a mass of approximately 12.0g, while 1 gram-atom of hydrogen is about 1.0g.


This means that in our carbon compound, for every 1 gram-atom of carbon (12.0g) there are 3 gram-atoms of hydrogen (3 x 1.0g). Thus the empirical formula of our compound is CH3.


On the other hand, if you know the empirical formula of a compound, you can determine the mass ratio of its elements.


The empirical formula CH3, for example, tells you that there is 1 gram-atom of carbon for every 3 gram-atoms of hydrogen. Thus the mass ratio of carbon to hydrogen in this compound is approximately 12:3, or 4:1.


Determining formula from percentage composition The empirical formula of a compound can be determined if the percentage composition of the compound and the atomic masses of the elements in the compound are known.


The molecular formula of a molecular compound likewise can be determined if the molecular mass is known.


Example What is the empirical formula of a compound that consists of 58.80% barium, 13.75% sulfur, 27.45% oxygen by mass?


Example By chemical analysis, a molecular compound was found to consist of 80% carbon and 20% hydrogen by mass. By measuring the volume of a known mass of the compound in the gaseous phase, its molecular mass was found to be 30. Find the empirical and molecular formulas of the compound.

chemical equations the mathematics of chemical formulas

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gram molecular mass

molea gram atomic mass

gram atomic mass of

relationshipsthe mass

case of gram atomic

number of atoms

chemical equationa number

chemical reaction