Unit 3 Stochiometry Part 1: Chemical formula Summary The composition of a compound is expressed through its chemical formula. When the compound is composed of molecules, the molecular formula indicates how many atoms of each element make up the molecule. The formula for compounds made up of ions indicates the relative number of ions. One mole of an element has the Avogadro constant of atoms and has a mass, that corresponds to the relative atomic mass of an element in grams. A mole of a compound has the Avogadro constant in formula units; in molecular compounds it is the Avogadro constant in molecules. The mass in grams of a mole of a compound is found by adding the relative atomic masses of the participating elements according to the chemical formula of the compound. A compound’s formula can be used to calculate the percentage composition (mass fraction of the element expressed in %). From the percentage composition, the empirical formula can be determined; this is the formula with the simplest numerical ratio of the atoms. Vocabulary Please look up the following definitions (a Wikipedia search is sufficient): 1. Molecule 2. Molecular formula 3. Structural formula (constitutional formula) 4. Empirical formula 5. Anion 6. Cation 7. Monoatomic ion 8. Polyatomic ion 9. Mole 10. Avogadro constant 11. Molar mass 12. Molecular mass 13. Relative formula mass 14. Mass fraction 15. Chemical bond 16. Ionic bond 17. Covalent bond 18. Van der Waals forces Modern chemistry began when Lavoisier recognized the importance of careful measurements and began to ask questions that were quantitative in nature. Stoichiometry (from the Greek stoicheion = Element and metron = measure) is the study of the mass ratios of elements in compounds and the quantitative relationships between compounds or elements, that participate in chemical reactions. The atomic theory of matter is the corresponding basis. Unit 3.1 Molecules and Ions Only the nobles gases, the elements Helium, Neon, Argon, Krypton, Xenon and Radon are found in nature as single atoms. All other elements appear in large units, in which atoms are linked with one another. Examples: Oxygen O2, Carbon monoxide CO, Water H2O, Carbon dioxide CO2, Ammonia NH3, Methane CH4. Structure formula for Ammonia. Ilustración 1. Structural formula for ammonia. Molecules Molcules are particles in which two or more atoms are “firmly” joined to one another. Molecules behave as units in chemical and physical processes. Some elements and a large number of compounds are made of molecules. The composition of a pure substance is given by its chemical formula. Every element is represented by its symbol followed by a subscript number to indicate the relative number of atoms. In compounds that are composed of molecules, the number of atoms is given in the molecule. H2O for example, is the molecular formula for water. Some elements are found as diatomic molecules such as: H2 (Hydrogen) N2 (Nitrogen) O2 (Oxygen) Cl2 (Chlorine) Some elements make up larger molecules; Sulphur for example, is made up of 8-atomic molecules. The molecules of compounds are made up of atoms from two or more different elements. The formula for a molecule, for example NH3 (ammonia) only indicates the number atoms of each element that make up the atom. To show which atoms are connected to one another, one uses structural or constitutional formulas, where line segments show the type of bond. The structural formula in general, does not display the actual spatial distribution and arrangement of the atoms. The ammonia molecule for example, has a trigonal pyramidal geometry, that is not expressed by the formula above. The relative molecular mass Mr is the sum of the relative atomic masses of all atoms of the molecule. The single molecule has a mass in u-units (atomic mass units), that are the same as Mr in number. Ions What is an ion made of? What are its components? An ion is an atom or molecule, that carries an electric charge. One differentiates: ▪ A cation is positively charged. The name comes from the fact that a cation is attracted to a cathode, i.e. the negative pole of an electric voltage. Cations form when atoms of molecules give up electrons. ▪ An anion is negatively charged. It is attracted to an anode (= plus pole) and are formed when an atom or a molecule take up electrons. Monoatomic ions are formed from single, charged atmos. Metallic elements generally form monoatomic cations, for example, calcium ions Ca2+, while nonmetal monoatomic atoms form monoatomic anions, for example chlorine Cl -. Polyatomic ions, also called molecular ions, are made up of more than one atom, for example: NH4+ (Ammonia ion) SO42- (Sulfate ion) OH- (Hydroxide ion) What is a crystal? Crystal structure types? What does a sodium chloride crystal look like? Is it possible to make crystals in the lab? Find images of different salt crystals online. The symbol for the charge, for example, -2 in the case of the sulfate ion, refers to the charge of the entire particle, regardless of which element symbol it stands next to. Ionic compounds are made of cations and anions. In the solid state they build crystals that are organized in a defined, geometric arrangement. Sodium chloride (cooking salt) for an example, is made of sodium cations Na+ and chloride anions Cl. The crystal is made of a large number of such ions, that are held together by the plus-minus-attraction. In each “elementary cell,” exactly one Na+-ion is joined to one Cl—ion. The chemical formula NaCl does not describe the molecule in this case, but only indicates the composition in summarized form, of the relative number ratio of the ions. Barium chloride is composed of barium ions Ba 2+ and chloride ions Cl-. A barium chloride crystal is electrically neutral, each Ba2+ ion is met by two Cl- ions; the formula is BaCl2. Example 3.1 Iron oxide is made of iron ions Fe3+ and oxide ions O2-; what is its formula? In order for it to be electrically neutral, two Fe3+ ions and three oxide ions O2- must join, the formula is Fe2O3. Other atomic aggregates Some elements and compounds are neither made of molecules nor ions. Diamonds for example, are made up of only carbon atoms, that are joined in a network with bonds similar to molecules. A diamond crystal can be seen as a gigantic molecule; the number of atoms is not fixed, it depends on the size of the crystal. Similar conditions are present in compounds as well, for example, silicon dioxide; its formula SiO2, just like ionic compounds, describes the relative ratio of its atoms. 3.2 Empirical formulas What is a molecular formula? What is a molecular structural formula? What is hydrazine used for? What is the structural formula of hydrogen peroxide? What about its empirical formula? What is an oxide? What about an oxide? The molecular formula for hydrogen peroxide, H2O2, shows a molecular structure of two hydrogen and two oxygen atoms. The number ratio 2:2 of the atoms is not the simplest number ratio, but rather 1:2. An empirical formula indicates only the simplest number ratio; the empirical formula for hydrogen peroxide is HO. Ilustración 2 Structural formula for hydrogen peroxide. Only the empirical formula of a pure substance can be determined through a chemical analysis. To determine the molecular formula, additional information is necessary. Some compounds have identical empirical and molecular formulas, such as H2O, CO2, NH3. For other compounds, this is not the case; for the substance with the molecular formula N2H4 (Hydrazine), the empirical formula is NH2; both compounds with the molecular formulas C2H2 (acetylene or ethyne) and C6H6 (benzene) have the same empirical formula CH. In simple ionic compounds, which formulas such as NaCl or CaCl2, whose formulas only indicate the number ratio of their ions, the chemical formula is the same as the empirical formula. When molecule ions are present, the formula should indicate the composition of the molecule. Sodium peroxide is composed of Na+ ions and peroxide ions 𝑂22− ; in this case, the empirical formula is not given (NaO), but rather Na2O2. 3.2 The mol The relative atomic mass of fluorine is 19.0; hydrogen’s is 1.0. When the atomic mass of any number of fluorine atoms and an equal number of hydrogen atoms is added, the total mass of the fluorine atoms will always be 19 larger than the mass of the hydrogen atoms. This number ratio is fulfilled when we take 19.0 g of fluorine and 1.0 g of hydrogen, that means we take the same number of grams as the numerical value of the relative atomic mass. Since the mass ratio of 19:1 is fulfilled, both elements must have the same number of atoms. This statement is true in general: the amount in gram of an element that corresponds to the numerical value of the atomic mass always contains the same number of atoms. The corresponding number is called the Avogadro Number NA. This number can be determined experimentally. The amount of substance that contains NA = 6.02214 * 1023 particles is called a mole (SI-Symbol: mol). It is defined as the number of particles that are contained in 12 g of 126𝐶 atoms. Particles in this sense can be atoms, ions, molecules or electrons. A mol of a molecular substance is composed of 6.02214 * 10 23 molecules and has the mass in gram of the numerical value of the relative molecular mass. The relative molecular mass Mr is the sum of the relative atomic masses of all the atoms of the molecule; this was previously called molecular weight. The mass of one mole is called the molar mass. The relative molecular mass for water Mr (H2O) is 18.015. In 18.015 grams of water, there are NA H2O-molecules. A single water molecule has the mass m(H2O) = 18.015 u. When quantities are given in mol, it needs to be specified as to which particles are referenced. A mol of H-atoms contains 6.02214 * 1023 hydrogen atoms and a mass of 1.008 g; a mol of H2-molecules contains 6.02214 * 1023 H2-molecules and has a mass of 2.016 g. A quantity in mole for a given substance with formula X is expressed as n(X). The amount of substance n(X) is given by the mass m(X) of the sample divided by the molar mass M(X). The numerical value for atomic and molecular masses is given by three units. ▪ ▪ ▪ ▪ ▪ ▪ The relative atomic mass Ar and the relative molecular mass Mr are purely numerical values, without a unit. The relative atomic mass is a number ratio, namely, the ratio of the average atomic mass of an element to one twelfth the mass of a 126𝐶 . Sodium has the relative atomic mass 22.98977; A r (Na) = 22.98977. Water has the relative molecular mass 18.015; Mr (H2O) = 18.015. A 126𝐶 atom has per definition, an atomic mass of 12 u. The average mass of an atom of an element is given in the unit u. The mass of a Sodium atom is 22.98977 u. The mass of a water molecule is 18.015 u. The mole of an element or a compound has the numerical value of the relative atomic mass or the relative molecular mass M in grams per mole. The molar mass of sodium is 22.98977 g/mol. M(Na) = 22.98977 g/mol. 3.4 Percentage composition of compounds The mass percentage of an element in a compound can be calculated easily from its chemical formula. The sub-indexes in a formula indicate the number of moles of each element in a compound. Together with the molar mass of each element, the corresponding total mass of each element can be determined. Through division by the molar mass of the compound, one obtains the mass percentage w of the element; multiplication by 100 gives the corresponding percentage. One can also report this as cg/g in order to avoid confusion as to whether the percentage refers to mass, volume, or another dimension. Assume that a percentage always refers to mass when no other information is available. Example 3.3 What percentage of iron is found in Iron (III) oxide is Fe2O3? A mol of Fe2O3 contains: n(Fe) = ____ mol ; n (O) = _______ mol m(Fe) * M(Fe) = __________________ = _____________ m(O) * M(O) = ___________________ = ______________ Mass portion of Fe in Fe2O2: w(Fe) = m(Fe)/m(Fe2O3) = _________ = _____________ Mass percentage of Fe in Fe2O3: w(Fe)*100% = __________________ The chemical analysis of a compound obtains the mass percentage of each compound. The empirical formula is formulated with this information. Example 3.4 illustrates the typical path of analysis for an organic compound. The mass percentage of an element in a sample can also be determined even if foreign substances are present, see example 3.5 Take note that the calculated values are given in so many significant figures as the original values. Example 3.4 Nicotine contains carbon, hydrogen, and nitrogen. When 2.50 g of nicotine are burned, 6.78 g of CO2 are released, 1.94 g of H2O and 0.432 g of N2. What is the composition (in percent) of nicotine? All carbon of the sample is found in the 6.78 g of CO 2, all hydrogen is found in the 1.94 g of H2O. Step 1: Determine the relative molecular mass of both the CO2 and the H2O. Step 2: Determine the portion of carbon in CO2 as a decimal (not in percent). Step 3: Determine the mass of carbon in the 6.78 g of CO2 (not in percent). Step 4: Determine the portion of hydrogen in H2O as a decimal (not in percent). Step 5: Determine the mass of hydrogen in the 1.94 g of H2O (not in percent). Through division with the original sample mass one obtains the percentages of the elements in nicotine: Example 3.5 What is the mass percentage of iron in a mineral that is made of 70.0% Fe 2O3? Step 1: Calculate the mass portion of iron in Fe2O3, then take 70% of that amount: 3.5 Determining chemical formulas The values of the chemical analysis of a compound serves to determine its empirical formula. The analysis gives the relative mass portion of the elements in the compound. Since the mole of one element contains the same number of atoms as a mole of another element, the ratio of mole numbers is the same as the ratio of atom numbers. The number of moles of an element in a sample is easy to determine with the mass of element in the sample. The simplest whole number ratio of moles of the different elements in a compound results in the empirical formula. The procedure goes as follows.