Relative Atomic Mass & Molar Mass; Chemical Formulas

10 Minute Chemistry – The Mole and Molar Conversions

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Section 2: Relative Atomic Mass and Chemical Formulas Objectives:

• Use a periodic table or isotopic composition data to determine the average atomic masses of elements. • Infer information about a compound from it chemical formula. • Determine the molar mass of a compound from its formula.

Key Term:

• Average Atomic Mass: Key Concepts and Outline Topics

1. Average Atomic Mass and the Periodic Table The masses on the periodic table are averages of the isotopes of each element. These averages are based on a percent abundance of that element. (See Chemistry Resources – List of the Elemental Isotopes) These isotopes are then averaged together and then weighed against carbon-12 in order to get a relative atomic mass. These relative atomic masses are in units of amu(atomic mass units) which we can think of as atom masses based on the number of protons, electrons and neutrons.

a. Most Elements are mixtures of isotopes When elements are formed we know that they exist with a specific number of protons and depending on their charge more or less electrons. We also know that there exists another subatomic particle called the neutron – which until now has been left out of discussion. We are now able to bring back the neutron into discussion as it plays a large role in the determination of the ‘isotope’ of an element. A series of isotopes are a family of the same element and the share the same number of protons but will differ in the number of neutrons and exhibit different properties. We utilize carbon-12 as the reference atom and ‘declare’ it to have an atomic mass of 12 amu. We have tables that allow us to determine the relative atomic masses which we then factor in the percent abundance and sum the products to determine the average atomic mass. Example 1: Average Atomic Mass of Hydrogen Relative Atomic mass(RAM) of H-1 = 1.0078250321 amu, % abundance(RIC) 99.9885% Relative Atomic mass(RAM) of H-2 = 2.0141017780 amu, % abundance(RIC) 0.0115% RAM = Relative Atomic Mass, RIC = Relative Isotopic Composition (RAM H-1)*(RIC H-1) + (RAM H-2)*RIC H-2) = Average Atomic Mass of Hydrogen (1.0078250321)*(99.9885%) + (2.0141017780)*(0.0115%) = 1.0079430754 amu This answer does not have the correct number of significant figures, the accepted values are 1.008 amu or 1 amu(estimation purposes only) with 1.00794 is a generally accepted precise value.

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2. Chemical Formulas and Moles Chemical formulas are expression for the composition of a compound by telling us what is in a compound and how many of each atom is in the compound. It also tells us the general structure through a standardized formulation dependent on the subject area. We will see various nomenclature methods that differs from organic chemistry to inorganic chemistry as we are focused on different aspects of the molecule and we have more variation in the inorganic molecules.

a. Formulas express composition The chemical formula is a series of letters and numbers each with a specific purpose with brackets or parentheses thrown in every so often. They can be broken down by function:

• Atomic Symbol • Functional Group or Polyatomic ions

• Charge • Quantity

There are capital letters that indicate the beginning of a new element which are sometimes followed by a lowercase letter the remaining portion of the elemental symbol. Most atomic symbols are two letters that generally follow start with the same letter as the name. However elements do have old names after which we obtain our atomic symbols. On some periodic tables the elements 115 – 118 are symbolized by a three letter code that indicates their position and they are temporary names as given by IUPAC(International Union of Pure and Applied Chemistry). This is the governing body for the names, weights and rules that are used in chemistry- many other governmental agencies take their recommendations which then become laws for a country. (NIST National Institute of Standards and Technology)

Atomic Symbols

When we see parentheses these indicate grouping elements together allowing us to form polyatomic ions(ionic bonding) or functional groups(organic chemistry). They show the reader that those atoms will act together on the central atom and normally have a charge (polyatomic ions) or determine the methodology of reaction (organic chemistry). A polyatomic ion is simply a grouping of bonding atoms that maintain stability enough that they stay together however they do not completely neutralize charge and can carry either a positive or negative charge. There are molecules that can be induced to have a dipole(charge) based on Electronegativity differences from one end to the other and thus act like an ion. These type of dipole moments allow for the entire molecule to bond with a molecule and due to increased stability stay together. Functional groups on the other hand are molecules that direct behavior based on Electronegativity, geometry(spatial), reactivity. Knowledge of functional groups at this point is not of great importance, however knowing polyatomic ions is extremely important.

Functional Groups or Polyatomic Ions

There are times that we will see superscripts which can indicate either a charge or oxidation number. At this point these superscripts will always indicate the charge of the atom which tells us the relative number of electrons the atom has compared to its neutral state (Electrons=Protons for neutral atoms). We are able to calculate the charge of an atom based on its distance from a noble gas. As the elements want to be isoelectronic (have the same number of electrons) as a noble gas they will take the shortest distance. An atom will give electrons and become positive if the closest is to the left, and will take electrons and be positive if the closest noble gas is to the right. Many times brackets are used with superscripts to indicate overall charge on

Charge




an the ion. We then use this overall charge to calculate the individual charges of each atom which is indicated by superscripts.

We have subscripts that determine the quantity of the preceding atom or atomic group. Subscripts that exist on the outside of parentheses are distributed via multiplication to those atoms inside. If there are additional subscripts applied to individual atoms inside the parentheses they are multiplied with those outside. The absence of a subscript indicates there is only one atom.

Quantity

Example 1: Magnesium Chlorate, Mg(ClO3)2 is a herbicide that is relatively toxic

Mg(ClO3)2 Formation of Ammonium Acetate, CH3COONH4

CH3COOH + NH3 → CH3COONH4

CH3COO- +NH4

+ → CH3COONH4

Atomic Symbol for Magnesium (Capital M, Lowercase g)

Note () indicating the polyatomic ion ClO3

Subscript, that indicates the quantity of the oxygen atom (3)

Subscript outside the () indicates the quantity of the polyatomic ion. We can derive the qty of the individual atoms by distributing the subscript to each atom in the () using multiplication.

Functional Group

Polyatomic Ion

Charges

Note that even though there are polyatomic ions, they are not always indicated by parentheses. It is important to recognize them as they will help indicate a potential pathway to formation(reaction mechanism).




b. Formulas give ratios of polyatomic ions The chemical formulas that utilize polyatomic ions will use parentheses to indicate multiple groupings of polyatomic ions. This was seen in the example above in magnesium chlorate. The polyatomic ion chlorate has a -1 charge compared to the 2+ charge on the magnesium. In order for a stable product to form there must be a net neutral charge which is obtained by adding another chlorate ion. We could as easily neutralized the charge by adding another 1- ion however we would not obtain the compound magnesium chlorate. We differentiate the compound magnesium chlorate with the formula Mg(ClO3)2 from magnesium chloride with the formula MgCl2. The difference between is the addition of oxygen which changes the ending of chlorine from –ide, to –ite, to –ate depending on the quantity of oxygen atoms that are added to get to the neutral magnesium.

c. Formulas are used to calculate molar masses Chemical formulae are used to calculate individual molar masses as they indicate the quantity of atoms within a compound. We utilize subscripts to increase the quantity of an indicated atom and multiply the quantity of an atom by its average atomic mass which is obtained from a periodic table. The Steps to Determining Molar Mass (units will always be grams/mole(g/mole))

• Atom Inventory(list the elements left to right, and then the qty of each) • Assign the atomic masses to each atom • Sum the series, with each series being the product of the qty of an atom by its atomic mass

Example 1: Calculate the Molar mass of water, H2O

1. Atom Inventory H2O

H – 2(atomic mass) O – 1(atomic mass)

2. Assign the atomic mass for each element H – 2(1.00794 g/mole) = 2.01588 g/mol

= 18.01528 g/mole O – 1(15.9994 g/mole) = 15.9994 g/mol

When reporting the molar mass of a compound it is essential to have the correct unit of grams/mole(g/mol) and that you report a reasonable number of significant digits. As a rule of thumb we will have 2 digits after the decimal point.


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Relative Atomic Mass & Molar Mass; Chemical Formulas