Mass-Mass Stoichiometry

In a mass-mass calculation you are given information in grams and asked for information in grams.  To complete stoichiometry problems you must know the ratio of particles.  The only way to determine this is by writing a balanced reaction.  The coefficients will provide you with the MOLE RATIO.

Remember that a reaction tells you the ratio of particles or moles, NOT MASS!  A gram of one substance will not have the same number of particles as a gram of another substance. That means you will need to convert grams to moles using molar mass.

We approach this type of problem using the same problem solving steps that we've been using all semester.

1. What are we given?
2. What are we looking for?
3. What additional information is needed?

Let's walk through an example problem:

     Example 1:  An excess amount of sodium chloride reacts with 25.0 grams of lead (II) nitrate in water.  How many grams of precipitate will be formed?

1. What are we given?
   excess NaCl, 25.0 g Pb(NO3)2
2. What are we looking for?
   grams of solid (?)
3. What additional information is needed?
   reacts means a reaction, so you need a balanced reaction
   grams means at some point molar mass will be needed
   solid, means you need to know what precipitates, so you need states

Example 2: How many grams of NaCl are actually needed to react all 25.0 g of lead (II) nitrate?

Empirical Formulas from Percent Composition

One way of determining the identity of an unknown in a lab is by analyzing its mass to determine its empirical formula (lowest whole number ratio of each element in a compound).  There are several types of problems, but all of them use the same concepts to start.

Example 1:  An unknown substance is composed of 24.7% potassium, 34.7% manganese and 40.5% oxygen.  Determine the empirical formula for this compound.

Problem!  You can't compare percentage by mass to determine the ratio of ATOMS!

1. The first step is to convert the percentages to MOLES using the MOLAR MASS for each element.
2. Once you have all the substances in moles, you can compare them to find the mole ratio.  There are several ways of doing this.  The easiest is to divide by the smallest value.  This usually works, but remember that an empirical formula is written in the LOWEST WHOLE NUMBER ratio, so if you a left with a fraction, you must multiply the entire ratio by a factor that will convert the fractions into WHOLE NUMBERS.
   
3. Therefore the ratio of K:Mn:O is 1:1:4, so the empirical formula is KMnO4.

Mole Conversions

While we tend to measure amounts in grams, the only way to compare amounts of atoms, molecules or ions is by using moles.  Unit analysis allows us convert one set of units to another.

To convert grams to moles, or visa-versa, we use molar mass that has the units grams/1 mole.

To convert number of particles to moles, or visa-versa, we use Avogadro's number (6.02 x 10^23) that has the units particles/1 mole.

Example: How many chlorine atoms are in 75.0 grams of sodium chloride?

Percent Composition

Percent always allows us to compare a part of something to the whole.
In general

% = part x 100

total

For percent composition

% = total mass of particles requested x 100

molar mass

Example: Determine the % oxygen in sulfuric acid.

% O =       4 oxygen          x 100

(2 H + 1 S + 4 O)

%O =               4(16.0) ___  _  x 100 = 48.9% O

                                                                     2(1.0) + 32.1 + 4(16.0)

Example: Determine the % sulfate in sulfuric acid.

%SO4 =               32.1 + 4 (16.0)___  _  x 100 = 97.9% O

                                                                    2(1.0) + 32.1 + 4(16.0)

Hydrates

Hydrates are ionic salts that trap water molecules in their crystal lattice.  This added mass must be used when making calculations therefore the ration between molecules of ionic salt and water is given in the name.

For instance, calcium sulfate hexahydrate states that for every molecule of calcium sulfate there are 6 water molecules surround it.  We represent a hydrate with a large dot then the number of water molecules.  This dot is NOT a multiplication sign, it is actually a ratio.

To determine the molar mass of hydrate, determine the mass of the salt then add the mass of however many water molecules are attached to it.

1 Ca + 1 S + 4 O + 6(2 H + 1 O)

40.1 + 32.1 + 4(16.0) + 6(18.0)

244.2 g/mole

The Mole

Mole is a term used in chemistry to represent the number 6.02 x 10^23.  Just as we use the word "dozen" to mean 12 objects, "mole" represents 6.02 x 10^23.

Amedeo Avogadro studied molecular theory in the early 19th century and built on the ideas of Dalton and Guy Lussac.  The number of particles in a mole was actually discovered later in the century and named in his honor.

Atoms and molecules are VERY small. Remember we measure their mass in atomic mass units, amu.  An amu is equal to 1/12th the mass of a carbon-12 atom or approximately the mass of a proton or neutron. The wonderful thing about the very odd number is it allows to work with measurable quantities.

One mole of atoms of any element is equal to its atomic mass (average mass number) in grams.  This is called molar mass.

The molar mass of a compound is simply the sum of the masses of each of its atoms.

water is H20
there are 2 Hydrogen and 1 Oxygen
therefore its molar mass is 2(1.0) + 1(16.0) or 18.0 grams/mole

This means that if you have 18.0 grams of water, you will also have 6.02 x 10^23 molecules of water.

Driving Forces

The driving force for a reaction is the reason the reaction moves forward.  It is the reason the reactants become the products.  To truly analyze the driving force, you must write the ionic reaction.  At this point in the semester, we will use the following reasons.

• a solid is produced from an aqueous solution
• a gas is produced
• water is produced
• a more active metal replaces a less reactive metal in a single replacement reaction
• a more reactive nonmetal replaces a less reactive nonmetal in a single replacement reaction
• neutral elements combine to form an ionic compound in a synthesis reaction

The last 3 reasons are types of redox reactions where electrons are transfered.  We will discuss redox reaction in the future.

Solubility Rules

Soluble means a substance will dissolve in water, whereas insoluble means it will not dissolve appreciably. If an insoluble product is created in an aqueous solution, it will precipitate out of solution as a solid.

Solubility Rules

Mainly soluble:

all nitrates & acetates

all halogens, except with silver, mercury and lead

all chlorates, except with silver, mercury and lead

all sulfates, except with calcium, strontium, barium, lead, mercury, and silver

all chromates, except with calcium, strontium, barium, lead, mercury, and silver

Mainly insoluble:

all sulfides, except with groups 1 & 2, and ammonium

all hydroxides, except with groups 1 & 2, and ammonium

all carbonates, except with group 1 and ammonium

all phosphates, except with group 1 and ammonium

Basic Types of Reaction

Synthesis (also called Addition, Composition and Combination)

     Atoms and or molecules are combined to make ONE more complex molecule.

A  +  B --> AB

Fe  +  S -->  FeS

metal oxide + water --> metal hydroxide

nonmetal oxide + water --> oxyacid

Decomposition (also called Analysis)

     A complex molecule is broken into simpler molecules and or atoms

AB --> A + B

KClO3 --> KCl  +  O2

metal chlorate --> metal chloride + oxygen

metal carbonate --> metal oxide + carbon dioxide

Single Replacement

     A single element replaces one component of a compound.  A metal must always replace a metal and a nonmetal must replace a nonmetal.  A single replacement replacement is a type of redox reaction where electrons are transfered from one atom to another.

A  + BX --> AX + B

K + CsCl --> KCl + Cs

X + AY --> AX  + Y

Cl2  +  MgBr2 --> MgCl2  +  Br2

Double Replacement (also called Ionic and Precipitation Reactions)

     Ionic compounds switch "partners."  Remember that a neutral compound must have a cation combined with an anion.

AX  +  BY --> AY  +  BX

CuCl  +  NaS --> CuS  +  NaCl

Reactions: Basics

Law of Conservation of Mass- Matter can neither be created nor destroyed, only rearranged in

a chemical reaction.

 Steps in balancing a chemical reaction:

1. predict the products in words

2. write the formula for all the reactants and products

(balance the charges and look for diatomic elements)

diatomic elements - H₂ , O₂ , N₂ , F₂ , Cl₂ , Br₂ , I₂

3. balance the polyatomic ions (nitrate. sulfate, hydroxide ...)

4. balance all other elements except hydrogen and oxygen

5. balance the hydrogen and oxygen  (don't forget to look for H and O in all compounds)

6. check every reaction again element by element 

Naming Acids

 All acids begin with a H⁺  and are combined with one of the three types of anions.

            -ide             to            hydro----ic acid                        H2S          hydrosulfuric acid

            -ate             to                        -ic acid                        H2SO4      sulfuric acid

            -ite              to                        -ous acid                     H2SO3      sulfurous acid

                        I -ate something and it made me s-ic.

                                        and you m-ite give it to -ous.

Ionic Compounds

Ionic compounds are formed between oppositely charged particles called ions.  Ions are formed when electrons are lost, called cations, or when electrons are gained, called anions.

A molecule must be neutral.  The total amount of positive charges must cancel out the total amount negative charges to create an overall charge equal to zero.

Covalent Compounds

Covalent bonds are formed by 2 or more atoms sharing electrons.  Typically this is between 2 non-metals since both atoms want to gain electrons to acquire a full outer shell.

To name covalent compounds, use the following prefixes to represent the subscripts and change the suffix of the more electronegative (always on the right) element to -ide.

1  mono

2  di

3  tri

4  tetra

5  pent

6  hex

7  hept

8  oct

9  non

10 dec

Isotopic Notation

Isotopes are atoms with the same number of protons but have a different number of neutrons.  They are basically different varieties of the same element.  Two of the most common isotopes that people hear about are Carbon-14 and Carbon-12.  Both isotopes are carbon because they each have 6 protons.  They are different because C-14 has 8 neutrons and C-12 only has 6.  While C-12 is the most abundant (common) isotope of carbon, both are called isotopes.

The number of protons in an atom is also called the atomic number.  The number of protons determines the identity of an atom, no matter how many neutrons or electrons are in the atom.  Atomic number is listed on the periodic table.  It is a whole number and is usually listed above the symbol for the element.  If you change the number of protons in an atom, the element has also changed.

Mass number is the total number of particles in the nucleus of an atom.  In other words, it is the number of protons plus the number of neutrons.  Isotopes have the same atomic number, but different mass numbers.  Mass numbers are NOT listed on the periodic table.  When you name a specific isotope, you MUST include its mass number, for instance Carbon-14 or Uranium-135.

The number below the symbol of the element on the periodic table is called the atomic mass.  It is the weighted average mass number of all the isotopes of a particular element.  Because it is an average, it has significant digits.

We can represent an isotope in an abbreviated form.  This is called the isotopic notation.

Here is the isotopic notation for carbon 14.

From looking at the isotopic notation, you can determine the number of protons, neutrons and electrons for a given atom.

In a neutral carbon 14 atom, how many protons, neutrons and electrons are there?
Protons- The atomic number is 6, therefore there are 6 protons
Electrons- If the atoms is neutral the number of protons equals the number of electrons, therefore there are also 6 electrons.
Neutrons- The mass number equals the number of protons + neutrons, therefore 14-6 leaves 8 neutrons.

Chemical Reactions: The Basics

Chemical Reactions describe chemical changes.  Chemical Equations are shorthand descriptions of chemical reactions that use coefficients, symbols and subscripts to describe the ratios of a reaction.  We call the substances before a reaction the reactants and we call the substances that are formed the products.

Antoine-Laurent de Lavoisier (1743-1794) is considered by many to be the father of chemistry. He was the first to clearly state the Law of Conservation of Mass.  This states that matter is neither created nor destroyed in a chemical change.  We can now add to that the idea that the atoms or building blocks of matter are simply rearranged in a chemical reaction.

John Dalton (1766-1844) took Lavoisier’s ideas further by developing the first basic atomic theory.  He stated that an atom is the smallest unit of an element that can exist either alone or in combination with other atoms of the same or different elements.

His supporting evidence:

1. All matter is made up of very small particles called atoms.

2. Atoms of the same element are all chemically alike: atoms of different elements are chemically different.

3. Individual atoms of the same element may not have the same exact mass (isotopes), but for all practical purposes, they all have a definite average mass.

4. The atoms of different elements have different average masses.

5. Atoms are not subdivided in chemical reactions, they unite in simple ratios to form compounds.

He also developed the Law of Multiple Proportions.  If two elements combine to form more than one compound, they will combine in distinct whole number ratios.

Matter: Part 2 Mixtures

Pure substances are uniform throughout with a definite composition and properties, while mixtures are physical combinations of two or more pure substances. The properties of the substances in a mixture retain their own properties.

We can further divide pure substance in chemistry into elements and compounds.  An element is basically the name of a type of atom defined by the number of protons in the nucleus.  A compound in a chemical combination of two or more elements.  A compound is the name of a type of molecule (chemically bonded atoms).

Note:  Physical combination means that substances are just dispersed or close together. A chemical combination means that the atoms are chemical attached creating new molecules with new properties.  Chemical bonds cannot be separated by physical means.

Mixtures can be divided into homogeneous mixtures that appear to be a single substance and heterogeneous mixtures that are obviously two or more substances.

All mixtures are composed of a solute and a solvent. The solute is the substance that is dissolved or dispersed, while the solvent is the substance that does the dissolving.  The solvent separates and keeps the solute particles apart.

Mixture can be divided into three categories:

Solutions are homogeneous and clear.  The particles are so small they cannot be seen and do not reflect light.

     Ex:  windex, tap water, air

Colloids are homogeneous but appear cloudy.  Some of the particles are large enough to reflect light even though they can’t be seen with the naked eye.

     Ex:  milk, fog, mayonnaise

Suspensions are heterogeneous.  Given time gravity will separate a suspension with the most dense particles on the bottom, and the least dense (lightest) particles rising to the top.

     Ex:  Italian salad dressing, oil and water

Matter: Part 1 Describing Matter

In lab we make both qualitative and quantitative measurements.  We can further describe matter in terms of extensive and intensive properties.  Extensive properties are quantity specific, such as mass and volume. The mass of a sample of water depends on how much water you have in a sample.  Intensive properties are dependent only on the type of matter, not the quantity.  The density of water is 1.0 g/mL whether you have a drop or a swimming pool full.

We can further divide observations into physical and chemical properties.  Physical properties describe matter without changing its composition.  Chemical properties describe how matter interacts or changes with other matter.

Physical Properties                                Chemical Properties

Color                                                                Rusting

Odor                                                                 Burning

Density                                                            Tarnishing

Boiling Point

Malleability

The state of matter, and its boiling and melting points are all physical properties.  The state of matter is determined by the arrangement of its particles.

The change of state of a substance is a physical change.

                                    Boiling                                                Evaporating

                                    Melting                                               Condensing

                                    Freezing                                              Sublimation

                                    Solidifying

If the identity of a substance is changed, or a new substance is formed, it is a chemical change.

Density with UA

You must use unit analysis to solve density problems in chemistry.  Remember you are learning the process  of unit analysis not simply finding the correct answer!

Use the technique you have learned in problem solving:  what are you looking for, what are you given, put the units together to cancel and solve.

Example #1

A sample of a known metal is dropped into a graduated cylinder with 25.0 mL of water. The level rises to 31.5 mL. If the given density of the metal is 2.56 kg/L, what is the mass of the sample in grams?

Example #2

What is the volume of a sample of aluminum in L that weighs 56.7 g?  The density of aluminum is 2.71 g/mL.

Possible Questions

Why flip the density?  To make sure the units of volume will be in the numerator.

I got a different answer, why? Remember that 2.71 is in the denominator.  You must divide not multiply. You can either punch in 56.7 first or start with 1/2.71.

Problem Solving with UA

Unit Analysis can make solving complex word problems much easier.  First, DON’T BE INTIMIDATED!  The problem is not going to jump off the page and bite you if you get it wrong!  Just TRY!  Follow these basic steps to simplify problem solving.

1. What are your looking for?  Read through the problem and determine the exact units requested.

          WRITE THAT DOWN!

2. What are you given?  Sometimes, there is so much information given it is a good idea to write it all down or underline it in the problem.  It also helps if you will label what type of given information it is.  For instance:  mass, distance, …

3. Is there any other information you need?  Conversions, molar mass, reactions, …

4. Put the units together in such as way that you cancel out the units you don’t want and end up with only the units requested.  If the units are reversed, just flip your calculation.

Example #1

A farmer has 2 cows and he decides to change to chickens.  He can barter 4 emu for each cow, 3 emu for 5 pigs, 8 pigs for 3 llama,  a llama for 20 rabbits and 3 rabbits for 2 chickens.  How many chickens can he get for both his cows?

1. What are you looking for?  chickens

2. What are you given?  Many ridiculous ratios with animals.

3. Is there any other information needed?  Not for this problem, just watch out where you step.

4. Use UA to determine the units requested.

Example #2

A machine produces 4.5 x 10³ m of spaghetti noodles each minute. A package of noodles contains 128 noodles that are each 12.5 inches long.  The company sells the noodles in cartons containing 20 packages for $75.50.  If the machine runs 12.0 hr a day, 5 days a week, 50 weeks a year, how much money can the company make each year from that one machine?

Unit Analysis: Both Numerator & Denominator

Changing both the unit in the numerator and the denominator is just like changing only one set of units.  Just remember that all the units except the ones needed must cancel.

Change 3.40 m/sec to km/yr.

Unit Analysis: The Basics

Unit analysis or dimensional analysis is a method used to calculate values based on the units of each measurement.  We will start by using this method to simply convert one measurement in one unit to another unit. This technique may seem more complicated than necessary at this point, but remember you are learning how to use the units.  Later in the semester you will see that unit analysis will make problem solving so much easier!

Unit analysis is based on two very fundamental mathematical principles.

1. any number multiplied by one is equal to itself
2. a fraction equals one if the value of the numerator equals the value of the denominator

These two properties allow us to let the measurements determine how to do the calculation.  The final answer must have the units desired and all other units must be canceled.

Measurement, Part 2: Measurement & Uncertainty

There are two types of numbers in science: exact (counting) numbers and inexact (measurements and calculated quantities).  Exact or counting numbers represent objects.  For instance, a dozen eggs has exactly 12 eggs.  You can’t have 12.01 eggs.  Measurements and numbers based on calculations will always have some uncertainty. Significant digits are used to represent that uncertainty or the amount of confidence you have in a measurement.

Uncertainty occurs because we use equipment to make measurements.  You can only measure a length as exact as the increments on the ruler you are using.  Significant digits are the numbers we know with certainty plus one more that is estimated.

Basic Rules:

1. All non-zero digits are significant
2. All zeros between non-zero digits are significant
3. Zeros to the right of the decimal and to the right of a non-zero digit are significant
4. Zeros to the right of the decimal, but to the left of all non-zero digits are not significant
5. If there is no decimal, zeros to the right of the last non-zero digit are not significant

Rules for Calculations:

1. In addition and subtraction, use the LEAST number of DECIMALS.
2. In multiplication and division, use the LEAST number of SIGNIFICANT DIGITS.
3. Apply each rule using the order of operations.

Measurement, Part 3: Accuracy and Precision

Accuracy and precision are terms used to explain the sources of error in a data set.  Accuracy describes how close a measurement is to the correct answer. Precision describes the spread of the data or how close the measurements are to each other.

To determine the accuracy of a measurement, the correct or accepted value must be known.  The most common calculation associated with accuracy is percent error.

percent error = |(accepted value - experimental value)|   x   100

                                   experimental value

The precision of a data set can be determined in a number of ways, including range, standard deviation and percent deviation. Range is determined by subtracting the smallest value from the largest value in a data set.

Deviation literally means difference, so we can calculate it using subtraction.  By finding the difference between an individual measurement and the average of all the measurements in a data set, we can find how "off" that single measurements is from all the others. A very basic way of looking at standard deviation is to think of it as the average of all the deviations of the individual measurements from the average of the data set.  

The problem with simply using standard deviation to determine precision is magnitude (the size of the numbers.) A standard deviation of 1.00 may sound large or small without some idea of the magnitude of the measurements in the data set.  If your measurements range from 1.20 to 3.56, it is huge!  But if the range of the data is 1000.0 to 1002.0, it would be much more acceptable.

Percent compares the part to the whole, so it takes away the uncertainty of magnitude.  Percent deviation allows us to compare the standard deviation to the average of the data set.  The lower the percentage that each individual measurement differs from the average of the data set, the better the precision.

percent deviation = standard deviation  x  100

                                average of the data set

Measurement, Part 1: Introduction

All science is based on analyzing data. There are two types of data in chemistry. Qualitative data is based on descriptions such as color, state and luster. Quantitative data is based on numerical measurements.

Chemistry represents its quantitative data using the metric system.  Mass is measured in grams, volume in liters, length in meters, and temperature in Celsius or the Kelvin scale. EVERY QUANTITATIVE MEASUREMENT MUST HAVE BOTH A QUANTITY AND A UNIT.

Numbers mean nothing without a unit!