There are many devices & units that are used to quantify properties of matter
All measuring devices are limitedin their accuracy
To communicate the accuracy of a measurement, we used significant figures(or digits)
All counted values are significant(in essence, meaningful) figures (or sig fig for short)
Significant figures, when using a measuring device,are all of the values that can be read off of the device, as well as one that is estimated
Even with electronic measurement devices, the last digit is an estimate
Sig Fig Rules
All non-zero digits are significant
321 has 3 sig fig because none of the digits are 0
Zeros in between non-zero digitsare significant
301 has 3 sig fig because the 0 is between 3 and 1, which are both non-zero
Leading zeros are not significant
0.0321 has 3 sig fig - the two zeros are placeholders and aren't significant
Trailing zeros are only significantwhen there is a decimal
3210 has 3 sig fig because the zero at the end is a placeholder
321**.**0 has 4 sig fig because the zero at the end is measured and is not a placeholder as it tells us more about the quantity
A and P Method:
If the decimal is Absent, start counting sig figs from the first non-zero digit starting from the right side(AKA the Atlantic side)
40200 ⇐ right side, start at the first non-zero digit –– 3 sig fig
If the decimal is Present, start counting sig fig from the first non-zero digit starting from the left side(AKA the Pacific side)
Left side, start at the first non-zero digit ⇒ 0.0420 –– 3 sig fig
All digits written in scientific notation are significant!!
Scientific notationis a way of expressing values with exponents - very bigor very smallnumbers are expressed this way
Always move the decimal point so that it is one digit in from the side with the non-zero digits
Eg. 34000000⇒ 3.4 x 10⁶
Eg. 0.0000034 ⇒ 3.4 x 10⁻⁶
Adding and subtractingwith significant figures
Cannot be more accurate than the least accurate measurement
When adding or subtracting values, the answer will have the same number of digits after the decimal as the least accurate measurement
Chop offwhat is more accuratethan the least accurate measurement
Chop it off, you can't calculate a number you don't have!!!
Multiplying and dividingwith significant figures
The sig fig in the answer from multiplying and dividing measured values have the same number of total sig figs as the value with the leastamount of sig figs in the question
Chop offdigits that have more than the least amount of sig figs in the question
Rounding Rules
Values between 1 and 4, round down
Eg. round 52.36 to 2 sig fig ⇒ 52
Values between 6 and 9,round up
Eg. round 52.74 to 2 sig fig ⇒ 53
Values with a 5 will round to the nearest EVEN value
Round 52.51 to 2 sig fig ⇒ 52 (because it's nearer than 54)
Round 53.57 to 2 sig fig ⇒ 54 (because it's nearer than 52)
Many calculations involve converting, from one unit to another, for many purposes
These require conversion factors& can be organized using the factor label method, which is also called dimensional analysis
Conversion factor: a relationship between one unit and another unit
Factor label method can be broken into 3 steps:
Write the name or unit of the quantity that you're looking for& an equal sign; this is your target
Write the given value that you have to begin with
Multiply the given value by conversion factorsarranged so that the given units are cancelled (divided out) and the target unit remains
Conversion factors can be multiplied together in the same equation, if more than one is needed to reach your target unit!
You can add as many conversion factors “blocks” if it helps you “build a road” to your target unit
Benefits of using this method:
You don't have to remember as many formulas
You keep your units organized & make fewer mistakes as a result
Can be applied to many subjects like chemistry, physics, math, phone bill, and more
In chemistry, quantities like mass & volume are measured in units like grams and litres
Tiny particles, like atoms & molecules are measured relative to each other, in atomic mass units, or amu, using a mass spectrometer
On paper, we balance equations using particles, but in the lab we can only measure large units like masses & volumes
THE MOLE IS A BRIDGE BETWEEN THESE TWO KINDS OF MEASUREMENTS
Quantities of invisible tiny particles Quantities of measurable amounts
like molecules and atoms ⟺ like mass and volume
Mole logic
If you know the relative mass of 2 items, then you can always determine when you have equal quantities of both
For instance: a helium atom has 4 times the mass of a hydrogen atom. What mass of helium has the same number of atoms as 5.0 g of hydrogen?
If each helium is4x the mass of hydrogen, and we have 5 gramsof it, 4x5=20, so 20.0g heliumwill have the same number of atoms
Molar mass
There are the same number of atoms in the mass of an element represented by the average atomic mass of an element measured in grams
This is one mole of the element
For compounds: just add the mass of each element in the compound together
Eg. what is the mass of 15.5 moles of carbon dioxide (C = 12, 0 = 16 (x2) – 44 g)
Mass = 15.5 mol = 44 g = 682g Use factor label method!
1 mol
Avogadro's number
The quantity of particles in a mole is named after Avogrado, who discovered that equal volumes of gases must contain the same number of particles
This quantity of particles in the mass elements on the periodic table turns out to be:
6.02 x 1023particles/mol
Avogrado determined that equal quantities of gas occupy the same volume under standard temperature & pressure
Under standard temperature & pressure, one mole of any gas occupies 22.4 L
Mole map
Note: not all substances are made of molecules!The particles that make up most elements are atoms. Ionic compounds are a repeating pattern of ions, the smallest of which can be called a formula unit.
The formula of a compound gives the ratio (proportion of particles) of atoms present
Using the mole concept, a formula can also give you the percentage of massof each element in a compound
Eg. One mole of water (H2O -- 18g/mol) contains 2 moles of Hydrogen (1g/mol + 1g/mol = 2g/mol) and 1 mole of Oxygen (16g/mol)
General formula to find the percent mass of something
Grams of element you're looking for x 100% = % of element you were looking for
Grams of the compound you have
An empirical formula is the lowest whole number ratio of elements in a compound
Theempirical formula can be determined by working backwards from the percentage mass data to find the ratio of element moles
Steps
Find moles of each element
Convert to lowest whole number ratio
MASS → MOLES → LOWEST WHOLE NUMBER RATIO
Always assume you have 100gif grams aren't given so that you have an easy starting point
Eg. a sample was found to contain 50% sulfur and 50% oxygen by mass - what is the empirical formula?
Then, you can see that the formula created is SO2because the lowest wholesrepresent the quantities of the elements in the formula
Sometimes...the moles of each element do not give you a nice even whole number,and you'll need to multiply to find the best ratio
For aratio of 1:1.5 ⇒ multiply by 2 to get 2:3
For a ratio of 1:1.333⇒ multiply by 3 to get 3:4
For a ratio of 1:1.25⇒ multiply by 4 to get 4:5
Sometimes, the percentages are not given- masses need to be found in another way….
Eg. a 50.51 g sample of a compound made from iron and oxygen is decomposed, and 35.36 g of the iron remains. Find the empirical formula
Mass Moles Lowest whole
Fe: 35.36 x 1 mol Fe =0.6331 mol ⇒ 1 x 2
55.85 g 0.6331O: 50.51-35.36 = 15.15 x 1 mol O = 0.9469 mol ⇒ 1.5 x2
(subtract whole sample 16 g 0.6331
from Fe which was also
given)
A molecular formula is not always the lowest whole number ratio
In order to determine the molecular formula, you can divide the empirical molar mass into the molecular molar mass and then multiply the empirical formula by the same factor
Eg. If the empirical formula of a molecule is CH3and the molar mass of the compound is 30 g/mol, what is the molecular formula?
The empirical formula & formula of a molecule are different, & the empirical formula may not be the same formula for the compound
Balanced equationsmake sure that the number of atoms of each elementare the same on each side of an equationby adding coefficients
Since a mole is simply a large number of particles, we can use moles in the same way as we would use particles in a balanced equation
Eg.
2H2 + O2 → 2H2O
2particles H2+ 1particle O2 → 2particles H2O
2moles H2 + 1mole O2 → 2moles H2O
Mole ratio:the coefficients from the balanced equation can be used to convert between moles consumed and moles produced in a reaction
Use factor label method
Eg. If 5.0 moles of Hydrogen are consumed, how many moles of oxygen are also consumed?
Moles O2= 5.0 mol H2x 1 mol O2= 2.5 mol O2
2 mol H2
Eg. if 5.0 moles of oxygen are consumed, how many moles of water are produced?
Moles H2O = 5.0 mol O2x 2 mol H2O = 10.0 mol H2O
1 mol O2
Use the quantities from the balanced equation (equivalent in moles) to calculate what you need
Stoichiometry: involves 3 stepsto determine the quantity involved in a chemical reaction
Convert given quantity to moles
Convert given moles to moles of the quantity that you want (target, whatever you’re asked for)
Convert the target moles to the unit you want
Eg. Quantity consumed: what mass of oxygenis consumed when reacting with 5.0 g of Hydrogen?
2H2+ O2→ 2H2O
Steps
Step 1 - convert into moles
Moles H2= 5.0 g H2x 1 mol H2= 2.5 mol H2
2g
Step 2 - convert the given moles to the moles of the quantity you want (target)
Moles O2= 2.5 mol H2x 1 mol O2 = 1.25 mol H2
2 mol H2
Step 3 - convert target moles to the unit you want
Mass O2= 1.25 mol O2,x 32g = 40 g O2
1 mol
Putting it all together:
Mass O2 = 5.0 H2x 1 mol H2 x 1 mol O2 x 32g = 40 g O2
2g 2 mol H2 1 mol O2
Generalized formula
[target unit] [target element/compound] = [given amount of given e/c] x [1 mol/molar mass of given e/c] x [quantity of target e/c in balanced equation/quantity of given e/c in balanced equation] x [conversion factor to get into target units]
Always 3 steps!
Expanded map
A chemical reaction is like a factory with input components (reactants) and output (products)
If one of the reactants runs out, the reaction will then stop
Therefore, that reactant then controls how much product can be made
The reactant that runs out = the limiting reagent
The leftover reactant = the excess reagent
Whenever you have more than one quantity of a reactant, you will need todetermine the limiting reagent before any other quantities can be found
Finding the limiting reagent:
Convert the reactant quantities into moles (given amt x 1mol/molar mass of given)
Divide what you get by the coefficient in the balanced equation
The smaller value is the limiting reagent
Eg) if 3.0g of H2reacts with 6.0g of O2
2H2+O2→ 2H2O
H2: O2:
3.0g H2x 1 mol = 1.5mol H= 0.75 6.0g O2x 1 mol= 0.25 = 0.25
2g 2 32g 1
0.25 is smaller than 0.75 ∴ O2 is the Limiting Reagent
Product Yield
Yield = the quantity of a product that can be expected to be made
Eg) What mass of water can be formed from 3.0g of H2reacting with 6.0g of O2?
*********you need to use the limiting reagent to solve this question!!!
MassH2O = 6.0g O2x 1 mol O2x 2 mol H2O x 18g H2O = 6.8g H2O
(yield) ↑ 32 g 1 mol O2 1 mol
Given quantity LR ↑ ↑ ↑
1 mol/molar mass target/given target molar mass
of LR equation to get into grams
coefficients
Excess Reagent: what mass of excess reactant remains from 3.0g of H2reacting with 6.0g of O2?
*******you also need to use the LR here too
MassH2 = 6.0g O2 x 1 mol O2 x 2 mol H2 x 2gH2 = 0.75g H2
(used) ↑ 32g 1 mol O2 1 mol
Given quantity LR ↑ ↑ ↑
1 mol/molar mass target/given target molar mass
of LR coefficients to get into g
Remaining H2= 3.00g - 0.75g = 2.25g
↑ ↑
Given Used
amount amount
Yield = the amount of product that is produced in a chemical reaction
Theoretical yield = maximum amount of product that is possiblefrom a calculation
Actual yield = the amount of product that was actually collected from the real, actual experiment
Percentage yield = Actual yield x 100%
Theoretical yield
Why isn't the yield always 100%
Incomplete reactions (like incomplete combustion)
Side reactions (where more than one reaction occurs)
Experimental error (your experiment wasn't set up optimally)
Purity
Purity = how much of a given sample is actually one substance
It can be expressed as a percentage
Percentage purity = Mass of a pure substance x 100%
Total mass of a sample
Percentage Error
Error percentage = a measure of the difference between a measured value and a known/accepted value
This percentage is often used in labs to quantify the closeness that an experiment comes to producing the expected value
Percent error = |Experimental value - Accepted value| x 100%
Accepted value
