Calculating the Empirical and Molecular Formula and Percent Composition

There are two kinds of formulas that we can express in chemistry "11".   The empirical and molecular formula.

The Empirical Formula


-Gives the lowest terms of atoms OR moles.
-All formulas of ionic components are empirical formulas.

The Molecular Formula


-Gives all atoms which make up a molecule.
-This can be ionic or covalent compounds.


EG: C6H12O6

To put it into empirical formula, reduce to lowest terms.  Therefore C6H12O6 = CH2O(empirical).

Remember: 1) molecular  = empirical x whole #
2) molecular formula mass = empirical x whole #
3) mass(mole) = EFM(g) x whole #

How to determine empirical formula given mass


EX: Determine the empirical formula of Fe and O given 10.87g of Fe and 4.66g of O.

1) Convert grams ------> moles

10.87 x 1/55.8g = 0.1948 mol
 4.66 x 1/16.0g = 0.0291 mol

2) Divide each molar amount by the smallest molar amount.

Fe 0.1948/0.1948 = 1
O 0.291/0.1948 = 1.49 ~ 1.5

3) Scale ratios to whole #'s by multiplying.

1.5 x "2" = 3(whole number)
1 x "2" = 2(whole number)


Therefore, the empirical formula is Fe2O3

PERCENT COMPOSITION


- The % by mass of the elements in a compound.
                -calculate molar mass.
                -calculate each element's % of that total(ONE DECIMAL PLACE)
This tells what part of a compound each component element makes up.

Remember: %composition = mass of element/mass of compound x 100%


The ratio of moles can be determined from percent composition.  How?

1)Assume 100.0g of all material
2)Convert all %'s to grams.
3)Follow the steps to solve empirical formula.

The Mole

• Scientists in early days found masses for hydrogen, oxygen and carbon dioxide.
• Discovered that equal volumes of different gases have a constant ratio. For example, oxygen : hydrogen 16:1

Relative Mass

• Is expressed by comparing it mathematically to the mass of another thing.
• Hydrogen and oxygen were used as standard for comparison.
• Now, carbon is used as standard. Assigned "12" amu therefore the mass of 1 atom = 1/12 the mass of carbon.

Avogadro's Hypothesis

• Equal volumes of different gases at the same temperature and pressure have the same number of particles. Which means that their mass ratio is due to mass of the particles.

Formula Mass

• All atoms of a formula is ionic (in amu)

Molecular Mass

• All atoms of formula in a covalent compound (in amu)

Molar Mass

• Mass of one mole of each element (in g/mol)
• The atomic/ molecular/ formula mass of any pure substance
• Eg. 1 mole of oxygen = 16.0g/mol ALL OF THESE HAVE THE SAME NUMBER OF PARTICLES.

Avogadro's Number

• The number of particles in a mole of any amount of substance
• 6.022 x 10^23 particles/ mole
• Is a counting unit like a dozen.
• Eg. A mole of atoms equals 6.022 x 10^23 atoms.

Lab 2E Determining Aluminum Foil Thickness

  During this lab. We learn how to get the value of some tiny measurements. For example, it's hard to measure the thickness of a Aluminum Foil's thickness. Therefore, we use the density and volume formula to calculate it. The density of aluminum is 2.70g/cm^3

     1. measure the length and width of each piece of foil. Record the measurements in th table we made.
     2.use a centigram balance to find the mass of each piece, record the mass.
     3.use the density fomula d=m/v, change it to v=m/d to get the volume of the foils
     4.use height=volume/width·length to get the thickness.

Here is an example of our calculation.

v=m/v=0.98g/2.70g/cm^3=0.363 cm^3
h=v/wl=0.363cm^3/15.47cm x 15.14cm=1.55 x 10^-3 cm


In this lab, we learn that not all the measurements need to be measured directly. We can use formula and other things to calculate it. It's easier and more accurate.

Graphing

As we all know : Density = mass/volume
In order to draw a " mass vs volume " graph, we have to consider volume as the dependent variable and mass is the independent one.
So , the x axis contains volume and y contains mass.
The slope of an straight line = rise / run = y / x = volume / mass
If we are to find the density , density will equal to 1/ slope = mass / volume

Here's how to make a graph by Microsoft Excel to save more times.
1. Open Excel then click on INSERT tab

2. Choose Scatter graph ( scatter with only markers )
3. Then the graph panel appears, right click on the graph, choose " Select Data"

4. Click " Add"

5. Enter the value for X and Y then click OK
6. Here we have a graph

7. Click on " Layout " tab then choose trendline --> then choose linear trendline to get the line of best fit

8.If you want to have the computer calculated the line's slope, click on trendline button again --> trendline option --> tick on the " Display Equation on chart " in the bottom of the panel.
9.Now we have finished the mass vs. volume graph! As I mentioned on top, density = 1/slope

Density

Density - The density of a material is defined as its mass per unit of volume.

Equation - mass/volume  (MEMORIZE THIS EQUATION)


Units
-For a solid, the unit is g/cm^3
-For a liquid, the unit is g/mL, Kg/L


1 cm^3 water = 1mL water
The density of water is 1000g/L or 1.0g/mL


Remember--> density of object > density of liquid = sink


density of object < density of liquid = float.

       

Measurement and Uncertainty

• No measurements are exact; there is always some degree of uncertainty. For example, 13.995m.
• The only time when we are "certain" about a measurement is when we count. For example, 31 people.

Absolute Uncertainty

• Expressed in units of measurement.
• Method 1: Make at least three measurements and calculate the average. You should disregard the measurement that is farthest apart from the rest of the other measurements before you calculate average. The absolute uncertainty is the largest difference between the average and the lowest or highest reasonable answer.
• Method 2: Determine the uncertainty of each instrument you're using. Always make the measurement to the best precision that you can. Therefore, you should estimate to fraction 0.1 of the smallest segment on the instrument scale.

On a ruler, the smallest division is 1mm. The best precision is to break this into 10 equal pieces = 0.1mm.

Relative Uncertainty = Absolute Uncertainty/ Estimated measurement

• Can be expressed as a percentage or in sig figs

Accuracy and Precision

In this class, for those of the people in physics, we reviewed accuracy and precision followed by significant digits.

Precision - how reproducible a measurement is compared to other similar measurements

EG: bounces of a basketball on one spot

Accuracy - how close the measure(or average measurement) comes to the accepted or real value.

EG: 2 + 2 = 4 (not 4.1 or 4.2 etc)

SIGNIFICANT FIGURES


-measured or meaningful digits
-more precise = more significant digits
-The last digit is considered uncertain(it could be one digit higher or lower).
-Includes all certain digits and the first uncertain****

Note: Leading 0's are not counted

EG: 0.00000000005 <--- only one significant digit
-Trailing 0's are counted

EG: 10.9029000
-If there is a decimal, count the zero as a significant digit.


EG: 100000.

EXACT NUMBERS


-Some quantities are defined exactly a certain amount and no rounding is required
-Exact numbers have an infinite amount of sig figs.


ROUNDING RULES


1) Look at the digit after the position of rounding
2) If >5 round up
3) If <5 keep it the same
4) If = 5 and more non-zero digits, round up
5) If = 5 and ends at five, round to make it even.

MATH RULES FOR SIG FIGS


-When adding or subtracting, round to the fewest number of decimals.
-When multiplying or dividing, round to the fewest number of sig figs.

MULTIPLYING AND DIVIDING

- When multiplying and or dividing, round to the fewest number of sig figs

E.g. 12.54 x 1.3 = 16.302 <-- you must round that to 16.30.

12.540/1.3 = 9.64 <-- you must round to 2 sig figs (2<4) or the first uncertain digit.