Stoichiometry

Stoichiometry

Significant Figures:

     Every measurement value has an uncertainty. The last digit of any measurement is usually an estimate. This last digit is the last significant figure in a number.

Measurement	Sigfigs	Measurement	Sigfigs
495g	3	0.25cm	3
206kM	3	0.05g	1
4000sheep	1	10.00 years	4

Atlantic/Pacific Rule (from a North American Perspective):

     When the decimal is Absent = Atlantic Rule. Start counting the number of Sigfigs from the Atlantic/Right side ignoring any initial zeros 

     When a decimal is Present = Pacific Rule. Start counting Sigfigs from the Pacific/ Left side also ignoring any initial zeros. 

SigFigs in Calculations:

     +/- 

eg.1       50.0mL  (tenths place)

         +  8.56mL  (hundredths place)

             59.16mL = 59.2mL        

When adding or subtracting measurements, round to the least accurate place value available. In this case the hundredths place is a more accurate measurement than the tenths place, therefore the answer should be rounded to the tenths place

eg.2       400g  (hundreds place)

         +  49.9g  (tenthss place)

             449.9g = 400g

     x/÷
When multiplying or dividing measurements, round to the least number of sigfigs.
eg.1       600.0(4sigfigs) ÷ 150 (2sigfigs) = 4.0 (2sigfigs)
eg.2       25.0 (3sigfigs) x 4.0 (2 sigfigs) = 100 = 1.0x10^2 (2sigfigs) (NOTE: the answer of 100 is not suitable in some cases because 100 only has 1 sigfig.)

Uncertainty in Calculations:
     When adding or subtracting equations, add the absolute uncertainties. These are the uncertainties (±

 values) that are added to the measurements in a equation. An absolute uncertainty is usually the error found in a measurement, measuring device or when reading the value on such device.
 eg.1       0.87 ± 0.01m

         -    0.30 ± 0.01m

               0.57 ± 0.02m

eg.2       T1 = 18.6 ± 0.2˚C                T2 = 23.9±0.3˚C

             What is the total change in temperature?  

             18.6 ± 0.2˚C

        -    23.9±0.3˚C

             5.3±0.5˚C    

     When multiplying or dividing equations, add the relative uncertainties. The uncertainty is found based on the size of the measurement. 

eg.1     Distance = 42.5 ± 5km

            Time = 16 ± 1 hour

Find Velocitty:

V =d/t

      Uncertainty: (5/42.5) + (1/16) = 0.074 = 7.4%

      Calculation: 42.5km/16hr = 26.5625km/h                26.5625 x 7.4% = ±1.859

                                             = 27 ± 1.86 km/h    

The Mole (N)

    The mole, also known as Avogardro's constant, is defined as 6.022 x 10^23 or simply as N_A.  The mole is just another unit used to measure quantity.

Relative Atomic Mass

     C-12 is defined as having a mass of exactly 12.000g per mole. The periodic tables gives the average atomic mass of each atom as well as the different isotopes (isotopes of an element have different amounts of neutrons). The relative atomic mass (Ar) add up to the relative molecular mass (Mr)

eg.1 Find the Mr of H2O:

1 - H: 2 - 1.01g/mol.

1 - O: 16g/mol

1.01+1.01+16 = 18.02g/mol 

eg.2 Find the mass of 1.8mol of CuO

1 - Cu: 63.5g/mol

1 - O: 16g/mol

63.5+16 = 79.5g/mol

1.83mol x 79.5g/mol = 145.6g = 146g

Empirical Formulas:

     Empirical formulas are the simplest or smallest whole number ratio of atoms within a compound.

eg.1 A samlpe of 100g of gas contains 50.1g of sulfer and 49.9g of oxygen. Find the empirical formula

S: 50.1g..................  50.1g x 1mol/32.06g = 1.56mol

O: 49.9g.................  49.9g x 1mol/16g = 3.12mol

1.56mol of S : 3.12mol of O

            simplified to

      1mol of S:2 mol of O

therefore the empirical formula would be  SO2 

Molarity (M):

     Molarity is a measure of concentration. It is a measure of how much 'stuff' is contained in a certain volume. For example if you have 'x' moles of sugar in a 300mL container this is more concentrated than having that same 'x' moles in a 1.2L container because the container would be less saturated with sugar. 

     Molarity or concentration is measured in MOLES/LITRE or written as c=n/v or as M=mol/L. Make sure the volume is always in litres. 

eg.1 What is the concentration of a solution with 0.0635mol NaCl in 452mL of H2O

C= n/v     C=0.0635mol/0.452L = 0.14mol/L  (notice how the volume is in Litres rather than milliliters

eg.2
How many grams of LiF are present in 300.0mL of a 4.62M solution?

To find the grams, you first need to the the number of mols in the compound

M=mol./L     mol=M x L    mol = 4.62M x 0.3L = 1.386mol = 1.4mol

Once the number of mols are found, simply multiply it by the molecular mass (Mr) to leave you with the number of grams

1 - Li: 6.94g/mol

1- F: 19g/mol

6.9+19 = 25.94g/mol

25.94g/mol x 1.386mol = 36.316g = 36.3g.

eg.3
2.476g of an oxide of copper is found to contain 2.199g of copper. Determine the emperical formula

2.476-2.199 = 0.277 oxide
0.277g x 1mol oxygen/16g = 0.0173 mol of oxygen

2.199g copper  x  1mol copper.63.5g = 0.0346 mol of copper

Cu0.0346 O0.0173      Divide by the smaller amount
Cu2O


Percent Composition:
     When given percentages:
1.Assume 100g of substances. percentage equals the number of grams
2. Convert grams to moles
3. Find smallest ratio of moles for each element

Eg.
What is the percent composition for C2H2O?

2 - C = 2mol x 12g/mol = 24g            24g/mol  ÷ 42g/mol = 57%
2 - H = 2mol x 1g/mol = 2g                  2g/mol  ÷ 42g/mol = 5%
1 - O = 1mol x 16g/mol = 16g            16g/mol  ÷ 42g/mol = 38%
                                         42g total mass

Molecular Formula:
     - multiples of empirical formulas.
           ex. if an empirical formula is C2H5
                a molecular formula could be C4H10

eg.1 A hydrocarbon contains 92.24% by mass of carbon and its Mr=78.1g/mol. Determine its molecular formula
        92.24 carbon           92.24g x 1mol ÷ 12g/mol = 7.6875
        7.76 hydrogen          7.76g x 1mol ÷ 1.01g/mol = 7.7683mol
                 C7.6875H7.7683 divided by the smallest number gives the empirical formula of:   CH

        1 x C = 12g/mol
        1 x H = 1g/mol   
                    13g/mol      -----> but the Mr = 78.1g/mol
SO 78.1g/mol  ÷ 13g/mol = 6
            6mols of ch -----> C6H6

eg. 2   56g of Fe reacts with 32g of S. what is the empirical formula.

     Fe = 56g ÷ 55.8g/mol = 1.0035mol = 1
     S = 32g ÷ 32.1g/mol = 99.68mol = 1
      Empirical formula is: FeS

Mole Ratios aka Balancing Chemical Equations
     Balancing chemical equations ensures that there is an equal number of a molecule on each side of a chemical equation. 

Number	÷ NA	= Moles	X Mole ratio	= Moles	X NA	Number
Mass	÷ Mr				X Mr	Mass
Volume	÷ 22.4				X 22.4	Volume

For example, if a mass is given, this needs to be converted into moles by dividing the relative mass.

eg.1     3Cu + 8 HNO3 1 --> 3CU(NO3)2 + 2NO + 4H2O
If 3 moles of CU react, 8 moles of HNO3 are needed and 2 moles of NO are produced. 
IF 4 moles of CU react then:
     HNO3 needed : (4mol of CU ÷ 1)  x (8HNO3 ÷ 3CU) = 10.7mol 
     NO Produced: (4mol of CU ÷ 1) x (2NO ÷3CU) = 2.6mol

eg. 2)  C3H8 + 5O2 --> 3CO2 + 4H2O  There are 3.5 Grams of C3H8, Find the mass of H2O.

     Mass C3H8 --> Moles C3H8 --> 3H2O --< Mass H2O

3.5g ÷ 44.11g/mol of C3H8 x (4H2O ÷1C3H8) x 18.02g/mol of H2O = 5.7g

 
Avogadro's Hypothesis:
     Avogadro's hypothesis was that 1 mol of any gas at the same emperature and pressure has the same volume as any other gas. At STP (Standard conditions for temperature and pressure) the molar volume is 22.4L/mol. From the IB chemistry data book, it is seen that the standard temperature is 0˚C or 273K. Standard pressure is 1atm (atmosphereic pressure) which is equivilant to 101.3kPa or 1.01 x 10^5 Pa.