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The equation can also be used to calculate mass and molar mass, using the following equations:

m = n × M

and

M = m n

The following diagram may help to remember the relationship between these three variables. You need to imagine that the horizontal line is like a 'division' sign and that the vertical line is like a 'multiplication' sign. So, for example, if you want to calculate 'M', then the remaining two letters in the triangle are 'm' and 'n' and 'm' is above 'n' with a division sign between them. In your calculation then, 'm' will be the numerator and 'n' will be the denominator.

Calculate the number of moles of copper there are in a sample that weighs 127 g .

  1. n = m M
  2. n = 127 63 , 55 = 2

    There are 2 moles of copper in the sample.

You are given a 5 mol sample of sodium. What mass of sodium is in the sample?

  1. m = n × M
  2. M Na = 22 , 99 g · mol - 1

    Therefore,

    m = 5 × 22 , 99 = 114 , 95 g

    The sample of sodium has a mass of 114 , 95 g .

Calculate the number of atoms there are in a sample of aluminium that weighs 80 , 94 g .

  1. n = m M = 80 , 94 26 , 98 = 3 moles
  2. Number of atoms in 3 mol aluminium = 3 × 6 , 022 × 10 23

    There are 18 , 069 × 10 23 aluminium atoms in a sample of 80 , 94 g .

Some simple calculations

  1. Calculate the number of moles in each of the following samples:
    1. 5 , 6 g of calcium
    2. 0 , 02 g of manganese
    3. 40 g of aluminium
  2. A lead sinker has a mass of 5 g .
    1. Calculate the number of moles of lead the sinker contains.
    2. How many lead atoms are in the sinker?
  3. Calculate the mass of each of the following samples:
    1. 2,5 mol magnesium
    2. 12 mol lithium
    3. 4 , 5 × 10 25 atoms of silicon

Molecules and compounds

So far, we have only discussed moles, mass and molar mass in relation to elements . But what happens if we are dealing with a molecule or some other chemical compound? Do the same concepts and rules apply? The answer is 'yes'. However, you need to remember that all your calculations will apply to the whole molecule . So, when you calculate the molar mass of a molecule, you will need to add the molar mass of each atom in that compound. Also, the number of moles will also apply to the whole molecule. For example, if you have one mole of nitric acid ( HNO 3 ), it means you have 6 , 022 × 10 23 molecules of nitric acid in the sample. This also means that there are 6 , 022 × 10 23 atoms of hydrogen, 6 , 022 × 10 23 atoms of nitrogen and ( 3 × 6 , 022 × 10 23 ) atoms of oxygen in the sample.

In a balanced chemical equation, the number that is written in front of the element or compound, shows the mole ratio in which the reactants combine to form a product. If there are no numbers in front of the element symbol, this means the number is '1'.

e.g. N 2 + 3 H 2 2 N H 3

In this reaction, 1 mole of nitrogen reacts with 3 moles of hydrogen to produce 2 moles of ammonia.

Calculate the molar mass of H 2 SO 4 .

  1. Hydrogen = 1,008 g · mol - 1 ; Sulphur = = 32,07 g · mol - 1 ; Oxygen = 16 g · mol - 1

  2. M ( H 2 S O 4 ) = ( 2 × 1 , 008 ) + ( 32 , 07 ) + ( 4 × 16 ) = 98 , 09 g · mol - 1

Calculate the number of moles there are in 1 kg of MgCl 2 .

  1. n = m M
    1. Convert mass into grams
      m = 1 kg × 1 000 = 1 000 g
    2. Calculate the molar mass of MgCl 2 .
      M ( MgCl 2 ) = 24 , 31 + ( 2 × 35 , 45 ) = 95 , 21 g · mol - 1
  2. n = 1000 95 , 21 = 10 , 5 mol

    There are 10 , 5 moles of magnesium chloride in a 1 kg sample.

Barium chloride and sulphuric acid react according to the following equation to produce barium sulphate and hydrochloric acid.

BaCl 2 + H 2 SO 4 BaSO 4 + 2 HCl

If you have 2 g of BaCl 2 ...

  1. What quantity (in g) of H 2 SO 4 will you need for the reaction so that all the barium chloride is used up?
  2. What mass of HCl is produced during the reaction?
  1. n = m M = 2 208 , 24 = 0 , 0096 mol
  2. According to the balanced equation, 1 mole of BaCl 2 will react with 1 mole of H 2 SO 4 . Therefore, if 0 , 0096 mol of BaCl 2 react, then there must be the same number of moles of H 2 SO 4 that react because their mole ratio is 1:1.

  3. m = n × M = 0 , 0096 × 98 , 086 = 0 , 94 g

    (answer to 1)

  4. According to the balanced equation, 2 moles of HCl are produced for every 1 mole of the two reactants. Therefore the number of moles of HCl produced is ( 2 × 0 , 0096 ), which equals 0 , 0096 moles .

  5. m = n × M = 0 , 0192 × 35 , 73 = 0 , 69 g

    (answer to 2)

Group work : understanding moles, molecules and avogadro's number

Divide into groups of three and spend about 20 minutes answering the following questions together:

  1. What are the units of the mole? Hint: Check the definition of the mole.
  2. You have a 56 g sample of iron sulphide ( FeS )
    1. How many moles of FeS are there in the sample?
    2. How many molecules of FeS are there in the sample?
    3. What is the difference between a mole and a molecule?
  3. The exact size of Avogadro's number is sometimes difficult to imagine.
    1. Write down Avogadro's number without using scientific notation.
    2. How long would it take to count to Avogadro's number? You can assume that you can count two numbers in each second.

Khan academy video on the mole - 1

More advanced calculations

  1. Calculate the molar mass of the following chemical compounds:
    1. KOH
    2. FeCl 3
    3. Mg(OH) 2
  2. How many moles are present in:
    1. 10 g of Na 2 SO 4
    2. 34 g of Ca(OH) 2
    3. 2 , 45 × 10 23 molecules of CH 4 ?
  3. For a sample of 0,2 moles of potassium bromide ( KBr ), calculate...
    1. the number of moles of K + ions
    2. the number of moles of Br - ions
  4. You have a sample containing 3 moles of calcium chloride.
    1. What is the chemical formula of calcium chloride?
    2. How many calcium atoms are in the sample?
  5. Calculate the mass of:
    1. 3 moles of NH 4 OH
    2. 4,2 moles of Ca ( NO 3 ) 2
  6. 96,2 g sulphur reacts with an unknown quantity of zinc according to the following equation: Zn + S ZnS
    1. What mass of zinc will you need for the reaction, if all the sulphur is to be used up?
    2. What mass of zinc sulphide will this reaction produce?
  7. Calcium chloride reacts with carbonic acid to produce calcium carbonate and hydrochloric acid according to the following equation: CaCl 2 + H 2 CO 3 CaCO 3 + 2 HCl If you want to produce 10 g of calcium carbonate through this chemical reaction, what quantity (in g) of calcium chloride will you need at the start of the reaction?

Questions & Answers

how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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The fundamental frequency of a sonometer wire streached by a load of relative density 's'are n¹ and n² when the load is in air and completly immersed in water respectively then the lation n²/na is
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Properties of longitudinal waves
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Source:  OpenStax, Siyavula textbooks: grade 10 physical science [caps]. OpenStax CNX. Sep 30, 2011 Download for free at http://cnx.org/content/col11305/1.7
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