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Multiple conversions between mass, volume and number of particles


Find the number of atoms in a given number of molecules.( two steps)

Step a) Count the number of atoms in one molecule.
Step b) Multiply the number of molecules


Example 1:
How many atoms are in 3 molecules of (NH4)2SO4

a) the number of atoms in 1 molecule.
N: N×2=2
H: H×4×2=8
S: S×1=1
O: O×4=4
Total atoms in 1 molecule has 2+8+1+4=15
b) there are 3 molecules 15×3=45
Therefore, there are 45 atoms in 3molecules of (NH
4)2SO4

Find a part of atoms in a given number of molecules.
Step a) Count the number of the atoms that you need to find in 1 molecule.
Step b) Multiply the number of molecules.

Example 2:
How many hydrogen atoms are in 3 molecules of (NH4)2SO­4

a) H: H×4×2=8
Total atoms in 1 molecule of hydrogen atoms are 8
b) there are 3 molecules 8×3=24
Therefore, there are 24 hydrogen atoms in 3 molecules of (NH
4)2SO2­of molecules.


single step conversion

conversion
Conversion factor
Moles ←→ Number of particles
6.02×10^23particles/1 mole
1 mole/6.02×10^23 particles

Moles ←→ Mass
(molar mass)g/1 mole
1 mole/(molar mass)g

Moles ←→ Volume (gases at STP)
22.4L / 1 mole
1 mole/ 22.4L

Molecules ←→Atoms
(atoms count)atoms/1 molecule
1 molecule/(atoms count)atoms


Example:
1) How many molecules are there in 5 moles of molecules?
number of molecules= 5 moles ×(6.02 ×10^23 particles/1 mole) = 3.01×10^24 molecules

2) What is the mass of H
2O in 3 moles?
1) Molar mass of H
2O= 2H=2×1.0=2.0g, 1O=1×16.0=16.0g 2.0g+16.0g=18.0g
2) number of mass of H
2O= 3 moles ×(18.0gH2O/1moleH2O)=54.0gH2O

3) What is the volume occupied by 0.5 mol of SO
2 (g) at STP?
number of litres =0.5mol SO
2 ×(22.4L SO2/1mol SO2)=12.2L SO2

4) How many atoms are there in 7 molecules of H3PO4?
number of atoms =7 molecules H
3PO4×(8 atoms of H3PO4/1 molecule H3PO4)=56 atoms H3PO4







In the calculations, some questions should use conversions more than once; however, mole is in the centre, because all conversions between mass, particles and volume should be converted to mole at first.
These are some general calculations steps.
Particles ←→ mass:

Convert particles ←→ moles(using 6.02×10^23/1 mole) ←→ mass( using molar mass/1 mole)
Particles ←→ volume:
Convert particles←→ moles(using 6.02×10^23/1 mole) ←→ volume(using 22.4L/1 mole at STP)

Mass to volume:
Convert mass←→ moles(using molar mass/1 mole) ←→ volume(using 22.4L/1 mole at STP)

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Example 1:
What is the volume occupied by 40.0g of O2 (g) at STP
Plan: convert Mass to Moles then to Volume
mass×(1 mole/ molar mass)×(volume/ 1 mole)
1) molar mass: 2O: 2×16.0g= 32.0g O
2

2) 40.0g O2 ×(1 mole O2 / 32.0g O2)×(22.4L O2/ 1 mole O2)=28.0L O2

Example 2:
What is the mass of 3.00×10^18 atoms of Fe?
Plan: convert # of atoms to Moles then to Mass
mass= number of atoms ×(1 mole/ 6.02×1023 atoms) ×(molar mass/ 1 mole)
1) Molar mass: 1Fe= 1×55.8g= 55.8g Fe
2) Mass=3.00×10^18 atoms Fe×(1 mole Fe/6.02×10^23 Fe)×(55.8g Fe/1 mole Fe)=2.78g Fe



22.4L/1 mole used all refer to gases at STP, but if the density is mentioned at a point in a problem, we should use d=m/v.( three situation)

a) if the density is mentioned at a point in a problem, we should use d=m/v.
b) If the volume of a solid or liquid is unknown, calculate the volume from v=m/d
c) If the mass is unknown, calculate the mass from m=v×d



Example 1:
What is the volume occupied by 4.00 mole of Al203? (d=3.97g/ml)
Hint : density relates to volume to mass, mass is relates to moles.
number of ml= mole ×(molar mass/1 mole)×(1 ml/3.97g)
1) Molar mass:2Al=2×27.0g=54.0g, 3O=3×16.0g=48.0g 54.0g+48.0g=102.0g
2) number of ml= 4.00ml Al203×(102.0g Al203/1 mol Al203)×(1 ml Al203/3.97g Al203)=102.8ml Al203



Example2:

How many atoms of Al are in 200 ml of Al2O3? (d=3.97g/ml)
Plan: convert volume to mass, then to moles, then to Avogadro’s number, finally to number of atoms
number of atoms= volume×density×(1mole/molar mass)×(6.02×10^23 molecule/1 mole) ×(atoms count/1 molecule)
number of atoms=200ml×(3.97g/1ml)×(1mole/102.0g)×(6.02×10^23molecules/1mole)×(2Al atoms/1 molecule)=9.37×10^23 atoms