2-كتالوج اجهزة تجاليل المياه والهندسة الصحية النظرى(الحسابات والتحويلات الكيميائية)

Chemical definition & calculations

Molecular Mass (Molecular Weight, Formula Mass, Formula Weight)
Molecular Mass (Molecular Weight)

In theory, the relative molecular mass or molecular weight of a compound is the mass of a molecule of the compound relative to the mass of a carbon atom taken as exactly 12.

In practice, the molecular mass, MM, (molecular weight, MW) of a compound is the sum of the atomic masses (atomic weights) of the atomic species as given in the molecular formula.

In theory we can only refer to the Molecular Mass or Molecular Weight of a covalent compound since only covalent compounds are composed of molecules.
Formula Mass (Formula Weight)

The relative formula mass, FM, (formula weight, FW) of a compound is the sum of the atomic masses (atomic weights) of the atomic species as given in the formula of the compound.

Formula Mass (Formula Weight) is a more general term that can be applied to compounds that are not composed of molecules, such as ionic compounds.

Percent Composition (Percentage Composition)
Key Concepts

The percent composition (percentage composition) of a compound is a relative measure of the mass of each different element present in the compound.

To calculate the percent composition (percentage composition) of a compound

Calculate the molecular mass (molecular weight, formula mass, formula weight), MM, of the compound
Calculate the total mass of each element present in the formula of the compound
Calculate the percent compositon (percentage composition): % by weight (mass) of element
= (total mass of element present ÷ molecular mass) x 100

Definitions of a mole

Key Concepts

Mole is abbreviated to mol and given the symbol n

1 mole contains the same number of particles as there are in 12g of carbon-12 atoms by definition.

This number is called Avogadro's number or Avogadro's constant (NA) and is equal to 6.022 x 1023 particles.

1 mole of a pure substance has a mass in grams equal to its molecular mass (MM) [also known as molecular weight (MW) or formula mass (FM) or formula weight (FW)].

This is often referred to as the molar mass.

1 mole of an ideal gas has a volume of:
22.4 litres (22.4L) at S.T.P.

[Standard Temperature and Pressure, 0oC (273K) and 101.3kPa (1 atm)]
24.47 litres (24.47L) at S.L.C

[Standard Laboratory Conditions, 25oC (298K) and 101.3kPa (1atm)]
Mass-Mole Calculations (n = mass ÷ MM)

Key Concepts

1 mole of a pure substance has a mass equal to its molecular mass (MM)
So 2 moles would have a mass = 2 x MM
3 moles would have a mass = 3 x MM etc
This leads to the formula: mass = n x MM
mass is in grams,
n = moles of pure substance,
MM = molecular mass of the pure substance

This formula can be rearranged to give the following:
n = mass ÷ MM
MM = mass ÷ n
Concentration of Solutions Calculations (M = n ÷ V)

Key Concepts

The concentration of a solution is usually given in moles per litre (mol L-1 OR mol/L).

This is also known as molarity.

Concentration, or Molarity, is given the symbol M.

A short way to write that the concentration of a solution of hydrochloric acid is 0.01 mol/L is to write [HCl]=0.01M
The square brackets around the substance indicate concentration.

M = n ÷ V
M = concentration of solution in mol/L,
n = moles of substance,
V = volume of solution in litres (L)
This formula can be re-arranged:
n = M x V
V = n ÷ M
Dilution of Solutions Calculations (M1V1=M2V2)

Key Concepts

The concentration of a solution is usually given in moles per litre (mol L-1 OR mol/L).

This is also known as molarity.

Concentration, or Molarity, is given the symbol M.

A short way to write that the concentration of a solution of hydrochloric acid is 0.01 mol/L is to write [HCl]=0.01M

The square brackets around the substance indicate concentration.

The solute is the substance which dissolves.

The solvent is the liquid which does the dissolving.

A solution is prepared by dissolving a solute in a solvent.
When a solution is diluted, more solvent is added to it.

Since M = n ÷ V, and n (the moles of solute) is the same for the original solution and the new diluted solution, it follows that M1V1 = M2V2
where M1=original concentration of solution
V1=original volume of solution
M2=new concentration of solution after dilution
V2=new volume of solution after dilution
To calculate the new concentration (M2) of a solution given its new volume (V2) and its original concentration (M1) and original volume (V1):
M2 = (M1 x V1) ÷ V2
To calculate the new volume (V2) of a solution given its new concentration (M2) and its original concentration (M1) and original volume (V1):
V2 = (M1 x V1) ÷ M2

Definitions of a mole

Key Concepts

Mole is abbreviated to mol and given the symbol n
1 mole contains the same number of particles as there are in 12g of carbon-12 atoms by definition.

This number is called Avogadro's number or Avogadro's constant (NA) and is equal to 6.022 x 1023 particles.

1 mole of a pure substance has a mass in grams equal to its molecular mass (MM) [also known as molecular weight (MW) or formula mass (FM) or formula weight (FW)].


This is often referred to as the molar mass.

1 mole of an ideal gas has a volume of:
22.4 litres (22.4L) at S.T.P.

[Standard Temperature and Pressure, 0oC (273K) and 101.3kPa (1 atm)]
24.47 litres (24.47L) at S.L.C
[Standard Laboratory Conditions, 25oC (298K) and 101.3kPa (1atm)]


Temperature Conversions

Key Concepts

Temperature is a measure of the average kinetic energy of the particles in an object.

Adding energy, eg, heat, to an object increases the kinetic energy of the particles which is observed as an increase in temperature.

When an object loses energy, kinetic energy of the particles decreases and is observed as a decrease in temperature.

Several temperature scales are in common use:

Kelvin Scale based on the kelvin unit (K), the SI unit of temperature.

Celsius Scale based on degrees Celsius (oC), closely related to the Centigrade scale.

Fahrenheit Scale based on degrees Fahrenheit (oF), commonly used in North America.

Kelvin Scale is based on the following fix ed points:

The zero point is absolute zero, the lowest temperature theoretically obtainable.

The temperature at which solid, liquid and gaseous water can coexist indefinitely (the triple-point temperature of water) is assigned a value of 273.16K
Celsius Scale is based on a triple-point temperature of water of 0.01oC, and at 1atm pressure a freezing point of 0.00oC and a boiling point of 100.00oC.

Celsius units (oC) are the same size as kelvin units (K).

Fahrenheit Scale is based on a freezing point of water of 32oF and a boiling point of 212oF.

Temperature Conversions

Converting Celsius (oC) to kelvin (K)
kelvin (K) = oC + 273.15
Converting kelvin (K) to Celsius (oC)
oC = K - 273.15
Converting Fahrenheit (oF) to Celsius (oC)
oC = 5/9 x (oF - 32)
Converting Celsius (oC) to Fahrenheit (oF)
oF = (9/5 x oC) + 32


Mass Conversions

Key Concepts

Mass is a direct measure of the amount of matter in an object.

The SI unit of mass is the kilogram which is given the symbol kg .

Chemists in a laboratory usually deal with much smaller masses than kilograms, often grams or milligrams, so we need to be able to convert from one unit of mass to another.

Mass Conversions

SI Unit Conversions

factors 1012 109 106 103 102 101 10-1 10-2 10-3 10-6 10-9 10-12 10-15 10-18
prefix tera giga mega kilo hecto deca deci centi milli micro nano pico femto atto
symbol T G M k h da d c m µ n p f a
1 kilogram (1kg) = 103 grams (1000g) 1 gram (1g) = 1 ÷ 103 kilograms = 0.001kg
1 milligram (1mg) = 10-3 grams (0.001g) 1 gram (1g) = 1 ÷ 10-3 milligrams = 1,000mg
1 microgram (1µg) = 10-6 grams 1 gram (1g) = 1 ÷ 10-6 micrograms = 106µg





Volume Conversions

Key Concepts

The unit of volume derived from SI units is the cubic meter, m3.

Chemists in a laboratory usually deal with much smaller volumes than cubic meters and the metric but non-SI units of liter or litre (L) and milliliter or millilitre (mL or ml) are in common use.

In 1964 the litre was redefined as being equal to exactly 1 cubic decimetre:
1L = 1dm3

So 1 milliltre = 1 cubic centimetre
1mL = 1cm3 (= 1cc)

Non-metric units of volume can still be found in use around the world, eg, gallons of gas in the USA and a pint of beer in the UK.

Volume Conversions

Metric Unit Conversions

factors 1012 109 106 103 102 101 10-1 10-2 10-3 10-6 10-9 10-12 10-15 10-18
prefix tera giga mega kilo hecto deca deci centi milli micro nano pico femto atto
symbol T G M k h da d c m µ n p f a
1 litre (1L) = 103 millilitres (1000mL) 1 millilitre (1mL) = 1 ÷ 103 litres = 0.001L
1 megalitre (1ML) = 106 litres (1,000,000L) 1 litre (1L) = 1 ÷ 106 megalitres = 10-6ML
1 microlitre (1µL) = 10-6 litres 1 litre (1L) = 1 ÷ 10-6 microlitres = 106µL




Density Calculations

Key Concepts

Density is defined as mass per unit volume.

Density can be calculated using the formula:
d = m ÷ v
where d = density, m = mass, v = volume

The greater the density, the more mass per unit volume.

The unit of density derived from SI units is kilograms per cubic meter, kg/m3 or kgm-3.

More commonly, densities are given in g/mL (gmL-1) or g/cm3 (gcm-3 or g/cc).

Density is a characteristic property of pure substances so density can help identify a particular pure substance.

Densities of Some Pure Substances

Pure Substance State Density (g/mL)

at 25oC and 1atm
gold solid 19.3
mercury liquid 13.6
lead solid 11.4
silver solid 10.5
copper solid 9.0
zinc solid 7.1
aluminium solid 2.7
carbon (graphite) solid 2.3
sulfur solid 2.0
phosphorus solid 1.8
ethanoic acid (acetic acid) liquid 1.04
water liquid 1.0
ethanol liquid 0.79
chlorine gas 0.0029
oxygen gas 0.0013

In general metals are more dense than non-metals*.

For example, at 25oC the density of metallic lead is 11.4g/mL while the density of non-metallic sulfur is only 2.0g/mL.

The mass of 1mL of lead would be 11.4g, while the mass of 1mL of sulfur is only 2.0g

In general, solids are more dense than liquids which are more dense than gases**.

For example, at 25oC, solid sulfur has a density of 2.0g/mL, liquid water has a density of 1.0g/mL and gaseous oxygen has a density of 0.0013g/mL.

* There are quite a few exceptions, especially the Group I (alkali metals) which have unusually low densities compared with other metals.

**Note that mercury is an exception, it is a very dense liquid.

Density Calculations

density = mass ÷ volume
This equation can be re-arranged in order to calculate mass or volume given the density of a substance:
mass = density x volume
volume = mass ÷ density

Check for consistency in units:

If density is given in g/mL then the mass must be in grams and the volume in milliltres.

If the density is given in g/cm3 then the mass must be in grams and the volume in cubic centimetres.
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