Basic Calculations in A-level Chemistry

The Mole

Balancing chemical Equations

Molecular and empirical formulas

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Bond Angles

Valence-shell electron-pair repulsion (VSEPR) theory

• Assumes that each atom in a molecule will be positioned so that there is minimal repulsion between the valence electrons of that atom.

In simple molecules in which there are no nonbonding electrons, there are five basic shapes:

1. LINEAR - Bond angle = 180
   • All diatomic molecules are linear.
   • Molecules with two atoms around a central atom such as BF₂ are linear because positioning the two attachments at opposite ends of the central atom minimizes electron repulsion.
   • Generic Formula:  MX or MX₂ (where M is the central atom and X is are the bonding atoms).
     
2. TRIGONAL PLANAR - Bond angle = 120
   • Molecules with three atoms around a central atom such as BF₃ are trigonal planar because electron repulsion is minimized by positioning the three attachments toward the corners of an equilateral triangle.
   • Generic Formula:  MX₃ (where M is the central atom and X is are the bonding atoms).
     
3. TETRAHEDRAL - Bond angle = 109.5
   • Molecules with four atoms around a central atom such as CH₄ are tetrahedral because electron repulsion is minimized by position the four attachments toward the corners of a tetrahedron.
   • Generic Formula:  MX₄ (where M is the central atom and X is are the bonding atoms).
     
4. TRIGONAL BIPYRAMIDAL
   • Bond angle within the equatorial plane = 120
   • Bond angle between equatorial and axial plane = 90
   • Molecules with five atoms around a central atom such as PF₅ are trigonal bipyramidal.  Three of the attachments  are positioned in a trigonal plane with 120 bond angles.  The remaining two attachments are positioned perpendicular (90) to the trigonal plane at opposite ends of the central atom.  This arrangement of atoms minimizes electron repulsion.
   • Generic Formula:  MX₅ (where M is the central atom and X is are the bonding atoms).
     
5. OCTAHEDRAL - Bond angle = 90
   • Molecules with six atoms around a central atom such as SF₆ are octahedral.  Four of the attachments are positioned in a square plane with 90 bond angles.  The remaining two attachments are positioned perpendicular (90) to the square plane at opposite ends of the central atom.  This arrangement of atoms minimizes repulsion. 
   • Generic Formula:  MX₆ (where M is the central atom and X is are the bonding atoms).
      
     
     

Other shapes

BENT (ANGULAR or V-SHAPED)
• Molecules with two atoms and one or two pairs of nonbonding electrons around a central atom such as H₂O are bent.  It can be imagined that a linear molecule with two atoms attached to a central atom is altered when electrons are added to the top of the central atom.  The repulsion caused by the addition of these extra electrons causes the molecule to become bent.  The angle of bent molecules is less than 120 if there is one pair of nonbonding electrons and is less than 109.5 if there are two pairs of nonbonding electrons.
• Some molecules, such as NO₂ have two atoms and a single unpaired electron around a central atom.  These molecules are also bent due to the repulsion of the single atom added to the central atom.
• Generic Formula:  MX₂E or MXE₂ (where M is the central atom, X is are the bonding atoms, and E are nonbonding pairs of electrons).
  
TRIGONAL PYRAMIDAL
• Molecules with three atoms and one pair of nonbonding electrons around a central atom such as NH₃ are trigonal pyramidal.  These molecules are essentially tetrahedral molecules with one of the attached atoms replaced by a pair of nonbonding electrons.  The force of repulsion of these electrons makes the bond angle between the attached atoms less than 109.5.  For example, in NH₃, the H-N-H bond is 107.5.
• Generic Formula:  MX₃E (where M is the central atom, X is are the bonding atoms, and E are nonbonding pairs of electrons).
  

 

SQUARE PYRAMIDAL

• Molecules with five atoms and one pair of nonbonding electrons around a central atom such as BrF₅ are square pyramidal.  These molecules are essentially octahedral molecules with one of the attached atoms replaced by a pair of nonbonding electrons.  This leaves four atoms in a plane as a square base and one atom positioned perpendicular (90)  to this plane.
• Generic Formula:  MX₅E (where M is the central atom, X is are the bonding atoms, and E are nonbonding pairs of electrons).
  

SQUARE PLANAR

• Molecules with four atoms and two pairs of nonbonding electrons around a central atom such as XeF₄ are square planar.  These molecules are essentially octahedral molecules with two of the attached atoms opposite each other around the central atom each replaced by a pair of nonbonding electrons.  This leaves four atoms in a square plane.
• Generic Formula:  MX₄E₂ (where M is the central atom, X is are the bonding atoms, and E are nonbonding pairs of electrons).
  
  
  

  Source: http://library.thinkquest.org/C006669/data/Chem/bonding/shapes.html

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Chemical Bonding (Section 1 of 2)

Contents of this Page:

1. The Bond Energy
2. Factors affecting the Bond energy
3. The Four Main Types of Bonding
1. Ionic Bonding
2. Covalent Bonding
3. Dative Covalent Bonding
4. Metallic Bonding
4. Section 2

============================================

The Bond Energy
The energy required to break one mole of covalent bonds in gaseous state is called bond energy
For Example
H=H Bond Energy = +436 KJ/mol
I-I Bond Energy = +151 KJ/mol


Factors affecting Bond Energy

• Number of Bonds: Triple bonds are stronger than double bonds and double bonds are stronger than single bonds.
• Bond Length: Bond length is the distance between two nuclei of covalently bonded atoms as the bond length increases bond strength decreases, hence bond energy decreases

Ionic
•  between atoms on Left Hand Side and atoms on Right Hand Side of Periodic Table
•  electrons are TRANSFERRED between atoms
•  atoms end up as ions
•  strong electrostatic attraction between ions of opposite charge
•  giant ionic crystal lattice structure
•  Properties ... high melting points.....brittle.....water soluble....conduct when molten or in aqueous solution

 
Ionic Bonding; a video demonstration:

Drawing dot and cross diagrams

http://www.youtube.com/watch?v=8BZBzFwVXl4

Covalent Bonding
•  between atoms of the same element;   (e.g. in N2, O2, diamond, graphite)
•  between atoms of different elements on the RHS of table; (e.g. CO2,  SO2)
•  when one of the elements is in the middle of the table;  (e.g. C, Si)
•  head-of-the-group elements with high I.E.’s , (e.g. Be in BeCl2)
•  consists of a shared pair of electrons, one electron coming from each atom
•  atoms share to try and get an ‘octet’ of electrons
•  leads to the formation of simple molecules and giant molecules (e.g. silica)

Polar Covalent Bonds
In bonds between atoms of the same element the sharing of the electrons is equal between the two atoms. When two atoms of different elements make a bond, the electrons will not usually be shared equally. The electrons are pulled more toward the more electronegative element.

What is electronegativity?
Electronegativity is the measure of the ability of an atom in a molecule to draw bonding electrons to itself. In general, electronegativity increases from bottom to top and left to right on the periodic table. Fluorine is the most electronegative element since it has a tendency to pick up electrons easily and hold on to them strongly. An element like cesium has a low electronegativity. The unequal sharing of electrons is called a polar covalent bond. The definition of a polar covalent bond is a covalent bond in which the bonding electrons spend more time near one atom than the other.

 

Dative Covalent Bonding
•  consists of a shared pair of electrons, both electrons from one atom
•  one species is a lone pair donor - LEWIS BASE
•  other species has space in outer shell to accept a lone pair - LEWIS ACID
•  once the bond has been formed it is the same as a covalent bond

Metallic Bonding
•  metal atoms arranged in regular lattice give up outer shell electrons
•  electrons form a mobile ‘cloud’ which binds metal ions together
•  strength of bond depends on number of electrons and size of ions
•  mobile electrons ... allow electricity to be conducted

Strength of a Metallic Bond:
As we go down the group the atomic size increases, the attraction between the nucleus and free electrons decreases and therefore the melting melting point also decreases down the group.
As we move across the period, atomic size decreases and the strength of the metallic bond increases therefore melting point also increases

Sources:
Images and definitions: www.knockhardy.org.uk
Videos: Youtube.com

The VSEPR theory 
VSEPR theory proposes that the geometric arrangement of terminal atoms, or groups of atoms about a central atom in a covalent compound, or charged ion, is determined solely by the repulsions between electron pairs present in the valence shell of the central atom. To view more about VSEPR theory visit this page

The Sigma and Pie bonds

Click here for Section 2

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Atoms molecules and stoichiometry

Before proceeding with this section please make sure you have seen all the lectures on the Basic Calculations in A-level Chemistry page

Mass number and atomic number

Atomic Number (Z)      Number of protonsin the nucleus of an atom
Mass Number (A)       Sum of the protons and neutronsin the nucleus

What is the avogadro's constant?
The Avogadro Constant is a constant number used to refer to atoms, molecules, ions and electrons. Its value is 6.023 x 10²³ mol^-1 . I.E 1 Mole of Sodium contains  6.023 x 10²³ number of particles.

What is the Relative Atomic Mass (Ar)?


The mass of an atom relative to the 12C isotope having a value of 12.000 is called as the Ar.

Relative Isotopic Mass Similar, but uses the mass of an isotope Eg 238U
Relative Molecular Mass (Mr) Similar, but uses the mass of a molecule Eg CO2,  N2
Relative Formula Mass Used for any formula of a species or ion E.g NaCl,  OH¯




What are Isotopes?Definition Atoms with ...  the  same atomic number but different mass number                                                                                                              or
                         the  same number of protons but different numbers of neutrons.

Important: Chemical properties of isotopes are identical 

Example: Chlorine contains 75% by mass Cl (35) and 25% by mass Cl (37). Calculate the relative atomic mass of Chlorine.

Ar of Cl = (75 x 35) + (25 x 37)  = 35.5

                              100

What is the mass spectra?

A mass spectrum is an intensity(Abundance) vs. m/z (mass-to-charge ratio) plot representing a chemical analysis. Hence, the mass spectrum of a sample is a pattern representing the distribution of ions by mass (more correctly: mass-to-charge ratio) in a sample.

How to calculate the Relative Atomic mass from a mass spectra

What is the empirical formula

A formula that gives the simplest whole-number ratio of atoms in a compound.

How to calculate the empirical formula?

1. Start with the number of grams of each element, given in the problem. 
• If percentages are given, assume that the total mass is 100 grams so that 
the mass of each element = the percent given.
2. Convert the mass of each element to moles using the molar mass from the periodic table. 
3. Divide each mole value by the smallest number of moles calculated. 
4. Round to the nearest whole number.  This is the mole ratio of the elements and is 
represented by subscripts in the empirical formula. 
• If the number is too far to round (x.1 ~ x.9), then multiply each solution by the same 
factor to get the lowest whole number multiple. 
• e.g.  If one solution is 1.5, then multiply each solution in the problem by 2 to get 3. 
• e.g.  If one solution is 1.25, then multiply each solution in the problem by 4 to get 5.

Example;
A compound was found to contain 13.5 g Ca, 10.8 g O, and 0.675 g H.  What is the empirical formula of the compound?

Calculating empirical formula from combustion data
Example : Calculating the empirical formula of a hydrocarbon

The general procedure:

• Calculate the number of grams of carbon in the compound by calculating the number of grams of carbon in the given amount of CO₂.
• Calculate the number of grams of hydrogen in the compound by calculating the number of grams of hydrogen in the given amount of H₂O.
• If the compound contains oxygen, calculate the number of grams of oxygen in it by subtracting the masses of carbon and hydrogen from the given total mass of compound.

? g O  =  (given) g total  -  (calculated) g C  -  (calculated) g H

•  Calculate the empirical formula of the compound from the grams of carbon, hydrogen, and oxygen.

Sample Question: Dianabol is one of the anabolic steroids that has been used by some athletes to increase the size and strength of their muscles.The molecular formula of Dianabol, which consists of carbon, hydrogen, and oxygen, can be determined using the data from two different experiments. In the first experiment, 14.765 g of Dianabol is burned, and 43.257 g CO₂ and 12.395 g H₂O are formed. In the second experiment, the molecular mass of Dianabol is found to be 300.44.  What is the molecular formula for Dianabol?

Solution: Obtained via http://www.mpcfaculty.net/

? g O  =  14.765 g total  - 11.805 g C  -  1.3870 g H  =  1.573 g O

We now calculate the empirical formula.

The empirical formula is C₁₀H₁₄O. We use it to calculate the molecular formula:

Empirical formula mass  =  10(12.011)  +  14(1.00794)  +  1(15.9994)  =  150.22

molecular formula         C₂₀H₂₈O₂

 

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