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

Key Concepts

  • Relative molecular mass is also known as molecular weight, relative molar mass, molar weight, formula mass and formula weight.

  • Relative molecular mass is usually given the symbol Mr
        Other symbols commonly used are MM, MW, FM, FW1.

  • Relative molecular mass of a compound is defined as the mass of a formula unit of the compound relative to the mass of a carbon atom taken as exactly 12.

  • In practice, the relative molecular mass, Mr, of a compound is the sum of the relative atomic masses (atomic weights) of the atomic species as given in the chemical formula.

  • Relative molecular mass is a dimensionless quantity, it has no units 2.

Relative Molecular Mass Concepts

The diagram on the right shows a box containing 3 balls:
  • one red ball shown as o
  • two black balls shown as o

If a red ball has a mass of 16 g and a black ball has a mass of 1 g, then the mass of all three balls in the box is 16 + 1 + 1 = 18 g
We could write a mathematical expression to find the total mass of the balls in the box:
mass(total) = mass(red ball) + 2 x mass(black ball)
mass(total) = 16 + 2 x 1 = 16 + 2 = 18 g
o       o
    o    

Chemists often think of atoms as really tiny balls, and refer to this as the particle theory of matter.
If each ball in the box represents an atom making up a water molecule, H2O, then the diagram on the right shows a box containing a molecule of water in which
  • the red ball o is an oxygen atom
  • each black ball o is hydrogen atom
  • each diagonal line ( \ and / ) represents a chemical bond between an oxygen atom and a hydrogen atom

If an oxygen atom has a mass of 16 and a hydrogen atom has a mass of 1, then the mass of all three atoms in the water molecule is 16 + 1 + 1 = 18
We could write a mathematical expression to find the total mass of all the atoms in a water molecule:
mass(water molecule) = mass(oxygen atom) + 2 x mass(hydrogen atom)
mass(water molecule) = 16 + 2 x 1 = 16 + 2 = 18
o       o
  \   /  
    o    

This is exactly what we are doing when we calculate the relative molecular mass of a compound:

  • use the chemical formula to determine how many atoms of each element are present in the compound.
    compund XaYb contains:
        a atoms of element X
        b atoms of element Y

  • write a mathematical expression to calculate the total mass of all the elements in the compound (called the relative molecular mass of the compound)
    Mr(XaYb) = relative molecular mass of compound XaYb
        Mr(X) = relative atomic mass of element X
        Mr(Y) = relative atomic mass of element Y
        a = number of atoms of element X
        b = number of atoms of element Y

    Mr(XaYb) = a x Mr(X) + b x Mr(Y)

  • use the Periodic Table to find the relative atomic mass of each element
        Mr(X) = relative atomic mass of element X =
        Mr(Y) = relative atomic mass of element Y =

  • substitute the values for the relative atomic mass of each element into the equation and then solve the equation to find the relative molecular mass of the compund

Examples of Relative Molecular Mass Calculations

Example 1

Calculate the relative molecular mass (Mr) of the compound carbon monoxide, CO
  1. What is the question asking you to do?
    Calculate the relative molecular mass of carbon monoxide
    Mr(CO) = ?

  2. What information (data) has been given in the question?
    Chemical formula for carbon monoxide: CO

  3. What is the relationship between a chemical formula and its relative molecular mass?
    Relative molecular mass = sum of the relative atomic masses of each element in the compound
    A molecule of carbon monoxide (CO) contains 1 carbon atom (C) and 1 oxygen atom (O)
    relative molecular mass (CO) = 1 x relative atomic mass (C) + 1 x relative atomic mass (O)
    Mr(CO) = 1 x Mr(C) + 1 x Mr(O)

  4. Use the Periodic Table to find the relative atomic mass (atomic weight) for each element present:
        Mr(C) = relative atomic mass of C (carbon) = 12.01
        Mr(O) = relative atomic mass of of O (oxygen) = 16.00

  5. Calculate the relative molecular mass of carbon monoxide by substituting the values into the expression to find Mr(CO)
    Mr(CO) = 1 x Mr(C) + 1 x Mr(O)
    Mr(CO) = (1 x 12.01) + (1 x 16.00) = 28.01

Example 2

Calculate the relative molecular mass (Mr) of the compound carbon dioxide, CO2
  1. What is the question asking you to do?
    Calculate the relative molecular mass of carbon dioxide
    Mr(CO2) = ?

  2. What information (data) has been given in the question?
    Chemical formula for carbon dioxide: CO2

  3. What is the relationship between a chemical formula and its relative molecular mass?
    Relative molecular mass = sum of the relative atomic masses of each element in the compound
    A molecule of carbon dioxide (CO2) is composed of 1 atom of carbon (C) and 2 atoms of oxygen (O)
    relative molecular mass (CO2) = 1 x relative atomic mass (C) + 2 x relative atomic mass (O)
    Mr(CO2) = 1 x Mr(C) + 2 x Mr(O)

  4. Use the Periodic Table to find the relative atomic mass (atomic weight) for each element present:
        Mr(C) = relative atomic mass of C (carbon) = 12.01
        Mr(O) = relative atomic mass of O (oxygen) = 16.00

  5. Calculate the relative molecular mass of carbon dioxide by substituting the values into the expression to find Mr(CO2)
    Mr(CO2) = 1 x Mr(C) + 2 x Mr(O)
    Mr(CO2) = (1 x 12.01) + (2 x 16.00) = 12.01 + 32.00 = 44.01

Example 3

Calculate the relative molecular mass (Mr) of the compound calcium hydroxide, Ca(OH)2
  1. What is the question asking you to do?
    Calculate the relative molecular mass of calcium hydroxide
    Mr(Ca(OH)2) = ?

  2. What information (data) has been given in the question?
    Chemical formula for calcium hydroxide: Ca(OH)2

  3. What is the relationship between a chemical formula and its relative molecular mass?
    Relative molecular mass = sum of the relative atomic masses of each element in the compound
    Calcium hydroxide contains one Ca atom (actually an ion) and two hydroxide ions.
    Each hydroxide ion is composed of one hydrogen atom and one oxygen atom
    So calcium hydroxide contains 1 calcium atom (Ca), 2 oxygen atoms (O) and 2 hydrogen atoms (O)
    relative molecular mass of calcium hydroxide = 1 x relative atomic mass (Ca) + 2 x relative atomic mass (O) + 2 x relative atomic mass (H)
    Mr(Ca(OH)2) = 1 x Mr(Ca) + 2 x Mr(O) + 2 x Mr(H)

  4. Use the Periodic Table to find the relative atomic mass (atomic weight) for each element present:
        Mr(Ca) = relative atomic mass calcium = 40.08
        Mr(H) = relative atomic mass hydrogen = 1.008
        Mr(O) = relative atomic mass of oxygen = 16.00

  5. Calculate the relative molecular mass of calcium hydroxide by substituting the values into the expression to find Mr(Ca(OH)2)
    Mr(Ca(OH)2) = 1 x Mr(Ca) + 2 x Mr(O) + 2 x Mr(H)
    Mr(Ca(OH)2) = (1 x 40.08) + (2 x 16.00) + (2 x 1.008) = 40.08 + 32.00 + 2.016 = 74.10

        Alternatively, relative molecular mass = relative atomic mass of calcium + (2 x relative molecular mass of hydroxide ions)

        Mr(Ca(OH)2) = 40.08 + [2 x (16.00 + 1.008)] = 40.08 + [2 x 17.008]= 40.08 + 34.016 = 74.10

Problem Solving : Relative Molecular Mass Calculations

The problem: Chris the Chemist has just finished a detailed analysis of a molecule and has found that it is made up of two elements, phosphorus and oxygen. The molecule contains two phosphorus atoms and has a relative molecular mass of 141.94. Determine the molecular formula for this molecule.

Solving the Problem

Using the StoPGoPS model for problem solving:

STOP!
State the question. What is the question asking you to do?
Determine the molecular formula for the molecule

What chemical principle will you need to apply?
Apply stoichoimetry (chemical calculations)

What information (data) have you been given?

  • elements in molecule are phosphorus and oxygen

  • 2 atoms of phosphorus

  • Mr(molecule) = relative molecular mass of molecule = 141.94
PAUSE!
Plan. Step 1: Write the symbols for all the elements present in the molecule
Use the Periodic Table to find the symbols for:
    phosphorus
    oxygen

Step 2: Write a partial chemical formula based on the data provided
Molecule contains only phosphorus and oxygen atoms
    2 phosphorus atoms: phosphorus2
    let b equal the number of oxygen atoms: oxygenb
Partial chemical formula is phosphorus2oxygenb
    substitute in chemical symbols for phosphorus and oxygen

Step 3: Calculate total mass of phosphorus present in molecule
Determine the number of atoms of phosphorus in the molecule = 2
Use Periodic Table to find the relative atomic mass of phosphorus
    Mr(phosphorus)
Calculate the total mass of phosphorus atoms present in the molecule:
    total mass (phosphorus) = number of phosphorus atoms x relative atomic mass (phosphorus)
    total mass (phosphorus) = 2 x Mr(phosphorus)

Step 4: Calculate the total mass of oxygen atoms present in the molecule
mass(molecule) = total mass of phosphorus atoms + total mass of oxygen atoms
    Mr(phosphorus2oxygenb) = 2 x Mr(phosphorus) + [b x Mr(oxygen)]
    so, total mass of oxygen atoms present = [b x Mr(oxygen)] = Mr(phosporus2oxygenb) - 2 x Mr(phosphorus)
    so, total mass of oxygen atoms present = [b x Mr(oxygen)] = 141.94 - 2 x Mr(phosphorus)

Step 5: Calculate the number of oxygen atoms present
Use the Periodic Table to find the relative atomic mass of oxygen
    Mr(oxygen)
Substitute this value into the equation for the total of oxygen mass in the molecule:
    so, total mass of oxygen atoms present = b x Mr(oxygen)
    therefore, number of oxygen atoms = b = total mass of oxygen ÷ Mr(oxygen)

Step 6: Write the chemical formula for the molecule
Substitute the chemical symbols for phosphorus and oxygen, and, the value for b into the chemical formula for the molecule
phosphorus2oxygenb

GO!
Go. Step 1: Write the symbols for all the elements present in the molecle
Use the Periodic Table to find the symbols for:
    phosphorus = P
    oxygen = O

Step 2: Write a partial chemical formula based on the data provided
Molecule contains only phosphorus and oxygen atoms
    2 phosphorus atoms: phosphorus2
    let b equal the number of oxygen atoms: oxygenb
Partial chemical formula is phosphorus2oxygenb
    substitute in chemical symbols for phosphorus and oxygen
    P2Ob

Step 3: Calculate total mass of phosphorus present in molecule
Determine the number of atoms of phosphorus in the molecule = 2
Use Periodic Table to find the relative atomic mass of phosphorus
    Mr(phosphorus) = 30.97
Calculate the total mass of phosphorus atoms present in the molecule:
    total mass (phosphorus) = number of phosphorus atoms x relative atomic mass (phosphorus)
    total mass (phosphorus) = 2 x 30.97 = 61.94

Step 4: Calculate the total mass of oxygen atoms present in the molecule
mass(molecule) = total mass of phosphorus atoms + total mass of oxygen atoms
    Mr(P2Ob) = 2 x Mr(phosphorus) + [b x Mr(oxygen)]
    so, total mass of oxygen atoms present = [b x Mr(oxygen)] = Mr(P2Ob) - 2 x 30.97
    so, total mass of oxygen atoms present = [b x Mr(oxygen)] = 141.94 - 61.94 = 80.00

Step 5: Calculate the number of oxygen atoms present
Use the Periodic Table to find the relative atomic mass of oxygen
    Mr(oxygen) = 16.00
Substitute this value into the equation for the total of oxygen mass in the molecule:
    so, total mass of oxygen atoms present = b x Mr(oxygen)
    therefore, number of oxygen atoms = b = total mass of oxygen ÷ Mr(oxygen)
b = number of O atoms = 80.00 ÷ 16.00 = 5

Step 6: Write the chemical formula for the molecule
Substitute the chemical symbols for phosphorus and oxygen, and, the value for b into the chemical formula for the molecule
P2Ob
P2O5

PAUSE!
Ponder plausability. Does this solution answer the question that was asked?
Yes, we have determined the molecular formula for this compound.

Is the solution reasonable?
Work backwards by calculating the relative molecular mass for the molecular formula we have found:
Mr(P2O5) = 2 x Mr(P) + 5 x Mr(O) = 2 x 30.97 + 5 x 16.00 = 61.94 + 80.00 = 141.94
Since the relative molecular mass calculated using our chemical formula is the same as the one given in the question, we are satisfied that the answer is correct.

STOP!
State the solution. The molecular formula for this compound is P2O5


What would you like to do now?

1 recommended IUPAC symbol for relative molecular mass (relative molar mass) is Mr.
M is the IUPAC symbol recommended for molar mass

2Molar mass, M, does have units. The SI units for molar mass are kg mol-1

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