...Mathematical Equations Flashcards
How do you calculate the relative atomic mass of an element?
The atomic mass of an element when compared with 1/12 of the weight of a carbon-12 atom.
Relative Atomic Mass is expressed as Ar and used as an average across all the isotopes of a substance.
(% of isotope x mass) + (% of isotope x mass) / 100
Eg:
75% of chlorine isotopes have a mass of 35
25% of chlorine isotopes have a mass of 37
So…
(75 x 35) + (25 x 37) / 100
= 35.3 Ar
What is the equation for calculating density?
Density = mass / volume
D = m / V
Common units for density:
g/mL
g/mL 3
How do you calculate the Relative Molecular Mass of a substance?
Explain what to do when a substance has more than one atom of an element in its formula.
To find the Relative Molecular Mass (Mr) of a substance just add together the Ar values for all the atoms in its formula.
Eg: hydrochloric acid (HCl)
Atomic weights:
Hydrogen - 1
Chlorine - 35.5
Total - 1 + 35.5
Hydrochloric acid Mr = 36.5
If a substance has more than one atom of an element in it, then just multiply its weight by the quantity of atoms.
Eg: water (H2O)
H (1 x 2) + O (15.994 rounded to 16)
(1 x 2) + 16 = 18
Water Mr = 18
If we have a substance that we know contains water or oxygen (for example) how could we go about working out the chemical formula of the substance?
This could be done by reacting the substance then weighing it.
It can be inaccurate, but once the end result is achieved it can give an indication of the formula..
Eg:
2 substances
Substance x (Ar 18)
Substance y (Ar 11)
Total weight 94g
Substance y is removed through a reaction and all that is left is substance x at 72g.
Therefore substance y was 22g (94-72) with Ar being 11, so that substance would be 2y since 22/11 = 2.
Substance x was 72g with Ar 18, so substance must be 4y since 72/18 = 4
Therefore total formula = 2y4x
So long as we know the elements involved and the Ar, we can calculate the formula based in the proportion of weight of substance added or removed…
27g Al reacts with O and produces 43g of product. What has happened?
Furthermore, what if the reaction produces 59g of product?
If the resultant weight is 43g, the resultant would be AlO (aluminium oxide) - we know oxygen has an Ar of 16, so 27 + 16 = 43g
If the resultant weight is 59g then double the amount of oxygen has been added, making AlO2
If we can measure the weight of a substance with the Ar of the constituents, we can make strong estimations of the masses.
This is because the empirical/symbol formula can give a very good level of info about the proportions in terms of moles.
If a hydrocarbon was found to have 12g C and 4g H, how would we calculate the empirical formula?
Carbon Ar = 12 (1 mole of C)
Hydrogen Ar = 1 (4 moles of H)
So of every carbon present, there are four hydrogens.
Formula CH4.
Total Mr 16.
It is generally accepted that you will never get a complete conversion in a chemical reaction.
Some chemicals being used may react with equipment, or some atoms may not convert at all.
The final yield in this case is known as a percentage yield.
In simple terms, how would you calculate this?
Use reacting zinc with copper II sulphate to extract copper as an example, with 130g zinc…
Weight of yield / expected yield x 100
Eg:
Reacting 130g with copper II sulphate to exact copper.
130g zinc = 2 moles (Ar zinc = 65)
Formula:
Zn(s) + CuSO4(aq) -> ZnSO4 (aq) + Cu(s)
One for one, so 2 moles Zn should gain 2 moles of copper in return and as Ar of Cu is 64 we would expect a 128g copper yield.
But if we only gained 96g we would calculate the percentage yield as follows:
96 / 128 x 100 = 75% yield
