Relating amounts
The coefficients in the balanced equation for a reaction determine the ratio of the amounts in moles of reactants consumed or products produced in a chemical reaction.
In general for aA + bB
cC + dD
A, B, C and D are substances
a, b, c and d are coefficients in the balanced equation.
In practice, only two substances are involved in a particular problem so that the calculation uses an equation involving a pair of substances (for example, A and B or A and D or C and D).
An easy and foolproof way to calculate the amount in moles of a substance consumed or produced in the reaction of a known amount in moles of a second substance is to
In general for aA + bB
cC + dDA, B, C and D are substances
a, b, c and d are coefficients in the balanced equation.
| n(A) | = | n(B) | = | n(C) | = | n(D) |
| a | b | c | d |
As shown for the reaction below, the relationship above is a rearranged version of the simple ratio of the amounts in moles of the two substances.
1 × n(CO) = 2 × n(O2)
For the reaction:
2CO(g) + O2(g) → 2CO2(g)
Rearrangement by cross-multiplication (multiply each of the numerators by the denominator of the other fraction) gives:
This can be rearranged to a form consistent with the general equation above in that amount in moles of each substance is divided by its coefficient in the balanced equation:
| n(CO) | = | 2 |
| n(O2) | 1 |
| n(CO) | = | n(O2) |
| 2 | 1 |
For the reaction:
2CO(g) + O2(g) → 2CO2(g)
Rearrangement by cross-multiplication (multiply each of the numerators by the denominator of the other fraction) gives:
This can be rearranged to a form consistent with the general equation above in that amount in moles of each substance is divided by its coefficient in the balanced equation:
In practice, only two substances are involved in a particular problem so that the calculation uses an equation involving a pair of substances (for example, A and B or A and D or C and D).
An easy and foolproof way to calculate the amount in moles of a substance consumed or produced in the reaction of a known amount in moles of a second substance is to
- use the above and the balanced equation for the reaction to write the relationship between the amounts in moles of the two substances (the known and the unknown).
- substitute the known amount in moles and
dividing by the coefficient of that substance
- solve for the unknown amount in moles by multiplying by the coefficient of that substance.