Analysing problems: Single step and multistep
Examples of one-step problems
Calculating amount in moles (n) from a specified mass (m) a substance (and vice versa) is a one-step problem, provided the molar mass (M) of the substance can be calculated.
Calculating the amount in moles of one chemical entity from the amount in moles of another chemical entity is also one step if there is a relationship between the amounts in moles of these entities.
The relationship between amounts in moles of the formula unit CH3OH and amounts in moles of the atoms that comprise it is shown.
Multi-step problems
Relating a mass of one chemical entity (CH3OH molecules) to the mass of another chemical entity (O atoms) requires combination of the steps above with the relationship between the amount in moles of the known and unknown quantities being at the center.
Creating plans for solving problems
It is useful to plan your solution to a multistep problem. These analyses will help you to realise that many problems involve the same operations. The schemes
Calculating amount in moles (n) from a specified mass (m) a substance (and vice versa) is a one-step problem, provided the molar mass (M) of the substance can be calculated.
Two examples of such calculations are shown diagramatically below.
The required mathematical operation is given both as words and as an expression.
Note that the substance in the known and the unknown MUST be the same.
The required mathematical operation is given both as words and as an expression.
Note that the substance in the known and the unknown MUST be the same.
| Calculate the mass of CH3OH in 0.100 mol CH3OH. | ||
| n(CH3OH) Known | Multiply by M(CH3OH)  m = n × M | m(CH3OH) Unknown |
| Calculate the amount in moles of CH3OH in 10 g CH3OH. | ||
| m(CH3OH) Known | Divide by M(CH3OH)  | n(CH3OH) Unknown |
Calculating the amount in moles of one chemical entity from the amount in moles of another chemical entity is also one step if there is a relationship between the amounts in moles of these entities.
| n(CH3OH) | = | n(C) | = | n(H) | = | n(O) |
| 1 | 1 | 4 | 1 |
| n(CH3OH) Known | × 4 because
| n(H) Unknown |
Multi-step problems
Relating a mass of one chemical entity (CH3OH molecules) to the mass of another chemical entity (O atoms) requires combination of the steps above with the relationship between the amount in moles of the known and unknown quantities being at the center.
| Calculate the mass of hydrogen in 10.0 g CH3OH. | |||||||||||
| m(CH3OH) Known | Divide by M(CH3OH) | n(CH3OH) | ×4 | n(H) | Multiply by M(H) m = n × M | m(H) Unknown | |||||
| Step 1 | Step 2 | Step 3 | |||||||||
Creating plans for solving problems
It is useful to plan your solution to a multistep problem. These analyses will help you to realise that many problems involve the same operations. The schemes
- use symbols with formulae in brackets for given and unknown quantities
This is important because many chemical calculations involve more than one chemical entity. - show symbols with formulae in brackets for intermediate quantities that need to be calculated.