September 28, 2010: Dimensional Analysis (Angelo)

Dimensional Analysis:
- Want to know what 100 km/h (kilometres per hour) is in mi/h (miles per hour)?
- Just like converting between currencies, in chemistry, it is usually necessary to convert between units.
- This process is called Dimensional Analysis

Steps for the Dimensional Analysis process:

1. Find the unit equality
2. Find the conversion factor
3. Apply the conversion factor
4. Cancel Units

EXAMPLES:

1. How many miles are equal to 200 kilometres?

    Find the unit equality: 1 mile (mi.) = 1.6 kilometres (km.)
    Find the conversion factor: 1 = 1 mi. / 1.6 km.
    Apply the conversion factor: (200 km.) x (1 mi. / 1.6 km.)
    Cancel Units: 125 mi.

    Answer: 200 km. is equal to 125 mi.

2. What is 100 kilometres per hour in metres per second?

    Find the unit equality: 1000 metres (m.) = 1 kilometre (km.) and   
                                    3600 seconds (s.) = 1 hour (h.)
    Find the conversion factor: 1 = 1000 m. / 1 km. and 
                                           1 = 1 h. / 3600 s.
    Apply the conversion factor: (100 km/h) x (1000 m. / 1 km.) x (1 h. / 3600 s.)
    Cancel Units: 28 m./s.

    Answer: 100 km./h. is equal to 28 m./s.

Here's a helpful example of changing inches to feet using Dimensional Analysis: