The skill to convert a quantity into various units is important. Unit
conversion and dimensional analysis are also scientific methods.
There are many examples in Chem 120, and you will encounter them later.
At this point, one example is given to illustrate the technique.
The world's ocean contains 1.4e9 km3 of water.
What is the volume in liters?
What is the weight if the specific density is 1.1?
How many moles of water are present if all the weight is due to water?
How many moles of H (not H2) are there in the ocean?
How many H atoms are present in the ocean?
1000 m 10 dm
1.4e9 (------)3 (------)3
1 km 1m
= 1.4e21 dm3(----)
= 1.5e21 L(------)
1000 g 1 mol
= 1.5e21 kg (------)(-----)
1 kg 18 g
2 mol H atoms
= 8.3e22 mol H2O (---------------)
1 mol H2O
= 1.7e23 mol H (-------------)
= 5.0e46 H atoms
In this example, a quantity has been converted from a unit for volume
into other units of volume, weight, amount in mole, and number of atoms.
Every factor used for the unit conversion is a unity. The
numerator and denominator represent the same quantity in different ways.
Even in this simple example, several concepts such as the quantity in
mole, Avogadro's number, and specific density (or specific gravity) have
been applied in the conversion. If you have not learned these concept,
you may have difficulty in understanding some of the conversion
processes. Identify what you do not know and find out in your text or from
A typical city speed for automobiles is 50 km/hr. Some years ago,
most people believed that 10 seconds to dash 100 meter race was the
lowest limit. Which speed is faster, 50 km/hr or 10 m/s?
For comparison, the two speed must be expressed in the same unit.
Let's convert 50 km/hr to m/s.
km 1000 m 1 hr 1 min
50 -- (------) (------) (-----) = 13.89 m/s
hr 1 km 60 min 60 s
Thus, 50 km/hr is faster.
The speed of a Taiphoon is reported to be 100 m/s.
What is the speed in km/hr?
What is the speed in miles per hour?
Mr. Smart is ready for a T-bone steak. He went to market A and found the
price to be 4.99 dollars per kilograms. He drove out of town to road side
market, which sells at 2.29 per pound. Which price is better for Mr. Smart?
To help Mr. Smart, we have to know that 1.0 kg is equivalent to 2.206531 lb
or 1 lb = 453.2 g. By the way, are these the same?
$ 1 kg
4.99 -- (-----------) = 2.26468 $/lb
kg 2.206532 lb
Of course, with the money system in Canada, there is no point quoting
the price as detailed as it is given above. This brings about the
significant digit issue, and the quantization. The price is therefore
2.26 $/lb, better for Mr. Smart than the price of 2.29 $/lb.
Confidence Building Questions