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Dimensional Analysis
Dimensional Analysis is a mathetmatical method which allows you to covert from one set of units to another using multiplication so that the units cancel out, leaving only the desired units. (Hint: When converting between unassociated units, like cm to inches or ml to cm, a conversion factor will be needed.)
Procedure
1.) Write down the known or given number in parenthesis. (Be sure to include units!)
2.)In another set of parenthesis write the units of the first number in the denominator of the 2nd set of parenthesis.
3.)The numerator of the 2nd set of parenthesis is the desired units.(Some conversions take several steps and therefore the numerator will be the next step in the conversion; Steps 3-7 will be repeated until the desired units are obtained.)
4.)The numerical values for the units in the second set of parenthesis will be the conversion factor.(i.e. There are 1000ml in 1L)Be sure the number goes with the correct units.
5.)The units of the original number will cancel with those of the denominator in the set of parenthesis that follows it. (Hint:This is shown by making a slash mark through the units.)
6.Multiply through all of the parenthesis.(Each set of parenthesis is a fraction so be sure plug them into your calculator as a fraction and multiply them all together OR multiply all of the numerators and then divide the product by the product of the denominators)
7.) The answer will be the numerical value calculated with the units of the numerator in the final set of parenthesis.
Example 1:
A sample of Sulfide (S) is added to a 13.25g of Potassium (K); the reaction proceeds as follows:
2K + S --> K2S
How many moles of K2S will be produced?
1.) Write down the known/given number in parenthesis: (13.25gK)
2.) In another set of parenthesis write the units of the first number in the denominator of the 2nd set of parenthesis: (13.25gK)( / g)
3.)The numerator of the 2nd set of parenthesis is the desired units. Repeat Steps 3 and 4 until the desired units are located in the numerator of the final set of parenthesis: (13.25gK)( molK/ gK)( mol K2S/ mol K)
4.)The numerical values for the units in the second set of parenthesis will be the conversion factor: (13.25gK)(1mol K/39.098g K)(1mol K2S/2mol K)
5.)The units in the numerator of each parenthesis will cancel with the units of the denomiator of the next set of parenthesis, this is shown by crossing out the units that cancel. (The computer does NOT have the capabilities to show this.)
6.)Multiply through all of the parenthesis
7.)The answer will be the numerical value calculated with the units of the numerator in the final set of parenthesis. .1694mol K2S
"Example 2:"
If there is a 22.5g of Phorphorus (P) how many moles of Ca3P2 will be produced, the the reaction procedes as follows:
3Ca + 2P --> 1Ca3P2
"Answer:"
.3632mol Ca3P2