Help with dimensional analysis

Question

i still don't get dimensional analysis no matter how many times i try to solve a problem with it.

"you want to order a bicycle with a 25.5-in frame, but the sizes in the catalog are given only in centimeters. what size should you order?"

to me it's a lot easier to solve it with proportions.

2.54 / 1 = X / 25.5

cross multiply and get 64.8 cm.

I understand why they need to cancel out the units but i don't understand what you do after that.

can someone help?

i need to know how to use Dimensional analysis for the stoichiometry problems i have to do.

Answer 1

use like that: 2.54cm/in  25.5in*2.54cm/in=64.8cm

carbon:molecular mass=12g/mol;C+O2=CO2 read:1mole C+1mol O2=

1molO2

V0=22.41L/mol

gas: 4$/gallon*15gallon(s)=60$

Answer 2

your problem....

25.5 in x (2.54 cm / in) = 64.8 cm

the units of "in" cancel

Unit conversion is different from dimensional analysis.  And your problem looks to me like a unit conversion problem.   that said, this a very important topic.  it's studied in chemisty, engineering etc. and you need to learn it and become proficient in it.  

I highly recommend you read this and think about each individual rule before moving on to the next... then practice converting...I guarantee if you become proficient with this, you will never have trouble converting again...

There's a process for conversion called "factor label method" aka "unit factor method" that is taught in virtually all college chemistry and engineering classes. and it is probably the one most important technique to learn in either program...If you look through some of the answers here on yahoo answers, you will see people who use this process successfully have, in general, straightforward and simple answers and those who don't... well.. see for yourself...

you can google "unit factor method" and find several helpful links and I recommend you do...The following are my rules for the process....



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rule 1) units on top and bottom of a fraction cancel.

examples:

in / in = 1

ft / ft = 1

cm / cm cancels.

sec / sec cancel

sec² / sec² cancel

m³ / m³ cancels

got that down?

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rule 2) any number x 1 = that number

examples:

4 x 1 = 4

4 in x 1 = 4 in

5280 ft x 1 = 5280 ft

9.8 m / s² x 1 = 9.8 m / s²

easy right?

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rule 3) any equality can be rearranged to = 1

examples:

2.54 cm = 1 in

if we divide both sides by 2.54 we get

2.54 cm / 2.54 cm = 1 in / 2.54 cm

1 = 1 in / 2.54 cm

12 in = 1 ft

12 in / 12 in = 1 ft / 12 in

1 = 1 ft / 12 in

also... since 1/1 = 1....

1 / 1 = 1 / (1 ft / 12 in)

1 = 12 in / 1 ft

meaning for any equality of the form a = b, .....a / b = b / a = 1

a/b and b/a are called unit factors because they = unity and we will be using them in rules 4 and 5 to factor (or more precisely "change" units)

ok? this may be a bit more complicated than the first two rules but if you play around with it for a while I'm sure you will get it.

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rule 4) units can be changed by multiplying by an appropriate "unit factor".

this essentially combines rules 1, 2, and 3

example....

10 in = ? cm

10 in x 1 = 10 in right?

and 2.54 cm / 1 in = 1 right?

substituting

10 in x (2.54 cm / 1 in ) = 10 x 2.54 x in x cm / in = 25.4 cm

because inches cancel....

3 ft = ? in

3 ft x 1 = 3 ft x (12 in / ft) = 36 in

here is an important trick... if the units you want to cancel are on the top, put the matching units for the "unit factor" on the bottom.. and vice versa. if on the bottom, then put the matching ones one the top....

this will definitely take practice...

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rule 5) exponents....

since 1 to any power = 1... any "unit factor" raised to any power = 1

examples:

1² = 1

(2.54 cm / in) = 1

(2.54 cm / in)² = 1² = 1

similiarly

(2.54 cm / in)³ = 1³ = 1

how you use this is like this...

10 in³ = ? cm³

10 in³ x 1 = 10 in³ x (2.54 cm / in)³

= 10 in³ x (2.54 cm)³ / (1 in)³

= 10 in³ x 16.4 cm³ / 1 in³

= 164 cm³

and that's all there is to it...

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if you've made it this far..... here's an example

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let's say you have the reaction

1 N2 + 3 H2 ----> 2 NH3(g)

and you're given 56 grams of N2 reacts with XS H2 and the question is how many cubic feet of gas will be produced at STP.....  

via unit factor method....

1 mole N2 = 28 g N2

1 mole NH3 at STP = 22.4 L NH3

1 N2 ----> 2 NH3

1 L = 1000 ml

1 ml = 1 cm³

2.54 cm = 1 in

12 in = 1 ft....

ready???

56 g N2 x (1 mole N2 / 28 g N2) x (2 mole NH3 / 1 mole N2) x (22.4 L NH3 / 1 mole NH3) x (1000 ml / L) x (1 cm³ / 1 ml) x (1 in / 2.54 cm)³ x (1 ft / 12 in)³ = 3.16 ft³ NH3

the units progressively cancel and change from g N2  into ft³ NH3.  simple if you look at each value in () as 1 unit factor (which always = 1). That is I progressively multiplied x 1 x 1 x 1 and so on until the units were the units I wanted....do you see that...

alternately I could have solved this problem by....

moles N2 = mass / mw = 56 g / (28 grams / mole) = 2 moles

1 mole N2 / 2 moles NH3 = 2 moles N2 / X moles NH3

X = 2 x 2 moles = 4 moles NH3

22.41 L / X = 1 mole / 4 moles NH3

X = 22.41 * 4 = 89.2 L NH3 = 89200 ml = 89200 cm³ NH3

now what?  and do you see how complicated this is becoming with the proportions?   it would be very easy to get one setup incorrectly...

good luck..