A chemistry word problem:

A

Avery7701

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Hi.
I am attempting to become more proficient using the dimensional analysis technique on my own. Due to health problems my early math skills were shoddy due to a lack of math learning in early schooling. But I am taking it on now because of my love of chemistry. So... help is appreciated. Here is my question.

I have the 2 physics formulas in my mind: D=M/V and W=MG. Do you think I should use these formulas in order to solve this problem? If so, then I am confused about how to work with the UNITS. If not, is it a simple conversion problem? Would you mind showing your work so that I might understand this? Also - I'm afraid this is an embarrassing question: what is dimensional analysis in terms of labeling. Is it a form of algebra?
Thank you.

Vanadium metal is added to steel in order to impart strength to the alloy. Vanadium has a density of 5.96 g/cm^3. The metallurgist adds 580 lbs of vanadium to a batch of steel. What is the volume, expressed in cubic feet, of vanadium that has been added to the batch of steel?
 
Avery7701 said:
Hi.
I am attempting to become more proficient using the dimensional analysis technique on my own. Due to health problems my early math skills were shoddy due to a lack of math learning in early schooling. But I am taking it on now because of my love of chemistry. So... help is appreciated. Here is my question.

I have the 2 physics formulas in my mind: D=M/V and W=MG. Do you think I should use these formulas in order to solve this problem? If so, then I am confused about how to work with the UNITS. If not, is it a simple conversion problem? Would you mind showing your work so that I might understand this? Also - I'm afraid this is an embarrassing question: what is dimensional analysis in terms of labeling. Is it a form of algebra?
Thank you.

Vanadium metal is added to steel in order to impart strength to the alloy. Vanadium has a density of 5.96 g/cm^3. The metallurgist adds 580 lbs of vanadium to a batch of steel. What is the volume, expressed in cubic feet, of vanadium that has been added to the batch of steel?
Click to expand...

Do you what does D, M, V, W & G stand for - in the equations that you quoted?
 
Vanadium has a density of 5.96 g/cm^3. The metallurgist adds 580 lbs of vanadium to a batch of steel. What is the volume, expressed in cubic feet, of vanadium that has been added to the batch of steel?
Click to expand...

“Dimensional analysis” is actually quite simple: Keep all units of measurement in your equations, and treat them just like variables; i.e., they can be multiplied, canceled, etc. Be careful to keep track of which units are in the numerator and which are in the denominator.

To change from one set of units to another, use “conversion factors.” Conversion factors are things (expressed as ratios in the equation) that you know are true, e.g., 1 foot equals 12 inches: (1 ft/12 in) or (12 in/1 ft).

D = (5.96 g/cm^3)(1 lb/453.5924 g)(2.54^3 cm^3/1 in^3)(12^3 in^3/1 ft^3) = 372 lb/ft^3

Study the above density conversion equation until you understand how all the units are working/canceling out.

Finally, rearrange your density equation and solve:

D = M/V => V = M/D

Hope that helps.
 
wjm11,
Yes, this helps. I understand.
When I am doing a dimensional analysis problem, what kind of problem am I doing? Is this considered an algebra problem?
 
Thanks again for your help. I followed your example and I think I got this next one right. :)
Excuse the archaic units of measurement that are used in the example.

How many rundlets are there in 0.25 tons of acetylsalicylic acid? In the land of Yor, the density of acetylsalicylic acid is reported to be 1.28 scruples per mL.

My work:
1.28 scruples/1 mL (1.296 grams/1 scruple) (0.001 kg/ 1 gram) (1 short ton/907.18474 kg) (1 mL/0.001 L) (1 L/ 0.0146646105 rundlets) = 0.124694911 Tons/Rundlet

V=M/D
=2.0 Rundlets
 
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