Question

DIMENSIONAL ANALYSIS: A 55.0 gal drum weighs 75.0 lb when empty. What will it weigh when it is filled with ethanol, which has a density of 0.789 g/ml

Answer 1

Got a plan for this one? I'm sure you see that you'll have to do two conversions: grams to pounds and gallons to milliliters.

Answer 2

the only problem i have with the problem is that all of the units keep canceling out...

Answer 3

or i end with\[g ^{2}/ml ^{2}\]

Answer 4

Ah, make sure you arrange your conversion factors in the proper way. e.g. you'll have to convert the 55.0 gallons to ml to find the additional weight in grams.
So you could do (55.0 gal.)(4 qt./gal.)(1.06 l/qt.)(1000 ml/l).

Answer 5

So if the unit you want to cancel is in the numerator then you need to put that unit in the denominator of the conversion factor to cancel it.

Answer 6

lemme show you what i keep getting and you can tell me what im doing wrong...

Answer 7

\[ \frac{ 55.0 gal }{ 75.0 lb }\times \frac{ 4 qt }{ 1 gal } \times \frac{ 1.06L }{ 1qt } \times \frac{ 1,000mL }{ 1L } \times \frac{ 1 lb }{ 454 g } \times \frac{ .789 g }{ ml }\]

if i do this, every unit gets cancelled

Answer 8

Ah, I see. Don't start with 55gal/75lb. You don't need the density of the empty barrel.

Answer 9

what do you mean?

Answer 10

The 75 pounds is the empty weight; you add that on at the end to find the new total weight. You don't otherwise use it in the calculations.

Answer 11

Start by changing the 55 gallons into milliliters, then multiply by the density of the stuff to find the additional weight.

Answer 12

ohhh. okay. thanks. i was trying to put everything into one equation....but i guess thats not possible :)

Answer 13

Not in this case, no. Oh, what was that conversion factor for quarts to liters again? I have scribbled here from last time something that looks like 1.06 liters/quart, but that doesn't make sense because liters are bigger than quarts.

Answer 14

1.06 quarts to liters

Answer 15

Conversions:
1 gal = 3785.41 mL
1 kg = 2.20462lb

\[55*\frac{3785.41mL}{1gal}=208197.55mL\]Calculate how many grams that would be:\[\frac{0.789g}{1ml}*208197.55mL=164267.867g=164.267867kg\]Finally, convert the kg to lbs:\[\frac{164.267867}{1} \cancel{kg}*\frac{2.20462}{1\cancel{kg}}=362.4182249lbs\]

Answer 16

Of course you also need to adjust it for significant 3 figures.

Answer 17

You can do it all with a single line too. Using the factors provided by Shane:
\[New \space weight=(55.0 gal.) \cdot \frac{3785.41ml}{gal.} \cdot \frac{0.789g}{ml} \cdot \frac{pounds}{453.592g}+75.0 \space pounds.\]

Answer 18

Yep and note that I forgot all about adding the weight of the drum...so don't forget that :)

Answer 19

Thanks for those unit converters, I was about to go gallons to quarts to liters to milliliters.

Answer 20

Perfect :) Thanks so much!!!

Answer 21

heh...it's not like I memorized the first one. GOOGLE :)

Answer 22

:)