How Much Does It Cost to Scent an Aircraft Hangar with Vanillin?

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Discussion Overview

The discussion revolves around a homework problem involving the calculation of the cost to scent an aircraft hangar with vanillin, as well as a related problem regarding the extraction of magnesium from seawater. Participants are attempting to determine the necessary quantities and costs based on given thresholds and conversions.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant calculates the volume of the aircraft hangar in liters and the minimum amount of vanillin needed to reach the aroma detection threshold, but expresses uncertainty about the next steps.
  • Another participant questions the clarity of units used in the calculations, specifically regarding the amount of vanillin calculated.
  • A further reply clarifies that the amount of vanillin is not in liters, prompting a request for explicit unit notation in calculations.

Areas of Agreement / Disagreement

Participants do not appear to reach consensus on the correct units and next steps for the calculations, indicating ongoing confusion and disagreement regarding the approach to the problems.

Contextual Notes

There are limitations in the clarity of unit conversions and the application of physical principles, which remain unresolved in the discussion.

mahachit
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Homework Statement

1. Vanillin(used to flavour vanilla ice cream and other foods) is the substance whose aromathe human nose detects in the smallest amount. The threshold limit is 2.0 X 10^-11 g per liter of air. If the current price of 50g of vanilin is $112, determine the cost to suppply enough vanillin so that the aroma could be detected in a large aircraft hangar with a volume of 5.0 X 10^7 ft^3. (Leave our answer in dollars and cents)


The attempt at a solution

This is what I've done so far for #1 :

1ft^3 = 28.32 L
(5.0 X 10^7) X (2.832 X 10) = 14.16 X 10^8 L (volume of aircraft in L)
(2.0 X 10^-11) X (14.16 X 10^8) = 28.32 X 10^-3 (minimum amoun of vanillin needed)

This is the part where I got stuck; what do I have to do next?

Homework Statement

2. Magnesium (Mg) is a valuable metal use in alloys, in batteries, and in the manufacture of chemicals. It is obtained mostly from seawater, which contains about 1.3g of Mg for every kilogram of seawater. The total volume of seawater is 1.5 X 10^21 L. Its density is 1.03g/mL. Calculate the amount of seawater (in liters) needed to extract 8.0 X 10^4 tons of Mg, which is roughly the annual production in the United States. (1 ton= 2000 lb; 1lb = 453.6 g.)

The attempt at a solution

so...to find the mass i have to multiply the density and volume, right?

W=mg
1.5 X 10^21 L = 1500 X 10^21 mL
(1.5 X 10^24) mL X 1.03 g/mL = 1.545 X 10^24 g/mL^2 (mass of seawater)

So now I have to multiply the mass by gravity...but what is the formula gravity? And what do I have to do after that?
 
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It is all about units - for example, you have calculated amount of vanilin to be 28.32 X 10^-3 of what? Pounds? Stones? Moles? Atoms? Boxes?
 
ok so the amount of vanillin I have calculated is in Litres...but what step should I do next?
 
No, it is not in litres. Pay attention to your units. Write them explicitely.
 

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