Weight percent of element to give specific density for alloy

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Discussion Overview

The discussion revolves around calculating the weight percent of lithium (Li) required to achieve a specific density for an aluminum-lithium alloy, specifically targeting a density of 2.47 g/cm³. Participants explore various approaches to relate the densities and volumes of the two metals in the alloy.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses uncertainty about how to relate the quantities of aluminum and lithium given the lack of specific amounts in the problem statement.
  • Another participant suggests assuming additive volumes of the metals to compute the total mass and density of the alloy, although they note that this assumption may be flawed.
  • A different participant proposes using two equations based on the volumes of lithium and aluminum to express the total volume and density of the alloy.
  • Further contributions emphasize the need to calculate the masses of each metal based on their respective volumes and densities, and to use these to find the total mass and density of the alloy.
  • One participant arrives at a calculation yielding 2.3 wt% Li after substituting values and solving for volumes and masses, indicating a realization of the broader picture in the problem-solving process.

Areas of Agreement / Disagreement

There is no consensus on the best approach to solve the problem, as participants express varying levels of understanding and propose different methods. Some participants agree on the need to calculate volumes and masses, while others question the assumptions made about volume additivity.

Contextual Notes

Participants note the potential flaw in assuming additive volumes, which may affect the accuracy of the calculations. The discussion reflects a reliance on specific density values and the definitions of mass and volume without resolving the implications of these assumptions.

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Homework Statement


Aluminium-Lithium alloys have been developed by the aircraft industry to reduce the weight and improve the performance of its aircraft. A commercial aircraft skin material having a density of 2.47 g/cm3 is desired. Compute the concentration of Li (in wt%) that is required.


Homework Equations





The Attempt at a Solution


I've calculated the atoms/cm3 for both aluminium and Lithium, but I'm not sure how to relate them seeing as the question doesn't give an amount/quantity of either element. I assume there is an equation or something I should use but I can't think of it.
 
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You have to assume that volumes are additivie. Imagine you have melted 1 mL of lithium with 1 mL of aluminum. Assume the volume of the alloy is 2 mL. What is its mass? What is its density? Do you see how it is related to the original question?

Question is flawed, as volumes are not additive, but that's another story.
 
Thanks, but I'm still not quite getting it. After adding the densities and dividing the wanted density by this amount I know it needs to be 1.617e+0 times more dense, but i still don't understand how to work this out. Obviously I have to increase the ratio of Al/Li but I'm not quite sure how i do this.
 
You may try with two equations - let VLi be volume of lithium, VAl be volume of aluminum used. Express total volume and density of alloy in terms of these two unknowns (that will give you two equations). Then solve. Assume total volume to be 2 or 7 or whatever, just give it some number value.

It can be also done using volume fractions and in many other ways, but the one I have described is probably the most intuitive one.
 
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I think you might have to spell this one out for me Borek, I can't seem to get my head around it. I know you pretty much already have but it still isn't registering.
 
If you mix VLi and VAl of both metals - what will be total mass of the mixture?

Assuming VLi + VAl = 2, what will be the density of the mixture?

Do you see two equations in two unknowns?
 
Sorry, i just can't see it. It is probably really simple, but i can't figure it out.
 
You should know densities of lithium and aluminum.

What is mass of 1 mL of aluminum?

What is mass of VAl milliliters of aluminum? (hint: use density definition)

Do the same for VLi milliliters of lithium.

Now you should know both masses and you know both volumes.

What is total mass?

What is total volume?

Knowing mass of the alloy and volume of the alloy, use density definition to calculate alloy density.

Go back to my previous post now.
 
Ok, mass Al = 2.7VAl
mass Li = .543VLi

VAl + VLi = 2
VAl = 2-VLi
VLi = 2-VAl

2.7(2-VLi) + .534(2-VAl) = 4.94

1.528 = 2.7VLi + .534VAl

I can then substitute VLi for 2-VAl and solve for VAl. I can then calculate VLi and subsequently calculate masses and weight percents of both.

= 2.3wt% Li

I think my problem was not seeing the big picture. E.g. work out both volumes and masses in terms of volumes first, and then incorporate them BOTH into the main equation.

Thanks for your patience :).
 
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