Weight percent of element to give specific density for alloy

[physicsnnewbie]

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.

 

[Borek]

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.

 

[physicsnnewbie]

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.

 

[Borek]

You may try with two equations - let V_Li be volume of lithium, V_Al 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.

 

[physicsnnewbie]

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.

 

[Borek]

If you mix V_Li and V_Al of both metals - what will be total mass of the mixture?

Assuming V_Li + V_Al = 2, what will be the density of the mixture?

Do you see two equations in two unknowns?

 

[physicsnnewbie]

Sorry, i just can't see it. It is probably really simple, but i can't figure it out.

 

[Borek]

You should know densities of lithium and aluminum.

What is mass of 1 mL of aluminum?

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

Do the same for V_Li 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.

 

[physicsnnewbie]

Ok, mass Al = 2.7V_Al
mass Li = .543V_Li

V_Al + V_Li = 2
V_Al = 2-V_Li
V_Li = 2-V_Al

2.7(2-V_Li) + .534(2-V_Al) = 4.94

1.528 = 2.7V_Li + .534V_Al

I can then substitute V_Li for 2-V_Al and solve for V_Al. I can then calculate V_Li 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 :).