Need a math whiz

[SciFiJim]

I have a source of solder from a radiator shop. The solder is a binary alloy of Lead/Tin with no other metals mixed in. However, I want to make sure of the percentage of tin in what I recover.

Some facts I know.

The specific gravity of lead is 11.35
The specific gravity of tin is 7.28

By math a round ball of pure tin would weigh 64.14% of a pure lead ball. (7.28/11.35=.6414)

I have cast some pure lead .45 round balls that weigh 129.5 grains

By math a round ball of pure tin would weigh 83.1 grains

I have cast some radiator solder .45 round balls that weigh 107.8 grains

What is the formula to figure the percentage of tin?

a) 129.5/107.8 = 83.24% tin

b) 83.1/107.5 = 77.3 % tin

or am I all wet and using the wrong approach?

[bruce381]

I would go with B till someone smarter says otherwise

[Defcon-One]

No math whiz here, but I came up with this using the densities:

The density of Lead is 0.409 lb. per cubic inch or (2,863 gr. per cubic inch).
The density of Tin is 0.264 lb. per cubic inch or (1,848 gr. per cubic inch).

It is basic math now:

At 129.5 grains your .45 ball is .0452 cubic inches of pure Lead. (129.5/2,863=0.0452)

So, a .45 ball of pure Tin from your mould would actually be 1,848 X .0452 = 83.53 gr.

A .45 ball from your mould of the radiator solder is 107.8 grains. That works out to about 47.2% Tin and 52.8% Lead per this equation:

(X * 83.53 gr.) + (1-X * 129.5 gr.) = 107.8 grains

83.5X + 129.5 – 129.5X = 107.8

83.5X –129.5X = 107.8-129.5

-46X = -21.7 (the negatives cancel out, so)

X = 21.7/46 = 0.472 Tin

1-0.472 = 0.528 Lead

Proof:

(0.472 * 83.5) + (0.528 * 129.5) =

39.41 + 68.38 = 107.79 grains which is pretty close to 107.8 grains of your radiator solder ball!

*********

Someone better check this as I may be all wrong.....

[garym1a2]

You pretty close. Off the top of my head if you take a 129.5 gr ball plus 83.1 ball and add them/2 you get 106.3gr for 50/50. Since he got 107.8 I say thats a small bit over 50%. So my guess is you are right or not off by much.

No whiz here but I came up with this using the densities:

The density of Lead is 0.409 lb. per cubic inch or (2,863 gr. per cubic inch).
The density of Tin is 0.264 lb. per cubic inch or (1,848 gr. per cubic inch).

It is simple math now:

At 129.5 grains your .45 ball is .0452 cubic inches of pure Lead. (129.5/2,863=0.0452)

So, a bullet of pure Tin from your mould would actually be 1,848 X .0452 = 83.53 gr.

A .45 ball from your mould of the radiator solder is 107.8 grains. That works out to about 47.2% Tin and 52.8% Lead per this equation:

(X * 83.53 gr.) + (1-X * 129.5 gr.) = 107.8 grains

83.5X + 129.5 – 129.5X = 107.8

83.5X –129.5X = 107.8-129.5

-46X = -21.7 (the negatives cancel out, so)

X = 21.7/46 = 0.472 Tin

1-0.472 = 0.528 Lead

Proof:

(0.472 * 83.5) + (0.528 * 129.5) =

39.41 + 68.38 = 107.79 grains which is pretty close to 107.8 grains of your radiator solder ball!

Someone better check this as I may be all wrong....

[Uncle Jim]

Math is correct!

[SciFiJim]

A higher tin content than I expected, but not as high as I had hoped.

[NewbieDave007]

Your math and process is correct.

No math whiz here, but I came up with this using the densities:

The density of Lead is 0.409 lb. per cubic inch or (2,863 gr. per cubic inch).
The density of Tin is 0.264 lb. per cubic inch or (1,848 gr. per cubic inch).

It is basic math now:

At 129.5 grains your .45 ball is .0452 cubic inches of pure Lead. (129.5/2,863=0.0452)

So, a .45 ball of pure Tin from your mould would actually be 1,848 X .0452 = 83.53 gr.

A .45 ball from your mould of the radiator solder is 107.8 grains. That works out to about 47.2% Tin and 52.8% Lead per this equation:

(X * 83.53 gr.) + (1-X * 129.5 gr.) = 107.8 grains

83.5X + 129.5 – 129.5X = 107.8

83.5X –129.5X = 107.8-129.5

-46X = -21.7 (the negatives cancel out, so)

X = 21.7/46 = 0.472 Tin

1-0.472 = 0.528 Lead

Proof:

(0.472 * 83.5) + (0.528 * 129.5) =

39.41 + 68.38 = 107.79 grains which is pretty close to 107.8 grains of your radiator solder ball!

*********

Someone better check this as I may be all wrong.....

[digger44]

Just use them as tin adds for casting bullets and add more tin only as needed for bullet fillout.

[EDG]

Tin and lead do not necessarily mix and retain the same volume. When the atoms alloys the material may be more dense than just a mixture of 2 molten metals.

[Finarfin]

It's 50/50. The rest is rounding error. Rounding of the ball, that is. Lol. Consider your math whizzed.

[mikeym1a]

The local shop where I buy solder, when needed, keeps 50/50 solder in stock, primarily for the local radiator shop. So, unless there are state restrictions on the solder, it is most likely 50/50.

[Defcon-One]

It's 50/50. The rest is rounding error....Consider your math whizzed.

Yeah, I'm the guy who Whizzed it. I figured it was 50/50.

I didn't say it outright 'cause I thought that it was pretty obvious. It is too close to be anything else and, while the math may be perfect, there are lots of other errors in the "process".