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Both the descent and ascent stages of the Apollo Lunar Module were powered by silver-zinc batteries.

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Source: Apollo Lunar Module Electrical Power System Overview

The total weight of these batteries were 296 kg and 356 kg for the extended missions with longer stay on the Moon.

How much silver was at least left on the Moon by Apollo LM batteries?

Uwe
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TL;DR: 612kg

Well, as an approximate lower bound you can use the listed amp-hours of capacity and the battery chemistry to determine how many atoms of silver would be needed. To produce one amp-hour requires 3,600 Coulombs of charge. In silver-zinc batteries, each atom of silver is reduced twice, giving off two electrons.

A single electron has a charge of 1.602×10−19 Coulombs, so you would need (1/2) / 1.602×10−19 = 3.12x1018 silver atoms, or 3.12x1018 / 6.022x1023 = 5.18x10-6 moles of silver per Coulomb.

Multiplying this by the 3,600 Coulombs needed for one amp-hour, we get a minimum of 0.019 moles of silver per amp-hour. However, one cell of silver only produces ~1.55 volts, so the real battery has 20 cells. Therefore, we need 0.373 moles per full amp-hour. As silver weighs 107.87 g/mol, this would weigh 40.2g.

Finally, we can calculate the minimum silver for each type of battery:

LM Descent: 400 Ah x 4.5 batteries = 72.5kg of silver (out of 270kg total)
LM Ascent: 296 Ah x 2 batteries = 23.8kg of silver (out of 112kg total)
CSM: Returned to Earth.

Having 20-30% of the batteries be silver makes sense, as there was also roughly the same amount of zinc in the batteries, as well as electrolyte and a casing.

The descent stages obviously stayed on the Moon, and there were 6 of them: 72.5kg x 6 = 435kg.

The 6 ascent stages (which impacted the Moon after ascent): 23.8 x 6 = 143kg.

Also, although they were not included in your question, the lunar rovers used silver-zinc batteries of 23 cells each, and the batteries of the 3 lunar rovers, at 242 amp-hours each, would add 34kg of silver total.

Total: 612kg of silver, worth ~300,000 USD today. Of course, "Moon silver" would probably fetch a higher price.

IronEagle
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  • You forgot to use the number of serial cells to reach 29 V and the number of batteries (4 to 5 in descent stage and 2 in the ascent stage). So the weight is much higher. – Uwe May 12 '20 at 20:19
  • Right. I'll adjust for that. – IronEagle May 12 '20 at 20:48
  • See Wikipedia for the number of batteries. – Uwe May 12 '20 at 20:57
  • Hmm... although then the silver would weigh more than the battery, if 3.22kgx20 = 64.4kg... I'll check my math some more. – IronEagle May 12 '20 at 21:00
  • You did use the number of 2 electrons per silver atom wrong. You did multiply by 2, but you should divide by 2. The weight of silver within a 60 kg 400 Ah 29 V battery should be less than about 20 to 30 kg. – Uwe May 12 '20 at 21:06
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    Is your answer 2.5 tons? That's ridiculous. The whole LM weighed < 17 tons, wet. – Organic Marble May 12 '20 at 21:07
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    I assume IronEagle is talking about 6 LMs, not 1, but there's only 1647kg of battery, total, in the 6 descent modules on the lunar surface. https://en.wikipedia.org/wiki/Apollo_Lunar_Module#Descent_stage – Russell Borogove May 12 '20 at 21:11
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    I know, and that's still like .4 ton of silver per LM. No way. – Organic Marble May 12 '20 at 21:15
  • @Uwe - yep. So like 1/4 of the total. Which would be about 1/4 of the battery, which makes sense, as there's also zinc, and electrolyte, and spacers and casing. I'll update my answer. – IronEagle May 12 '20 at 21:40
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    @OrganicMarble I think we found the final issue. – IronEagle May 12 '20 at 22:22
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    @IronEagle There's no need to call out the edits in your answer. Anyone who wants to look at the edit history can do so. It's confusing the way it's written now. Suggest editing to show only your current values. That way someone can read the question and see immediately what the answer is. – Organic Marble May 12 '20 at 22:22
  • @IronEagle looks good! – Organic Marble May 12 '20 at 22:55
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    Possibly one more descent stage: Apollo 10's was never found and might also be on the moon. However, its ascent stage is in orbit around the Sun. – DrSheldon May 13 '20 at 02:16
  • Did you use the correct voltage of the lunar rovers: "Power was provided by two 36-volt silver-zinc potassium hydroxide non-rechargeable batteries with a charge capacity of 121 A·h each (a total of 242 A·h)"? Not 29 but 36 V. – Uwe May 13 '20 at 07:51
  • Assuming USD500/kg that makes USD 300k roughly. How much do they ask for a tonne of hydrazine on the Moon today? –  May 13 '20 at 13:48
  • @Uwe - I wasn’t able to find a source that listed the number of cells - unloaded, the 20-cell configuration gets 36V. – IronEagle May 13 '20 at 15:22
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    @Uwe - actually just found http://www.temjournal.com/content/74/TemJournalNovember2018_937_943.pdf , so apparently 23 cells instead of 20 for the rover. I'll update. – IronEagle May 13 '20 at 15:56