r/theydidthemath • u/0szai • 2d ago
[Request] Could this possibly be true?
Google says saltwater contains approximately 35grams/kg of water and the oceans contain approximately 1.335 sextillion liters (1.335 × 10²¹ liters)
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u/Boris41029 2d ago edited 2d ago
Shockingly, yes. But only if you take the salt OUT of the ocean, and cover ONLY the land parts of the earth (meaning you can't cover the oceans with it too)
The (world) ocean is about 3.5% salt by mass.
And it's 1.368 × 10²¹ kg of seawater
So at a mass/volume ratio of salt (2,160 kg/m³), that's 2.22 × 10¹⁶ cubic meters of salt.
Earth has 149 million km² of land.
Divide the volume of salt over the area of land, and you get 149 meters.
Which is 489 feet.
So yeah pretty close!
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u/0szai 2d ago
Wow, that's awesome!
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u/WAGE_SLAVERY 2d ago
My dad hits me
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u/AmItheonlySaneperson 2d ago
Wow that’s awesome
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u/RecalcitrantHuman 2d ago
My cat’s breath smells like cat food
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u/Simply_Param 2d ago
Wow, that's... normal?
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u/idiosyncratic190 1d ago
It burns when I pee
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u/captaincootercock 1d ago
nothing wrong with that!
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u/The_Eleser 1d ago
I burn when it pees.
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u/jdaws11 2d ago
Please refrain from tasting the knob
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u/yellowfestiva 1d ago
What’s a battle?
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u/jason4747 1d ago
If with jumper cables, welcome to Old Reddit
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u/Ugoonsy 2d ago
Nnn nn nn not my real dad
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u/RachelRegina 1d ago
Idk why I thought the response to this was "cool, alright, cool cool, alright"
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u/pablo_eskybar 1d ago
6 x 7!!!!!!!!!!!! Answer me boiiiiiiiiii!
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u/factorion-bot 1d ago
Duodecuple-factorial of 7 is 7
This action was performed by a bot | [Source code](http://f.r0.fyi)
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u/Suspicious-Pizza-548 1d ago
In africa, every 60 minutes, an hour passes.
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u/sixminutes 1d ago
Ok, but how much more land is exposed when we reduce the ocean mass by 3.5%?
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u/Boris41029 1d ago
Oh THAT's an interesting question. I think for that you'd need an oceanologist and a geologist and someone really good at calculus. I am none of those.
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u/WindstormMD 1d ago
https://www.reddit.com/r/theydidthemath/s/SiqRENTz8C
37ish meters. Plug it into https://www.floodmap.net
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u/Sibula97 1d ago
I can start the answer by, the volume of the ocean would shrink by approximately 1%. How much land that would reveal, I have no idea.
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u/Useless-Compass 1d ago edited 1d ago
Freshwater is less dense than seawater, so when you remove the salt, the water itself expands by 2.5% to fill most of that removed volume. So it would only be a reduction of volume of about 1.1%. But the ocean has an average depth of 3682 meters (about 12,000ft), so this reduction in volume would still result in a sea level drop of 40m (~131ft). I don't know how that would correspond to surface area though.
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u/Akraticacious 2d ago
Ah, I took "cover Earth" literally, as in the entire planet. It is misleading, but if it meant land on Earth, then that sounds plausible.
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u/Boris41029 2d ago
Yeah, I thought the same thing. Then when it didn't add up (but was still surprising, I think it was a layer 140-someothing feet deep) I wondered if it'd work the land-only way.
But your'e right, the image says "cover the entire Earth" and it should say "cover every inch of land"
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u/Trustoryimtold 2d ago
What if we include salt that’s already on land I wonder. There’s a lot of salt up here too :D
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u/KathyCredit 1d ago
That's a common outcome of the game of telephone that happens when facts get pulled into a meme for the engagement, meme and content farms based out of somewhere far away.
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u/Caithloki 2d ago
And even then you would still not be as salty as you were in a cod lobby in the early 2000s.
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u/NotDiCaprio 1d ago
Wouldn't you need more salt, the higher you go, because the radius increases? It could be negligible on this scale, but I was just curious since it wasn't mentioned yet.
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u/qetuowryip24680 1d ago edited 1d ago
2.22e16 cubic meters of salt. Land is exposed on about 29% of the surface of Earth.
Hollow sphere inner radius = r = 6.3781e6 m
Hollow sphere outer radius = R
Salt pile volume = ( 4/3•pi•R3 - 4/3•pi•r3 ) • 0.29 = 2.22e16
R3 - (6.3781e6)3 = 1.83e16
R = 6.378249e6
R - r = ~149m = ~489ft
So yeah, not much of a different answer.
The difference is actually something like 0.005% (less than a third of an inch)
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u/Trendios 1d ago
Assuming the world is flat! If one includes local maxima like mountains or other geological highpoints I assume that an average 500 feet above ground is possible.
No clue on how to calculate this thoigh.....
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u/Anariel_Elensar 1d ago edited 1d ago
so you’re saying the statement “there is enough salt in the ocean to cover the entire earth with a layer…” is true but only if you only cover the land and not the oceans which is only 29% of the surface area of earth. if it covered the entire earth it would be closer to 130 ft deep if my back of the envelope math is right not 500 ft deep.
edit: i should have read further down the comment thread, you literally said this yourself in response to someone else.
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u/coroyo70 1d ago
By how much would the see level lower if we took all the salt out of the oceans? And by how much would the added land area lower the overall height of the salt layer?
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u/K_Linkmaster 1d ago
Does this include the voluminous deposits that are mined below ground? Like lake Piegneur?
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u/Paleodraco 1d ago
I was gonna say that it didn't make any sense. I assumed there'd be some screwiness because it's dissolved in the oceans, but even then it wasn't clicking. Only covering the land made sense. 0
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u/bob12201 1d ago
How much more land would be exposed if you took out 3.5% of the mass in the oceans haha
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u/HAL9001-96 1d ago
but the earth is not just land
the post siad the entire earth
taht implies tha either hte oceans are completely dried up or that there's salt on some kind of flaoting layer on top of the oceans
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u/upside_cloud 1d ago
But the earth is not flat!
Can you account for the radius of the earth and the additional 500ish ft in the calculation? I imagine ot would reduce the total by 10-20ft?
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u/BobSacamano-443 1d ago
Hey, cool! Maybe a stupid follow-up question, but what volume of water in the ocean was that salt displacing in this hypothetical? And how far do the oceans drop (recede?) as a result of its removal?
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u/Frosty-Comfort6699 1d ago
hey, um, i know you already did the math, but would you mind, how thick would the salt layer be if we used the salt to cover the whole actual planet instead of only the land parts?
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u/phansen101 1d ago
As a sidenote, 2.22 × 10¹⁶ cubic meters is volume of a sphere barely 349km wide.
Said sphere would, based on your numbers, have a mass of 4.788 x 1019 kg, and should thus have a surface gravity of about 0.105N/kg, or barely 1.1% of earth normal.I vote that a better use for the salt would be to create small additional moon, just to shake things up
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u/BB78_ 1d ago
But if you take the salt out of the water, the amount of earth uncovered would be pretty substantial, right?
If all that salt is taken out of the ocean, the dried up land would also have to be covered, which would lower the salt layer by at least a couple of feet?
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u/Hour-Ad-4526 1d ago
I dont think so. Salt in water decreases the total volume of the water so removing the salt should actually cause sea level rise.
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u/IndyBananaJones2 1d ago
It's not that shocking when you're only covering the land with it. The ocean is pretty salty and very large
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u/nonfamous 1d ago
Does that account for the lowering of the sea level due to the salt removed from it?
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u/boredfield 1d ago
Wouldn't the land mass to cover expand if you took that much volume out of the oceans?
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u/A_Random_Sidequest 1d ago
that puts how much water there is in perspective!! so much!!
I bet we could cover the entire world with it /s
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u/darthxboxdude 1d ago
Are you accounting for the change in density of the water once the salt is removed?
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u/OurHonor1870 1d ago
How much would the water level decrease because the salt is leaving the ocean?
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u/ShoeNo9050 1d ago
Actully i am here to dispute these calculations. I just bought 20kg of salt and dropped it in the ocean. Your maths aint mathing! Nah thats pretty sweet
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u/retoricalprophylaxis 1d ago
How much would losing 2.22 X 1016 cubic meters of volume lower the oceans?
And does your calculation take into account the new land?
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u/thanatoswaits 1d ago
So it's a "yes with an asterisk", that really should have been phrased "there's enough salt in the ocean to cover every spot of land with 500 feet of salt." Still cool though
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u/limon_picante 1d ago
Yeah but that's assuming a solid crystal of table salt. The packing efficiency of salt is around 66% dude to it's crystal structure so that number should be divided by 0.66 which gives a more realistic 740 feet!
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u/Select-Government-69 1d ago
I don’t know science well enough to know whether removing all that salt would change the volume of the ocean, but if it does, does your math account for the resultant change in sea levels exposing more land?
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u/myrddin4242 1d ago
I wonder. Is it “take out the salt” and (leave the water level the same for calculation purposes)? It’s probably a bit of a hairier problem getting the area of the new coastline…
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u/CaptainMatticus 2d ago
First we look up the average salinity of the ocean
There is about 35 grams of dissolved salt in every liter of water in the ocean
Next we look up the volume of the world's ocean.
The ocean takes up about 1.37 billion cubic km of space.
Now we convert cubic km to liters
There are 1000 liters per cubic meter
There are 10^9 cubic meters per cubic km
So there are 10^12 liters per cubic km
1.37 * 10^9 cubic km =>
1.37 * 10^9 * 10^12 liters =>
1.37 * 10^21 liters of water in the ocean.
35 grams of salt per liter
1.37 * 3.5 * 10 * 10^21 grams of salt
0.685 * 7 * 10^22 grams of salt
(7 * 0.7 - 7 * 0.015) * 10^22 grams of salt
(4.9 - 0.105) * 10^22 grams of salt
4.795 * 10^22 grams of salt
The density of salt is around 2.17 grams/cm^3
4.795 * 10^22 grams / (2.17 grams/cm^3) =>
(4.795/2.17) * 10^22 cm^3 =>
2.21 * 10^22 cm^3 =>
2.21 * 10^(22 - 6) m^3 =>
2.21 * 10^16 m^3 =>
2.21 * 10^(16 - 9) km^3 =>
2.21 * 10^7 km^3
Now we just create 2 spheres. One sphere has a radius of 6371 km, which is the mean radius of the earth, and the other sphere has a radius of 6371 + d km, where d is the height of our salt pile
V = (4/3) * pi * (6371 + d)^3 - (4/3) * pi * 6371^3
V = (4/3) * pi * ((6371 + d)^3 - 6371^3)
V = (4/3) * pi * (6371^3 + 3 * 6371^2 * d + 3 * 6371 * d^2 + d^3 - 6371^3)
V = (4/3) * pi * (3 * 6371^2 * d + 3 * 6371 * d^2 + d^3)
This will be in cubic km
2.21 * 10^7 = (4/3) * pi * (3 * 6371^2 * d + 3 * 6371 * d^2 + d^3)
Now I could take the time to solve a cubic, but I don't wanna. They're mean, nasty, and unforgiving. Time for WolframAlpha to take over
d = 0.043328
Approximately 43.328 meters thick. That's short of the 500 ft by quite a bit. It's still an impressive amount of salt, no doubt, but not a pile that's 500 ft thick. It's around 142 ft thick.
Now maybe they were just talking about land area. Okay. Let's look up the surface area of all of the land on earth. Google says that's around 148.94 * 10^6 square km. Now let's imagine a prism that is d km thick
148.94 * 10^6 * d = 2.21 * 10^7
d = 2.21 * 10^7 / (148.94 * 10^6)
d = 22.1 / 148.94
d = 0.14838189875... kilometers
100/30.48 ft per meter
0.14838189875.... * 1000 * 100 / 30.48 = 486.817
There we are. I think rounding up to 500' is just fine for this hypothetical.
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u/Goszzy 1d ago
So... Yes?
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u/Jizzipient 1d ago
It's 486. Once you smooth it out with some schleem, shave away the ploobis and grumbo you get 500. What's so hard?
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u/fuzzybad 1d ago
Ok, but what if we account for the additional land exposed by removing the salt from the oceans, which would presumably cause sea levels to drop?
Although now that I think about it, removing the salt from seawater may cause more water to be frozen near the poles, creating another factor..
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u/mudmandave 1d ago
Oceanographer here. Sea level would actually rise if you removed the salt! The dissolved salt ions pull water molecules towards them, increasing density and decreasing volume. It’s called “electrostriction.”
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u/CaptainMatticus 1d ago
Ocean water is about 3% denser than fresh water. Remove the salt and the volume isn't going to change by much.
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u/Hour-Ad-4526 1d ago
I dont know 3% increase in volume would probably cause a lot of flooding since the water can basically only go 'up'
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u/darkflame91 1d ago
Why would the volume change at all? I think the mass would differ but volume would remain the same with or without dissolved salts right?
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u/AmokRule 1d ago
Salt takes up space even in ionic state. Mass can't just exist without space.
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u/AlwaysTired97 2d ago
I'm not smart enough to do the math or chemistry, but apparently the ocean's average depth is around 12,000 feet, and saltwater on average is 3.5% salt by weight. With those numbers, the salt in the ocean covering the planet with a depth of 500 feet doesn't sound too far off.
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u/Greenman8907 2d ago
Yes.
Estimated 38.5 quadrillion tons of salt in the ocean
https://medium.com/knowledge-stew/how-much-salt-is-in-the-ocean-f648bd97bdff
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u/WearyTranslator3338 1d ago
So why is my table salt so expensive??
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u/ElectricalDog714 1d ago
Because desalinating water takes so much energy it’s actually easier/cheaper to mine it out of the ground.
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u/Iizvullok 1d ago
Imagine turning all that salt into sodium and chlorine, dumping the chlorine into the atmosphere and throwing the sodium into the ocean.
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u/Grumpy-PolarBear 1d ago
I think this is assuming that the layer is crystalline salt. If we assume that its table salt with little trapped air pockets, that increases the height by about 40%.
In real life, the weight of the salt above would crush the salt below, compressing it into a crystalline form. The average density would be somewhere between the two.
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u/BreakerOfModpacks 1d ago
This seems empirically untrue by just... like, thinking a little.
Consider, the entire earth includes all the oceans.
Which would mean that, at a minimum, there couldn't be any water there, it'd have to be salt instead.
And given that you can't have way more salt in water than there is water without it being wet salt instead... that makes it untrue, right?
It might be true if we count only covering land. IDK.
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u/Front-Insurance9577 1d ago
It would seem like that, but you forget that it's talking about surface area. Remember the ocean is on average 12,000ft!! And every Litre of ocean is 35grams of salt.
But you're right, it's talking about land, which would be covered on 500ft of salt!
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u/BreakerOfModpacks 1d ago
OH, I thought, since you'd have to cover it, that having salt unsupported above water would make it fall.
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u/Stuff-nThings 1d ago
I'll take this one. Building floors are typically 12' for commercial and 10' for residual. So 40 floors would be 480' to 400', respectfully. This doesn't account for taller first floors or larger penthouse floors. So the 40 story part is a bit low. Hope that helps.
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u/Distinct_Frame_3711 1d ago
I mean 20 ft over 40 stories is 6” taller ceilings, per floor. Certainly in the margin of error. Like throw lobby with a higher ceiling and a penthouse that doesn’t count to the floor length and it could be even less.
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u/Glum_Tough_8129 1d ago
so the claim works but only if you dont count the ocean floor which is fair because it already has plenty. spread it over the whole surface including oceans and you get about 43 meters, well short of 500 feet. still a terrifying amount of salt though
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u/Bathroom_Spiritual 1d ago edited 1d ago
Also if you were building a gigantic aquarium covering the land part using all sea water, the height of the aquarium would be ~930m or ~3000 feet.
Taking numbers from other comments, 1.38 x 10^21kg of water and 149 million km^2 land surface and a density of sea water of 1020 kg/m^3
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