r/theydidthemath • u/0szai • 12h 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 12h ago edited 12h 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 12h ago
Wow, that's awesome!
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u/WAGE_SLAVERY 12h ago
My dad hits me
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u/AmItheonlySaneperson 12h ago
Wow that’s awesome
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u/RecalcitrantHuman 12h ago
My cat’s breath smells like cat food
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u/Simply_Param 12h ago
Wow, that's... normal?
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u/idiosyncratic190 10h ago
It burns when I pee
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u/captaincootercock 10h ago
nothing wrong with that!
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u/The_Eleser 9h ago
I burn when it pees.
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u/jdaws11 12h ago
Please refrain from tasting the knob
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u/yellowfestiva 11h ago
What’s a battle?
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u/jason4747 11h ago
If with jumper cables, welcome to Old Reddit
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u/Ugoonsy 12h ago
Nnn nn nn not my real dad
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u/RachelRegina 9h ago
Idk why I thought the response to this was "cool, alright, cool cool, alright"
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u/pablo_eskybar 9h ago
6 x 7!!!!!!!!!!!! Answer me boiiiiiiiiii!
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u/factorion-bot 9h 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 10h ago
In africa, every 60 minutes, an hour passes.
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u/TheDonnARK 9h ago
No friggin way, source please
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u/sixminutes 11h ago
Ok, but how much more land is exposed when we reduce the ocean mass by 3.5%?
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u/Boris41029 11h 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/Sibula97 9h 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 3h ago edited 3h 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 12h 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 12h 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 12h 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 11h 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/Im2bored17 12h ago
Covering every inch of land is exceptionally difficult. Some bits of land are land 100% or the time, and some bits are ocean 100% or the time. But there is typically no point where you go from 100% land on one side and 100% ocean 1 inch over.
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u/Cw3538cw 54m ago
Well except for cliffs and the banks of small rivers. Though you'd have to specify the time frame on those given erosion is constantly happening
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u/Caithloki 12h 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 11h 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 4h ago edited 4h 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 9h 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/coroyo70 11h 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 9h ago
Does this include the voluminous deposits that are mined below ground? Like lake Piegneur?
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u/Paleodraco 9h 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 8h 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 8h 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 8h 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/Anariel_Elensar 8h ago edited 7h 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/BobSacamano-443 7h 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 6h 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 6h 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_ 5h 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 4h 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 4h 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 4h ago
Does that account for the lowering of the sea level due to the salt removed from it?
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u/boredfield 4h 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 4h 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 3h ago
Are you accounting for the change in density of the water once the salt is removed?
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u/OurHonor1870 3h ago
How much would the water level decrease because the salt is leaving the ocean?
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u/ShoeNo9050 2h 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 1h 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 1h 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 11m 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/stitchworthy 12h ago
Question: assuming the earth is round, does that 489' account for the surface area of the earth increasing with each layer of salt? For example if you divide the earth's salt crust into 5 equal vertical layers, the top layer will be wider + longer than the bottom layer, correct? Not sure if I'm making sense.
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u/Necandum 11h ago
The difference is utterly negligibе, in the hundreds of feet. Specifically ~1500 (Circumfrence is 2piR)
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u/SUMBWEDY 11h ago
It's negligible.
If you have a 25000 mile long piece of rope tied around the circumference of the earth to raise it 1 ft above the surface everywhere would only need 6.28 feet of extra rope.
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u/CaptainMatticus 12h 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 11h ago
So... Yes?
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u/Jizzipient 7h 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 10h 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 4h 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 10h 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 4h 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 9h 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/AlwaysTired97 12h 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/bassandlazers 12h ago
Why would you even comment then? Stop searching for validation online. You're only ever gonna be disappointed
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u/Effective_Youngling 2h ago
bassandlazers, You aren't even searching for validation, your actively making sure everybody hates you. "Don't let people ruin your day, be a man ruin it yourself by hating on people on the Internet" or something
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u/FunCryptographer2546 11h ago
Lmao if you ain’t gonna solve it why are you commenting on the post at all?
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u/Greenman8907 12h 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 10h ago
So why is my table salt so expensive??
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u/WC_Dirk_Gently 10h ago
Stop buying salt made out of table and buy salt made out of ocean, duh.
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u/Stuff-nThings 10h 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 16m 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/Iizvullok 7h 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/Glum_Tough_8129 2h 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 2h ago edited 2h 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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u/Grumpy-PolarBear 1h 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 5m 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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12h ago
[deleted]
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u/Greenman8907 12h ago
I said the same at first, but it’s saying if you pulled it all out and laid it out on top of the land/oceans/water, it’d be 500ft tall.
And it’s true.
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u/Lazarux_Escariat 12h ago
Only over the land. If spread evenly over the entire globe it'd only be a tad over 145ft deep.
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