How many US dollars would it cost to extract the
145,000,000,000,000,000 tons of hydrogen from the Earth's oceans?

Is this just hypothetical, or do you actually want to decompose all the ocean water?

More than the hydrogen and the energy contained therein is worth.  It
takes more energy to extract hydrogen from water than you get back
when you burn it.

One liquid gallon equals 3.785411784 liters of gas


From http://www.physlink.com/education/askexperts/ae367.cfm

"The amount of hydrogen extracted from a gallon of water can be found
very easily using the molecular weight of H20 (water), Hydrogen and
Oxygen, along with mass conservation. the molecular weight of water is
2 H (molecular weight 1) + 1 Oxygen (Molecular weight 16) for a total
of 18. And for every Molecule of water converted, we would get 2
Molecules of Hydrogen.

So, now the question is, how many molecules of water are there in a
gallon of water? The density of water is 1g/(cm3) so in 1 gallon of
water ( about 3.785 Liters or 3785 cm3) the mass of the water is,
3785g. 1 mole of 6.02x1023 molecules of water is equal has the mass in
grams equal to the molecular weight or 18 grams per mole. so 3785
grams corresponds to about 1.265 x 1026 molecules of water.

Now, if every single one of those molecules were converted into
Hydrogen we would get twice as much hydrogen as we had of water. or
2.53 x 1026 molecules of hydrogen. however since hydrogen is a
diatomic molecule, meaning that the hydrogen that we talk about is H2,
we would get 1.265 x 1026 molecules of hydrogen. at 1 atmospheric
pressure and 273K, 1 mole of hydrogen fills approximately 22.4L of
volume. so 1.265 x 1026 molecules or about 210 moles, would fill 4707
Liters of volume."


From http://www.stardrivedevice.com/electrolysis.html

"A couple years ago, our initial research found that the end-user
price for liquid hydrogen was quite close to $4 per gallon when
produced commercially by water electrolysis, $3 per gal. by steam
reformation of methane (natural gas), and $2 per gal. by electrolysis
of methanol. The most accurate current figures we've been able to
develop are respectively $4.33, $3.25, and $2.17.]"

From http://www.dcr.virginia.gov/sw/amznstuf.htm

"The quantity of water on Earth is static - 326 million cubic miles.
One cubic mile contains 1,000,000,000,000 (one trillion) gallons of
water"



so using the cheapest option of $ 2.17 a gallon it would be 

326000000*1000000000000*16.5
	5379000000000000000000

or 

326 million x one trillion x (3.8*2 x 2.17)= $ 5,379,000,000,000,000,000,000.oo

buku bucks no doubt.

whops I just realized I made a big mistake... it should've been 

326000000*1000000000000*1238*2.17
	875785960000000000000000

or 

326 million x one trillion x (1,238 x 2.17)= $ 875,785,960,000,000,000,000,000.oo

but hey! what's 870 sextillions among friends....

>> but hey! what's 870 sextillions among friends....

Yeah, but when you got 870 sextillions here and 870 more sextillions
there, eventually it adds up to real money.

Them's my kind of friends!

The question also raises the problem of what to do with all the
hydrogen (how to contain it), plus the oxygen released, plus the salt,
etc.  - including a nice supply of gold.  And then there is the
consideration of the plants necessary to realize the project.
Somehow, I feel that one wouldn't even notice the ocean level's declining.

Nice job, elids.  One point you missed though was that only the
$4.33/gallon option is available for making hydrogen from water. 
Electrolysis of methanol to produce hydrogen obviously relies on a
supply of methanol as the starting material, rather than water.

So, the actual figure would be about double your 870 sextillion. 
Darn, just when things were looking feasible! ;)

To add something interesting rather than just poo-pooing the idea, I
figured out the energy required to produce 1.45 x 10^17 tons of
hydrogen.  I found one source that quoted hydrogen as having an energy
content of 142 MJ/kg.  Assuming 50% efficiency in converting water to
hydrogen it would require 4.1 x 10^22 MJ to convert the earth's
oceans.  To put this in perspective, this is about 7500 years worth of
the energy that the earth receives from the sun or ~360 million years
worth of current worldwide electrical generation capacity.