How fast does CO2 dissolve?

I racked 5 gallons of Kolsch into a corny on Sunday and primed with 2.5 oz of corn sugar. I pressurized the keg about 5lbs to seal it and attached a bleeder valve to monitor the pressure increase.
The next day the pressure was down to zero. Today I got around to repressurizing the keg to 5 lbs and spraying it down with Star San to find the leak. No bubbles. Now, about two hours later the pressure is down to zero.
Does it absorb that fast? I would think the pressure would stay the same even if it absorbed, correct? Keg is at 62F.

I'm sure the resolution on the gauge probably isn't capable of displaying PSI between 0-1 but that's about where it would be if you had no leaks. When you pressurize to 5psi, you're actually only achieving that pressure in the headspace which is quite small in a full corny. When it dissolves into the 5 gallons of beer, the pressure is effectively cut to a 10th. That's assuming the headspace is .5 gallons and the keg has 5 gallons of beer.

The headspace pressure doesn't remain until the beer and the headspace reaches equilibrium.

Two hours does seem a little faster than I'd expect so there's a small chance of a leak once the pressure starts dropping. Try putting 2psi on it and spray it down for leak test again.

Found it! I had a leak in my bleeder valve. Pilot error on the construction
The angle made it tough to get enough Starsan on the joint.

I was hoping to watch the pressure magically rise this week after priming. Perhaps now my dream will come true.