The solubility of N2 in blood at 37^∘ C and at a partial...

The solubility of $\mathrm{N}_{2}$ in blood at $37^{\circ} \mathrm{C}$ and at a partial pressure of 0.80 atm is $5.6 \times 10^{-4} \mathrm{mol} / \mathrm{L}$. A deep-sea diver breathes compressed air with the partial pressure of $\mathrm{N}_{2}$ equal to 4.0 atm. Assume that the total volume of blood in the body is $5.0 \mathrm{L}$. Calculate the amount of $\mathrm{N}_{2}$ gas released (in liters at $37^{\circ} \mathrm{C}$ and 1 atm) when the diver returns to the surface of the water, where the partial pressure of $\mathrm{N}_{2}$ is 0.80 atm.

Key Concepts

Henry's Law

Henry's Law states that the amount of a gas dissolved in a liquid at equilibrium is directly proportional to the partial pressure of that gas above the liquid. This law is fundamental in understanding how different pressures affect the concentration of gas in a solution and is widely used in fields such as chemistry, physiology, and environmental science.

Partial Pressure

Partial pressure refers to the pressure exerted by an individual gas in a mixture of gases. It is important in calculating the solubility of gases in liquids because the solubility is dependent on the specific partial pressure of the gas rather than the total pressure of the mixture.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas. It is an essential principle for converting between the amount of gas (in moles) and its volume under specific conditions, facilitating calculations where gases change conditions, such as during the decompression process in diver physiology.

Transcript

00:01 This is question 38 from chapter 13 and it's about dye nitrogen in the blood of the solubility and we are trying to see what is the pressure or the volume when diver is coming up to the surface.

00:19 So they said the dye nitrogen is equal to 4 .0 atmosphere and so the first thing we're going to do is actually use sulfur, use henry's constant.

00:36 Okay, so they do give us henry's constant.

00:43 I'm going to have this k.

00:45 That's what it stands for.

00:46 K is equal to.

00:47 And they give us a 5 .6 times 10 to negative 4 moles per liter.

01:01 And they also give us a pressure of 0 .80.

01:22 And that is going to come out to be 7 times 10 to negative 4 liters times atmosphere.

01:47 And we're going to take that and multiply that with the 4 .0 that they say it's equal to.

01:54 So 7 times 10 to negative 4 times 4 atmospheres pressure.

02:11 That is going to be equal to 2 .8 times 10 to negative 4th.

02:36 Okay, after that we have to find the di - nitrogen gas, so we have to find the number of moles of the gas dissolved.

02:45 So i'm going to take the 2 .8 and we are going to multiply that by the cell.

03:02 It was 5 liters.

03:04 So 5 .0 liters.

03:10 And that comes out to be 0 .028 moles.

03:28 Okay, now it's, i got ahead, just up .028, spoiler alert.

03:40 I'm going to basically half that, so it shouldn't have been 1, 14, my bad, so moles...

Please give Ace some feedback