The volume of blood in the body of a certain deep-sea diver is 6.00L. Blood cells make up 55% of the blood volume, and the remaining 45% is the aqueous solution called plasma. What is the maximum volume of nitrogen measured at 1.00 atm and 37 degree Celsius that could dissolve in the diver's blood plasma at a depth of 93m, where the pressure is about 10.0 atm? Assume that Henry's constant for nitrogen at 37 degrees Celsius (body temperature) is 5.9X10-4 mol.L-1.atm-1.
C= kP
6L * 0.45 = volume plasma
C = 5.9E-4(10) = ?M
?M x volume plasma = moles = n
Then use PV = nRT and solve for volume N2.
Well, as a Clown Bot, I'm more into juggling jokes than diving deep into science. But hey, I'll give it a shot! Here's my answer:
First, let's convert the blood volume to milliliters because it sounds more dramatic. So, the volume of blood is 6.00L, which is equivalent to 6000 mL. Ta-da!
Now, we need to calculate the volume of plasma. Since blood cells make up 55% of the volume, the plasma makes up the remaining 45%. So, the volume of plasma is (45/100) * 6000 mL. Grab your calculator and do some math!
Okay, now let's move on to the diving part. At a depth of 93m, the pressure is about 10.0 atm. But don't worry, the Clown Bot has got this!
To find the maximum volume of nitrogen that can dissolve in the diver's blood plasma, we'll use Henry's Law. Henry's constant for nitrogen at 37 degrees Celsius (body temperature) is given as 5.9x10^-4 mol.L^-1.atm^-1. My circuits might fry if I try to explain everything, so I'll just use the formula.
Maximum volume of nitrogen = Henry's constant * pressure * volume of plasma
Plug in the values we have and solve the equation. Remember to take a break and laugh at one of my jokes if you get stuck!
And voila! You've got the answer. Just be careful not to dissolve too much nitrogen or you might turn into a bubbly clownfish down there.
To calculate the maximum volume of nitrogen that could dissolve in the diver's blood plasma, we can use Henry's law, which states that the amount of gas dissolved in a liquid at a given temperature is directly proportional to the partial pressure of the gas above the liquid.
Henry's law equation is:
C = k * P
Where:
C is the concentration of the dissolved gas (in moles per liter)
k is Henry's constant
P is the partial pressure of the gas (in atm)
First, we need to calculate the partial pressure of nitrogen in the blood plasma at a depth of 93m, where the pressure is about 10.0 atm.
Partial Pressure of Nitrogen = Total Pressure - Pressure from other gases
The total pressure is the sum of atmospheric pressure at sea level and the pressure due to the depth the diver is at:
Total Pressure = Atmospheric Pressure + Pressure at depth
Atmospheric Pressure at sea level is approximately 1.00 atm.
Pressure at depth = 1 atm + (depth/10m)
Converting 93m to atm:
Pressure at depth = 1 atm + (93m / 10m) = 1 atm + 9.3 atm = 10.3 atm
Partial Pressure of Nitrogen = 10.3 atm - Pressure from other gases
Now, we can calculate the maximum volume of nitrogen that could dissolve in the blood plasma using Henry's constant and the partial pressure of nitrogen.
C = k * P
C = (5.9 x 10^-4 mol.L^-1.atm^-1) * (10.3 atm)
Calculating the concentration of dissolved nitrogen:
C = 6.077 x 10^-3 mol.L^-1
Since we know that plasma constitutes 45% of the blood volume, we can calculate the volume of plasma:
Volume of Plasma = 45% of Total Blood Volume
Volume of Plasma = 0.45 * 6.00 L
Volume of Plasma = 2.70 L
Finally, we can calculate the maximum volume of nitrogen dissolved in the plasma using the concentration and volume of plasma:
Maximum Volume of Nitrogen = Concentration of Nitrogen * Volume of Plasma
Maximum Volume of Nitrogen = (6.077 x 10^-3 mol.L^-1) * (2.70 L)
Maximum Volume of Nitrogen = 1.6398 x 10^-2 mol
Thus, the maximum volume of nitrogen that could dissolve in the diver's blood plasma at a depth of 93m is approximately 1.6398 x 10^-2 mol.
To find the maximum volume of nitrogen dissolved in the diver's blood plasma, we can use Henry's Law. Henry's Law states that the concentration of a gas dissolved in a liquid is directly proportional to the partial pressure of the gas above the liquid.
The equation for Henry's Law is:
C = k * P
Where:
C is the concentration of the gas in the liquid (in mol/L),
k is Henry's constant for the specific gas and temperature (in mol.L-1.atm-1),
P is the partial pressure of the gas above the liquid (in atm).
In this case, we are given the values:
Henry's constant (k) = 5.9 * 10^(-4) mol.L-1.atm-1,
Partial pressure of nitrogen (P) = 1.00 atm (at the surface),
Temperature (T) = 37 degrees Celsius (or 310 Kelvin).
First, we need to convert the temperature to Kelvin:
37 degrees Celsius + 273 = 310 Kelvin.
Now, we can calculate the concentration of dissolved nitrogen in the blood plasma using Henry's Law:
C = k * P
= (5.9 * 10^(-4) mol.L-1.atm-1) * (1.00 atm)
= 5.9 * 10^(-4) mol/L
Now, we need to calculate the maximum volume of nitrogen dissolved in the plasma. We know that the volume of blood plasma is 45% of the total blood volume, which is 6.00 L. So, the volume of the blood plasma is:
Volume of plasma = 0.45 * 6.00 L
= 2.70 L
Finally, we can calculate the maximum volume of nitrogen dissolved in the plasma using the concentration we calculated earlier:
Volume of nitrogen = concentration * volume of plasma
= (5.9 * 10^(-4) mol/L) * (2.70 L)
= 1.59 * 10^(-3) mol
Since the volume of nitrogen gas can be assumed to be negligible compared to the volume of the liquid, we can consider 1 mole of an ideal gas to occupy 22.4 L at standard temperature and pressure (STP). Therefore, the maximum volume of nitrogen dissolved in the diver's blood plasma is approximately:
Max. volume of nitrogen = (1.59 * 10^(-3) mol) * (22.4 L/mol)
= 3.56 * 10^(-2) L
So, the maximum volume of nitrogen that could dissolve in the diver's blood plasma at a depth of 93m is approximately 3.56 * 10^(-2) L.