A young male adult takes in about 4.0 10-4 m3 of fresh air during a normal breath. Fresh air contains approximately 21% oxygen. Assuming that the pressure in the lungs is 1.0 105 Pa and air is an ideal gas at a temperature of 310 K, find the number of oxygen molecules in a normal breath.

Calculate the number of moles of ALL gases present at that volume and pressure, and multiply it by 0.21 for the number of moles of O2. Then multiply that by Avogadro's number.

You could use the PV = nRT equation or the handy rule that one mole of gas occupies 2.4 liters at STP

4.0*10-4 m^3 is 0.40 liters
At STP, that would contain
0.4 l/22.4 l/mole = 0.179 moles

Apply a correction factor of 273/310 for the number density at the higher temperature, and multiply by .21 for the O2 mole fraction. 10^5 Pa is withing 1.3% of atmospheric pressure, so we can ignore the pressure correction factor 1.000/1.013

You should end up with about 0.033 moles of O2. Multiply by Avogadro's number to get the number of molecules.

To find the number of oxygen molecules in a normal breath, we can use the ideal gas law formula:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

First, let's calculate the volume of air in a normal breath:

Volume of air = 4.0 x 10^-4 m^3

Next, let's calculate the number of moles of air. We know that air contains 21% oxygen, so we can calculate the moles of oxygen using this percentage:

Moles of oxygen = 21% of volume of air

Now we can use the ideal gas law to find the number of moles of oxygen:

PV = nRT

n = PV / RT

where P is the pressure (1.0 x 10^5 Pa), V is the volume of air, R is the ideal gas constant (8.314 J/(mol·K)), and T is the temperature (310 K).

Substituting the values into the equation:

n = (1.0 x 10^5 Pa) x (4.0 x 10^-4 m^3) / (8.314 J/(mol·K) x 310 K)

n ≈ 0.00194 moles

Finally, we need to convert the moles of oxygen to the number of molecules. One mole contains 6.022 x 10^23 molecules (Avogadro's number).

Number of oxygen molecules = moles of oxygen x Avogadro's number

Number of oxygen molecules ≈ 0.00194 moles x 6.022 x 10^23 molecules/mol

Number of oxygen molecules ≈ 1.168 x 10^21 molecules

Therefore, there are approximately 1.168 x 10^21 oxygen molecules in a normal breath.

To find the number of oxygen molecules in a normal breath, we can use the ideal gas law which relates the number of molecules in a gas to its pressure, volume, and temperature.

The ideal gas law formula is:

PV = nRT

Where:
P = pressure
V = volume
n = number of molecules (in moles)
R = ideal gas constant
T = temperature

First, let's calculate the number of moles of oxygen molecules in the breath using the given information:

Volume of the breath (V) = 4.0 * 10^(-4) m^3
Pressure (P) = 1.0 * 10^5 Pa
Temperature (T) = 310 K
Ideal gas constant (R) = 8.314 J/(mol∙K) (using SI units)

Rearranging the ideal gas law formula to solve for the number of moles (n):

n = PV / RT

Substituting the values:

n = (1.0 * 10^5 Pa) * (4.0 * 10^(-4) m^3) / (8.314 J/(mol∙K) * 310 K)

Simplifying:

n = 0.0510048053733 mol

Now, we need to convert this to the number of oxygen molecules. 1 mole of any substance contains Avogadro's number (6.022 x 10^23) of molecules.

Number of oxygen molecules = n * Avogadro's number

Substituting the values:

Number of oxygen molecules = 0.0510048053733 mol * (6.022 x 10^23 molecules/mol)

Calculating:

Number of oxygen molecules ≈ 3.071 x 10^22 molecules

Therefore, there are approximately 3.071 x 10^22 oxygen molecules in a normal breath.