A healthy adult exhales about 5.0*10 exponent 2 ml, of a gaseous mixture with each breath. calculate the number of molecules present in this volume at 37C and 1.1atm.
Use PV = nRT and solve for n = number of moles. 1 mole will contain 6.022E23 molecules
To calculate the number of molecules present in a given volume, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure in atm
V = volume in liters
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin
First, let's convert the given volume from mL to L:
5.0 * 10^2 mL = 5.0 * 10^(-1) L
Given:
Temperature (T) = 37°C = 273 + 37 = 310 K
Pressure (P) = 1.1 atm
R = 0.0821 L·atm/(mol·K)
Now, let's calculate the number of moles (n) using the ideal gas law:
PV = nRT
n = PV / RT
n = (1.1 atm) * (5.0 * 10^(-1) L) / (0.0821 L·atm/(mol·K) * 310 K)
n ≈ 0.0215 moles
Finally, we can calculate the number of molecules using Avogadro's number, which is approximately 6.022 × 10^23 molecules/mol:
Number of molecules = n * Avogadro's number
Number of molecules ≈ (0.0215 moles) * (6.022 × 10^23 molecules/mol)
Number of molecules ≈ 1.29643 × 10^22 molecules
Therefore, there are approximately 1.29643 × 10^22 molecules present in the given volume at 37°C and 1.1 atm.
To calculate the number of molecules present in the given volume at a specified temperature and pressure, we can use the ideal gas equation:
PV = nRT
Where:
P = Pressure = 1.1 atm
V = Volume = 5.0 * 10² mL = 5.0 * 10² cm³ (since 1 mL = 1 cm³)
n = Number of moles (unknown)
R = Gas constant = 0.0821 L·atm/(mol·K) (since the given pressure is in atm, we use the appropriate value of R)
T = Temperature = 37°C = 37 + 273.15 K (convert from Celsius to Kelvin)
First, we convert the volume from cm³ to L by dividing by 1000:
V = 5.0 * 10² cm³ ÷ 1000 = 0.5 L
Next, we substitute the values into the equation and solve for the number of moles (n):
(1.1 atm) * (0.5 L) = n * (0.0821 L·atm/(mol·K)) * (37 + 273.15 K)
Simplifying the equation:
0.55 = n * 0.0821 * 310.15
Divide both sides by (0.0821 * 310.15):
n = 0.55 / (0.0821 * 310.15)
Calculating:
n ≈ 2.194 moles
Finally, we can convert the number of moles to the number of molecules by multiplying by Avogadro's number, which is approximately 6.022 * 10²³ molecules/mol:
Number of molecules = 2.194 mol * (6.022 * 10²³ molecules/mol)
Calculating:
Number of molecules ≈ 1.321 * 10²⁴ molecules
Therefore, there are approximately 1.321 * 10²⁴ molecules present in 5.0 * 10² mL of the gaseous mixture at 37°C and 1.1 atm of pressure.