Air consists of molecules of several types, with an average molar mass of 28.95g. About how many molecules does an adult who inhales 0.50L of air at sea level take in?
The answer should be 1.3x10^22
To calculate the number of molecules an adult inhales while taking in a certain volume of air, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas (assumed to be 1 atm at sea level)
V = volume of the gas (given as 0.50 L)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (assumed to be room temperature, around 298 K)
First, let's solve the ideal gas law equation for the number of moles:
n = PV / RT
n = (1 atm) * (0.50 L) / (0.0821 L·atm/mol·K * 298 K)
n ≈ 0.0201 moles
Next, we need to convert the number of moles to the number of molecules. We can use Avogadro's number to do this conversion:
1 mole = 6.022 × 10^23 molecules
0.0201 moles ≈ 0.0201 * (6.022 × 10^23) molecules
0.0201 * (6.022 × 10^23) ≈ 1.209 × 10^22 molecules
Therefore, an adult who inhales 0.50 L of air at sea level would take in approximately 1.2 x 10^22 molecules.