A container of volume 20.5 cm3 is initially filled with air. The container is then evacuated at 0oC to a pressure of 19 mPa. How many molecules are in the container after evacuation if we assume that air is an ideal gas?

To calculate the number of molecules in the container, we can use the ideal gas equation, which is given as:

PV = nRT

Where:
P = pressure of the gas (in Pascals)
V = volume of the gas (in cubic meters)
n = number of moles of the gas
R = ideal gas constant (8.314 J/mol*K)
T = temperature of the gas (in Kelvin)

First, we need to convert the given measurements to proper units. The volume is given in cm3, so we need to convert it to cubic meters by dividing by 1,000,000:

V = 20.5 cm3 ÷ 1,000,000 = 0.0000205 m3

The pressure is given in mPa (millipascals), so we need to convert it to Pascals by multiplying by 1,000,000:

P = 19 mPa × 1,000,000 = 19,000,000 Pa

The temperature is given as 0oC, so we need to convert it to Kelvin by adding 273.15:

T = 0oC + 273.15 = 273.15 K

Now, we can substitute these values into the ideal gas equation to solve for the number of moles (n):

(19,000,000 Pa) × (0.0000205 m3) = n × (8.314 J/mol*K) × (273.15 K)

Simplifying the equation:

n = (19,000,000 Pa * 0.0000205 m3) / (8.314 J/mol*K * 273.15 K)

n ≈ 8.33 × 10^-6 moles

Finally, we can use Avogadro's number (6.022 × 10^23) to convert the number of moles into the number of molecules:

Number of molecules = (8.33 × 10^-6 moles) × (6.022 × 10^23 molecules/mol)

Number of molecules ≈ 5.01 × 10^18 molecules

Therefore, there are approximately 5.01 × 10^18 molecules in the container after evacuation.