A container of volume 14.2 cm3 is initially filled with air. The container is then evacuated at 0oC to a pressure of 32 mPa. How many molecules are in the container after evacuation if we assume that air is an ideal gas?
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To determine the number of molecules in the container, we need to use the ideal gas law equation:
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 in Kelvin.
First, let's convert the pressure from millipascal (mPa) to pascal (Pa). Since 1 mPa = 0.001 Pa, the pressure becomes 32 x 0.001 = 0.032 Pa.
Next, we convert the volume of the container from cm3 to m3. Since 1 cm3 = 0.000001 m3, the volume becomes 14.2 x 0.000001 = 0.0000142 m3.
Now we need to convert the temperature from 0oC to Kelvin. The Kelvin temperature scale is obtained by adding 273.15 to the Celsius temperature. So 0oC + 273.15 = 273.15 K.
Using the ideal gas law equation, we can solve for the number of moles (n):
n = PV / RT
Substituting the given values, we have:
n = (0.032 Pa) x (0.0000142 m3) / [(8.314 J/(mol·K)) x 273.15 K]
Here, we've used the value of the ideal gas constant (R) as 8.314 J/(mol·K).
Simplifying the equation:
n = 0.0000362244 / 2279.66871
n ≈ 1.59 x 10^(-8) mol
To convert from moles to molecules, we need to use Avogadro's number, which is 6.022 x 10^23 molecules/mol.
Multiplying the number of moles by Avogadro's number, we can find the number of molecules in the container:
Number of molecules = (1.59 x 10^(-8) mol) x (6.022 x 10^23 molecules/mol)
Number of molecules ≈ 9.57 x 10^15 molecules
Therefore, there are approximately 9.57 x 10^15 molecules in the container after evacuation.