The air in a kitchen has pressure 1.0 × 105 Pa and temperature 22°C. A refrigerator of internalvolume 0.36 m3 is installed in the kitchen.(a) With the door open the air in the refrigerator is initially at the same temperature andpressure as the air in the kitchen. Calculate the number of molecules of air in therefrigerator.
Question
The air in a kitchen has pressure 1.0 × 105 Pa and temperature 22°C. A refrigerator of internalvolume 0.36 m3 is installed in the kitchen.(a) With the door open the air in the refrigerator is initially at the same temperature andpressure as the air in the kitchen. Calculate the number of molecules of air in therefrigerator.
Solution
To calculate the number of molecules of air in the refrigerator, we can use the ideal gas law equation, which is PV = nRT.
Here, P = pressure = 1.0 × 10^5 Pa V = volume = 0.36 m^3 R = ideal gas constant = 8.31 J/(mol.K) T = temperature = 22°C = 22 + 273.15 = 295.15 K (since temperature must be in Kelvin)
We need to find n, which is the number of moles.
Rearranging the ideal gas law equation, we get n = PV/RT.
Substituting the given values, we get n = (1.0 × 10^5 Pa * 0.36 m^3) / (8.31 J/(mol.K) * 295.15 K) = 1465.57 mol.
Now, to find the number of molecules, we multiply the number of moles by Avogadro's number (6.022 × 10^23 molecules/mol).
So, the number of molecules = 1465.57 mol * 6.022 × 10^23 molecules/mol = 8.82 × 10^26 molecules.
Therefore, there are approximately 8.82 × 10^26 molecules of air in the refrigerator.
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