Estimate the number of air molecules in a

Sarita Vishwakarma

Sarita Vishwakarma

Answered question

2022-07-19

Estimate the number of air molecules in a room with dimensions 2m ×3m×4m at the standard room temperature of 300K and the atmospheric pressure of 10^5 Pa .

Answer & Explanation

Nick Camelot

Nick Camelot

Skilled2023-06-10Added 164 answers

To estimate the number of air molecules in a room, we can use the ideal gas law and the concept of the Avogadro constant.
The ideal gas law states:
PV=nRT,
where:
P is the pressure,
V is the volume,
n is the number of moles of gas,
R is the ideal gas constant, and
T is the temperature.
We can rearrange the equation to solve for the number of moles:
n=PVRT.
The number of molecules can be calculated using Avogadro's law, which states that one mole of any gas contains Avogadro's number (NA) of molecules. Avogadro's number is approximately 6.022×1023 molecules/mol.
Therefore, the number of molecules can be calculated as:
N=n×NA.
Given the room dimensions of 2m×3m×4m, the temperature of 300K, and the atmospheric pressure of 105Pa, we can substitute these values into the equations.
First, let's calculate the number of moles:
n=PVRT=(105Pa)×(2m×3m×4m)(8.314J/mol·K)×(300K).
Evaluating the expression:
n322.96mol.
Now, let's calculate the number of molecules:
N=n×NA=(322.96mol)×(6.022×1023molecules/mol).
Evaluating the expression:
N1.946×1026 molecules.
Therefore, the estimated number of air molecules in the given room is approximately 1.946×1026 molecules.

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