Estimate the total number of air molecules (i | vedclass

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(C) Volume of the room,$V = 25.0 \; m^{3}$.Temperature of the room,$T = 27^{\circ} C = 300 \; K$.Pressure in the room,$P = 1 \; atm = 1.013 	imes 10^

Vedclass · Accepted Answer

$6.11 	imes 10^{26}$

Vedclass · Answer

(C) Volume of the room,$V = 25.0 \; m^{3}$.Temperature of the room,$T = 27^{\circ} C = 300 \; K$.Pressure in the room,$P = 1 \; atm = 1.013 	imes 10^{5} \; Pa$.The ideal gas equation is given by $PV = N k_{B} T$,where $k_{B}$ is the Boltzmann constant.Boltzmann constant,$k_{B} = 1.38 	imes 10^{-23} \; J/K$.The number of air molecules $N$ is given by $N = \frac{PV}{k_{B} T}$.Substituting the values: $N = \frac{1.013 	imes 10^{5} 	imes 25.0}{1.38 	imes 10^{-23} 	imes 300}$.$N = \frac{25.325 	imes 10^{5}}{414 	imes 10^{-23}} \approx 0.06117 	imes 10^{28} = 6.11 	imes 10^{26}$ molecules.Therefore,the total number of air molecules in the room is $6.11 	imes 10^{26}$.

Estimate the total number of air molecules (inclusive of oxygen,nitrogen,water vapour,and other constituents) in a room of capacity $25.0 \; m^{3}$ at a temperature of $27^{\circ} C$ and $1 \; atm$ pressure.

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