The number of molecules in a gas at pressure | vedclass

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Question

(A) Using the ideal gas equation in terms of Boltzmann constant: $PV = NkT$,where $N$ is the number of molecules.$N = \frac{PV}{kT}$Given:$P = 1.64

Vedclass · Accepted Answer

$6.02 	imes 10^{16}$

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(A) Using the ideal gas equation in terms of Boltzmann constant: $PV = NkT$,where $N$ is the number of molecules.$N = \frac{PV}{kT}$Given:$P = 1.64 	imes 10^{-3} 	ext{ atm} = 1.64 	imes 10^{-3} 	imes 1.013 	imes 10^5 	ext{ Pa} \approx 1.66 	imes 10^2 	ext{ Pa}$$V = 1 	ext{ cc} = 1 	imes 10^{-6} 	ext{ m}^3$$T = 200 	ext{ K}$$k = 1.38 	imes 10^{-23} 	ext{ J/K}$Substituting the values:$N = \frac{(1.64 	imes 10^{-3} 	imes 1.013 	imes 10^5) 	imes (10^{-6})}{1.38 	imes 10^{-23} 	imes 200}$$N = \frac{166.132 	imes 10^{-3} 	imes 10^{-6}}{276 	imes 10^{-21}}$$N = \frac{0.166132}{276 	imes 10^{-21}} \approx 6.02 	imes 10^{16}$

The number of molecules in a gas at pressure $1.64 \times 10^{-3} \text{ atm}$ and temperature $200 \text{ K}$ having the volume $1 \text{ cc}$ is:

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