Question

In a very good vacuum system in the laboratory, the vacuum atained was ${10}^{-13}$ atm. If the temperature the system was 300 K, the numbers of molecules present in a volume of $1c{m}^3$ is

• A. $2.4\times {10}^6$
• B. 24
• C. $2.4\times {10}^9$
• D. Zero

Answer 1

Answer: (A)

$2.4\times {10}^6$

From the Ideal gas Law we obtain, $PV=nRT$

$⟹n=$ number of moles present in the given volume=$\frac{PV}{RT}$

$=\frac{({10}^{-13}\times 1.01\times {10}^5)\times ({10}^{-2}{)}^2}{8.31\times 300}$

$\approx 4.05\times {10}^{-18}$

Thus number of molecules in the given volume=$n{N}_A=4.05\times {10}^{-18}\times 6.023\times {10}^{23}\approx 2.4\times {10}^6$