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12 . kinetic theory of gases — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics12 . kinetic theory of gases1 Mark
MCQ
The lowest pressure (the best Vacuum) that can be created in the laboratory at $27$ degree is $10^{-11} \;{mm}$ of $Hg$. At this pressure, the number of ideal gas molecules per ${cm}^{3}$ will be
  • A
    $3.22 \times  10^{12}$
  • B
    $1.61 \times  10^{12}$
  • C
    $3.21 \times  10^6$
  • ✓
    $3.22 \times  10^5$
✓

Answer

Correct option: D.
$3.22 \times  10^5$
d
$PV = nRT$

$\frac{ PV }{ nT }= R \quad$ (R here is a constant)

$ \frac{ P _{1} V _{1}}{ n _{1} T _{1}}=\frac{ P _{2} V _{2}}{ n _{2} T _{2}}$

$P _{1}=760 mm$ of $Hg$

$V _{1}=22400 cm ^{3}$

$T _{1}=273 K$

$P _{2}=10^{-11} mm$ of $Hg$

$T _{2}=300 K$

$n _{1}=6.02 \times 10^{23}$

$\frac{ n _{2}}{ V _{2}}=\frac{ P _{2} n _{1} T _{1}}{ P _{1} V _{1} T _{2}}$

$\frac{ n _{2}}{ V _{2}}=\frac{10^{-11} \times 6.02 \times 10^{23} \times 273}{760 \times 22400 \times 300}=3.32 \times 10^{5} \;molecules / cm ^{3}$

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