Question

The lowest pressure that can be created in laboratory at 27 degree celsius is${10}^{ - 11}$ mmy of hg. at this pressure, what is the number of ideal gas molecules per cm^3 ?

Answer 1

AAnswer: The number of ideal gas molecule per is .

Explanation:

Given that,

Temperature T = 27+273 = 300 K

Pressure

Gas constant R = 0.0821

Using ideal gas equation

Hence, the number of ideal gas molecule per is .

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Answer 2

The number of ideal gas is $0.32\times10^{6}\ molecules/cm^3$

Explanation:

Given that,

Temperature = 27°C

Pressure of Hg $P_{2}= 10^{-11}\ mm$

We need to calculate the number of ideal gas molecules per cm³

Using formula of ideal gas

$PV=nRT$

$R=\dfrac{PV}{nT}$

Here, R = constant

So, for Hg,

$\dfrac{P_{1}V_{1}}{n_{1}T_{1}}=\dfrac{P_{2}V_{2}}{n_{2}T_{2}}$

$\dfrac{n_{2}}{V_{2}}=\dfrac{P_{2}n_{1}T_{1}}{P_{1}V_{1}T_{2}}$

Where, $T_{1}$ = absolute temperature

$T_{2}$ = temperature in laboratory

$n_{1}$ =Avogadro number

$V_{1}$ = volume of Hg

Put the value into the formula

$\dfrac{n_{2}}{V_{2}}=\dfrac{10^{-11}\times6.02\times10^{23}\times273}{760\times22400\times300}$

$\dfrac{n_{2}}{V_{2}}=0.32\times10^{6}\ molecules/cm^3$

Hence, The number of ideal gas is $0.32\times10^{6}\ molecules/cm^3$

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Topic : number of molecules

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