Hey there!:
We are given P = 10⁻²² N/m2 ,
Volume, V = 1 cm3= 10⁻⁶ m³ and
T= 13ºC= 13+273= 286 K
Using gas law, P*V = n R T, where n is number of moles and R=8.314JK⁻¹.
n = PV/(RT) => n = 10-12*10⁻⁶/ (8.314*286) = 4.205*10₋²² moles
Hence number of molecules = number of moles * Avogadro's number
= 4.205*10-22 moles * 6.023*1023 molecules/mole
= 253
Number of molecules = 250 (upto 2 significant figures)
Number of molecules: N = 263.31
Some of the laws regarding gas can apply to ideal gas (volume expansion does not occur when the gas is heated),:
[tex] \displaystyle P = \dfrac {1} {V} [/tex]
[tex] \displaystyle V = T [/tex]
[tex] \displaystyle V = n [/tex]
So that the three laws can be combined into a single gas equation, the ideal gas equation
In general, the gas equation can be written
[tex] \large {\boxed {\bold {PV = nRT}}} [/tex]
where
P = pressure, atm , N/m²
V = volume, liter
n = number of moles
R = gas constant = 0.082 l.atm / mol K (P= atm, v= liter),or 8,314 J/mol K (P=Pa or N/m2, v= m³)
T = temperature, Kelvin
n = N / No
n = mole
No = Avogadro number (6.02.10²³)
n = m / m
m = mass
M = relative molecular mass
Known
P = 10−12 N / m2
V = 1 cm3 = 10-6 m3
T = 2 ºC = 2 + 273 = 275 K
R = 8,314 J / mol. K
[tex]\rm n=\dfrac{PV}{RT}\\\\n=\dfrac{10^{-12}\times 10^{-6}}{8.314\times 275}\\\\n=\boxed{\bold{4.374\times 10^{-22}}}[/tex]
then the number of molecules (N):
N = n x No
N = 4,374.10⁻²² x 6.02.10²³
N = 263.31
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