Number of moles added: 21,319
There are several gas equations in various processes:
• 1. The ideal ideal gas equation
[tex] \rm PV = nRT [/tex]
PV = NkT
N = number of gas particles
n = number of moles
R = gas constant (8,31.10 ^ 3 J / kmole K
k = Boltzmann constant (1,38.10⁻²³)
n = N / No
n = mole
No = Avogadro number (6.02.10²³)
n = m / m
m = mass
M = relative molecular mass
• 2. Avogadro's hypothesis
In the same temperature and pressure, in the same volume conditions, the gas contains the same number of molecules
So it applies: the ratio of gas volume will be equal to the ratio of gas moles
[tex] \rm V1: V2 = n1: n2 [/tex]
• 3. Boyle's Law
At a constant temperature, the gas volume is inversely proportional to the pressure applied
[tex] \rm p1.V1 = p2.V2 [/tex]
• 4. Charles's Law
When the gas pressure is kept constant, the gas volume is proportional to the temperature
[tex] \rm \dfrac {V1} {T1} = \dfrac {V2} {T2} [/tex]
• 5. Gay Lussac's Law
When the volume is not changed, the gas pressure in the tube is proportional to its absolute temperature
[tex] \rm \dfrac {P1} {T1} = \dfrac {P2} {T2} [/tex]
• 6. Law of Boyle-Gay-Lussac
Combined with Boyle's law and Gay Lussac's law
[tex] \rm \dfrac {P1.V1} {T1} = \dfrac {P2.V2} {T2} [/tex]
P1 = initial gas pressure (N / m² or Pa)
V1 = initial gas volume (m³)
P2 = gas end pressure
V2 = the final volume of gas
T1 = initial gas temperature (K)
T2 = gas end temperature
The initial condition of A flexible container
initial volume: 3.10 l contains 7.51 mol of gas
final volume: 11.9 l
we use Avogadro's hypothesis
V1: V2 = n1: n2
[tex]\rm \dfrac{3.10}{11.9}=\dfrac{7.51}{n_2}\\\\n_2=28,829[/tex]
Number of moles added:
28,829-7.51 = 21,319 mol
Which equation agrees with the ideal gas law
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Which law relates to the ideal gas law
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