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The pressure ($p$), the volume ($V$), the absolute temperature ($T$), and the number of moles ($n$) are related through the following physical laws:
• Boyle's law
• Charles's law
• Gay-Lussac's law
• Avogadro's law
These laws can be expressed in a more general form as:
$\displaystyle\frac{pV}{nT}=cte$
This general relationship states that the product of pressure and volume divided by the number of moles and temperature remains constant:
The Gay-Lussac's law states that when ERROR:5226,0 and the number of particles ($N$) are held constant, the ratio of the pressure ($p$) to the absolute temperature ($T$) equals the gay Lussac's law constant ($C_g$):
This implies that if a gas transitions from an initial state (the pressure in initial state ($p_i$) and the temperature in initial state ($T_i$)) to a final state (the pressure in final state ($p_f$) and the temperature in final state ($T_f$)) while keeping the pressure ($p$) and the number of particles ($N$) constant, Gay-Lussac's law must always hold true:
$\displaystyle\frac{p_i}{T_i}=C_g=\displaystyle\frac{p_f}{T_f}$
Thus, it follows:
Boyle's law states that with the absolute temperature ($T$) constant, the product of the pressure ($p$) and the volume ($V$) is equal to the boyle's law constant ($C_b$):
This means that if a gas transitions from an initial state (the pressure in initial state ($p_i$) and the volume in state i ($V_i$)) to a final state (the pressure in final state ($p_f$) and the volume in state f ($V_f$)), maintaining the absolute temperature ($T$) constant, it must always satisfy Boyle's law:
$p_i V_i = C_b = p_f V_f$
Therefore, it follows that:
Charles's law states that, with the pressure ($p$) constant, the ratio of the volume ($V$) to the absolute temperature ($T$) equals the charles law constant ($C_c$):
This implies that if a gas transitions from an initial state (the volume in state i ($V_i$) and the temperature in initial state ($T_i$)) to a final state (the volume in state f ($V_f$) and the temperature in final state ($T_f$)), while keeping the pressure ($p$) constant, it must always comply with Charles's law:
$\displaystyle\frac{V_i}{T_i} = C_c = \displaystyle\frac{V_f}{T_f}$
Therefore, we have:
When the pressure ($p$) behaves as an ideal gas, satisfying the volume ($V$), the number of moles ($n$), the absolute temperature ($T$), and the universal gas constant ($R_C$), the ideal gas equation:
and the definition of the molar concentration ($c_m$):
lead to the following relationship:
Examples
If a gas transitions from an initial state (i) to a final state (f) with the pressure ($p$) constant, then for the volume in state i ($V_i$), the volume in state f ($V_f$), the temperature in initial state ($T_i$), and the temperature in final state ($T_f$):
If a gas transitions from an initial state (i) to a final state (f) with the pressure ($p$) and the number of particles ($N$) held constant, it follows that for the pressure in initial state ($p_i$), the pressure in final state ($p_f$), the temperature in initial state ($T_i$), and the temperature in final state ($T_f$):
The particle concentration ($c_n$) is defined as the number of particles ($N$) divided by the volume ($V$):
If a gas transitions from an initial state (i) to a final state (f) with the absolute temperature ($T$) constant, the following relationship holds for the pressure in initial state ($p_i$), the pressure in final state ($p_f$), the volume in state i ($V_i$), and the volume in state f ($V_f$):
The pressure ($p$), the volume ($V$), the absolute temperature ($T$), and the number of moles ($n$) are related by the following equation:
where the universal gas constant ($R_C$) has a value of 8.314 J/K mol.
The pressure ($p$) can be calculated from the molar concentration ($c_m$) using the absolute temperature ($T$), and the universal gas constant ($R_C$) as follows:
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