Respuesta :
Explanation: For evaluating the combined gas law, we use four laws:
Charles' Law: Volume of a gas is directly proportional to the Temperature at Constant Pressure.
[tex]V\propto T[/tex] (at constant Pressure)
Boyle's Law: Volume of a gas is inversely proportional to the Pressure of a gas at constant Temperature.
[tex]V\propto \frac{1}{P}[/tex] (at constant Temperature)
Gay-Lussac's Law: Pressure of the gas is directly proportional to the Temperature at constant Volume.
[tex]P\propto T[/tex] (at constant Volume)
Avogadro's Law: Volume of gas is directly proportional to the number of moles of gas at constant Pressure and constant Temperature.
[tex]V\propto n[/tex] (at constant Pressure and Temperature)
Combining all the four laws, we get
[tex]PV\propto nT[/tex]
PV=nRT (Combined Gas Law)
where, R = Gas constant
Now, we need to calculate the pressure, rearranging the terms:
[tex]P=\frac{nRT}{V}[/tex]
When an ideal gas at Initial Pressure [tex]P_1[/tex], Volume [tex]V_1[/tex] and Temperature [tex]T_1[/tex] undergoes change in variables to Final pressure [tex]P_2[/tex], Volume [tex]V_2[/tex] and Temperature [tex]T_2[/tex] , we write
[tex]\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}[/tex]
[tex]P_2=(\frac{P_1V_1}{T_1})(\frac{T_2}{V_2})[/tex]
Answer : The variables in the numerator (a) will be, [tex]P_1,V_1,T_2[/tex] and the variables in the denominator (b) will be, [tex]V_2,T_1[/tex]
Explanation :
The combined gas law has arrived from the combination of the four laws:
1) Boyle's Law : It is defined as the pressure of the gas is inversely proportional to the volume of the gas at constant temperature and the number of moles.
[tex]P\propto \frac{1}{V}[/tex]
2) Charles' Law : It is defined as the volume of the gas is directly proportional to the temperature of the gas at constant pressure and number of moles.
[tex]V\propto T[/tex]
3) Gay-Lussac's Law : It is defined as the pressure of the gas is directly proportional to the temperature of the gas at constant volume and number of moles.
[tex]P\propto T[/tex]
4) Avogadro's Law : It is defined as the volume of the gas is directly proportional to the number of moles of the gas at constant pressure and temperature.
[tex]V\propto n[/tex]
By combining these four laws, we get the combined gas law.
[tex]PV\propto nT\\\\PV=nRT[/tex]
where, R = gas constant
An ideal gas at initial pressure [tex]P_1[/tex], initial volume [tex]V_1[/tex] and initial temperature [tex]T_1[/tex] undergoes changes with the variables to final pressure [tex]P_2[/tex], final volume [tex]V_2[/tex] and final temperature [tex]T_2[/tex].
By rearranging the gas law, we get the final pressure.
[tex]\frac{P_1V_1}{P_2V_2}=\frac{T_1}{T_2}\\\\P_2=\frac{P_1V_1T_2}{V_2T_1}[/tex]
Therefore, the variables in the numerator (a) will be, [tex]P_1,V_1,T_2[/tex] and the variables in the denominator (b) will be, [tex]V_2,T_1[/tex]
