Question

Using the combined gas law above, identify the variables that would be in the numerator (a) and denominator (b) if you were to rearrange the gas law to solve for final pressure.

Answer 1

Step-by-step 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.

`V\propto T` (at constant Pressure)

Boyle's Law: Volume of a gas is inversely proportional to the Pressure of a gas at constant Temperature.

`V\propto (1)/(P)` (at constant Temperature)

Gay-Lussac's Law: Pressure of the gas is directly proportional to the Temperature at constant Volume.

`P\propto T` (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.

`V\propto n` (at constant Pressure and Temperature)

Combining all the four laws, we get

`PV\propto nT`

PV=nRT (Combined Gas Law)

where, R = Gas constant

Now, we need to calculate the pressure, rearranging the terms:

`P=(nRT)/(V)`

When an ideal gas at Initial Pressure
`P_1`, Volume
`V_1` and Temperature
`T_1` undergoes change in variables to Final pressure
`P_2`, Volume
`V_2` and Temperature
`T_2` , we write

`(P_1V_1)/(T_1)=(P_2V_2)/(T_2)`

`P_2=((P_1V_1)/(T_1))((T_2)/(V_2))`

Answer 2

Answer : The variables in the numerator (a) will be,
`P_1,V_1,T_2` and the variables in the denominator (b) will be,
`V_2,T_1`

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.

`P\propto (1)/(V)`

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.

`V\propto T`

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.

`P\propto T`

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.

`V\propto n`

By combining these four laws, we get the combined gas law.

`PV\propto nT\\\\PV=nRT`

where, R = gas constant

An ideal gas at initial pressure
`P_1`, initial volume
`V_1` and initial temperature
`T_1` undergoes changes with the variables to final pressure
`P_2`, final volume
`V_2` and final temperature
`T_2`.

By rearranging the gas law, we get the final pressure.

`(P_1V_1)/(P_2V_2)=(T_1)/(T_2)\\\\P_2=(P_1V_1T_2)/(V_2T_1)`

Therefore, the variables in the numerator (a) will be,
`P_1,V_1,T_2` and the variables in the denominator (b) will be,
`V_2,T_1`