Question

Consider two bulbs seperated by a valce. Both bulbs are amintained at the same temperature. Assume that when the valve between the two bulbs is closed, the gases are sealed in their respective bulbs. When the valve is closed, the following data apply:

Bulb A Bulb B
Gas Ne CO
V 2.50L 2.00L
P 1.09 atm 0.73 atm


Assuming no temperature change, determine the final pressure inside the system after the valve connecting the two bulbs is opened. Ignore the volume of the tube connecting the two bulbs.

Answer 1

The pressure is
`P_f = 0.93 \ atm`

Step-by-step explanation:

From the question we are told that

The volume of Ne is
`V_N = 2.50 \ L`

The volume of CO is
`V_C = 2.00 \ L`

The pressure of
`Ne` is
`P_N = 1.09 \ atm`

The pressure of CO is
`P_C = 0.773 \ atm`

The number of moles of Ne present is evaluated using the ideal gas equation as

`n_N = (P_N * V_N)/(R T)`

=>
`n_N = (1.09 * 2.50 )/(R T) = (2.725)/(RT)`

The number of moles of CO present is evaluated using the ideal gas equation as

`n_N = (P_C * V_C)/(R T)`

=>
`n_N = (0.73 * 2.00 )/(R T) = (1.46)/(RT)`

The total number of moles of gas present is evaluated as

`n_T = n_N + n_C`

`n_T = (2.725)/(RT) + (1.46)/(RT)`

`n_T = (4.185)/(RT)`

The total volume of gas present when valve is opened is mathematically represented as

`V_T = V_N + V_C`

=>
`V_T = 2.50 + 2.00 = 4.50 \ L`

So

From the ideal gas equation the final pressure inside the system is mathematically represented as

`P_f = (n_T * RT )/( V_T)`

=>
`P_f = ([(4.185)/(RT) ] * RT )/( 4.50)`

=>
`P_f = 0.93 \ atm`