Answer:
The ratio of pressure in bottle B to that of bottle A is 1 : 4
Explanation:
We'll be by calculating the pressure in both bottles. This is illustrated below below:
For A:
Temperature (T) = T
Volume (V) = V
Number of mole (n) = n
Gas constant (R) = 0.0821 atm.L/Kmol
Pressure (P) =...?
PV = nRT
PV = n x 0.0821 x T
Divide both side by V
P = nT0.0821/V
Therefore, the pressure, in bottle A is
PA = nT0.0821/V
For B:
Temperature (T) = the same as that of A = T
Volume (V) = twice that of A = 2V
Number of mole (n) = half that of A = ½n
Gas constant (R) = 0.0821 atm.L/Kmol
Pressure (P) =...?
PV = nRT
P x 2V = ½n x 0.0821 x T
Divide both side by 2V
P = ½n x 0.0821 x T/2V
P = nT0.0821/4V
Therefore, the pressure in bottle B is:
PB = nT0.0821/4V
Now, we can obtain the ratio of pressure in bottle B to that of bottle A as follow:
Pressure in bottle A (PA) = nT0.0821/V
Pressure in bottle B (PB) = nT0.0821/4V
PB/PA = nT0.0821/4V ÷ nT0.0821/V
PB/PA = nT0.0821/4V x V/nT0.0821
PB/PA = 1/4
Therefore, the ratio of pressure in bottle B to that of bottle A is 1 : 4.
