Two identical bottles at the same temperature contain the same gas. If bottle B has twice the volume and contains half the number of moles of gas as bottle A, what is the ratio of the pressure in B to the pressure in A? Express to 2 sig figs.

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.

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