Air pressure decreases as you move higher into the atmosphere. The decrease in p

Question

Air pressure decreases as you move higher into the atmosphere. The decrease in pressure encourages the volume of the balloon to increase by quite a bit, whereas the drop in temperature will encourage some decrease in the volume. So in this case, the pressure and temperature play opposite roles in affecting the volume. Consider 4.80 L of a gas at 365 mmHg and 20. Degree C. If the container is compressed to 2.90 L and the temperature is increased to 40. A degree C. what is the new pressure. P_2. inside the container? Assume no change in the amount of gas inside the cylinder. Express your answer with the appropriate units.

Explanation / Answer

Initial conditions of gas:

Pressure P1 = 365 mmHg

Volume V1 = 4.8 L

Temperature T1 = 20oC = 20+ 273 K = 293 K

Final conditions of gas:

Pressure P2 = ?

Volume V2 = 2.9 L

Temperature T2 = 40 oC = 40+ 273 K = 313 K

We know that

P1V1/T1 = P2V2/T2

P2 = (P1V1/T1) (T2/V2)

                           = ( 365 mmHg x 4.8 L/ 293 K ) ( 313 K/ 2.9 L)

                          = 645.3 mmHg

P2 = 645.3 mmHg

Therefore,

new pressure in the container =  645.3 mmHg

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