Question

People buying food in sealed bags at high elevations often notice that the bags are puffed up because the air inside has expanded. A bag of pretzels was packed at a pressure of 1.00 atm and a temperature of 22.0°C. When opened at a summer picnic in Santa Fe, New Mexico, at a temperature of 32.0°C, the volume of the air in the bag is 1.38 times its original volume. What is the pressure of the air?

a) 0.73 atm

b) 1.00 atm

c) 1.38 atm

d) 1.92 atm

Answer 1

The pressure of the air inside the pretzel bag when opened at Santa Fe is approximately 0.73 atm based on the combined gas law. The pressure decreased from the original 1.00 atm due to the increased volume at a higher temperature. Option a, 0.73 atm, is the correct answer.

Step-by-step explanation:

The question addresses the concept of how temperature and volume changes affect the pressure of a gas, which is a cornerstone of the gas laws in chemistry. To find the pressure of the air in the pretzel bag at Santa Fe, New Mexico, we can use the combined gas law, which is PV/T = constant, where P is pressure, V is volume, and T is temperature in kelvins. We have the initial conditions: P1 = 1.00 atm, V1 is the original volume, and T1 = 22.0 + 273.15 = 295.15 K. At Santa Fe, the conditions are V2 = 1.38V1 and T2 = 32.0 + 273.15 = 305.15 K.

By applying the combined gas law, we obtain P2V2/T2 = P1V1/T1, so P2 = (P1V1/T1) x (T2/V2) = (1.00 atm x V1/295.15 K) x (305.15 K/1.38V1). This simplifies to P2 = (1.00 atm x 305.15 K) / (1.38 x 295.15 K) = 0.735 atm.

Therefore, the pressure of the air inside the pretzel bag when opened at the picnic is approximately 0.73 atm, which corresponds to option a. This decrease in pressure relative to the original 1.00 atm is due to the increased volume of the bag, as explained by the combined gas law, making option a the correct choice.