A particular balloon is designed by its manufacturer to be inflated tom a volume of no more than 2.5 L. If the balloon is filled with 2.0 L of helium at sea level, is released, and rises to an altitude at which the atmospheric pressure is only 500. mm Hg, will the balloon burst?

Not quite sure how far you need to take this question. It depends on whether you just use information supplied, or you are practising estimating and assumptions?

If we assume that atmospheric pressure at sea level is 760 mmHg, the we can use

P1V1=P2V2

however for an atomspheric pressure drop to 500 mmHg, you would need to be at about 18,ooo ft. So the temperature is much less than at sea level 20C(293K), say -20C (253K).

so you oculd use

P1V1/T1=P2V2/T2

To determine if the balloon will burst, we need to compare the pressure inside the balloon to the atmospheric pressure at the altitude it reaches.

Here's how you can calculate it:

1. Convert the atmospheric pressure from mm Hg to the standard unit of pressure called "atmospheres" (atm). To do this, divide the pressure value by 760 mm Hg (since 1 atm is equal to 760 mm Hg):
500 mm Hg ÷ 760 mm Hg/atm ≈ 0.658 atm

2. Use the ideal gas law, which states that the pressure of a gas (P) is proportional to its volume (V) when temperature (T) and the amount of gas (n) are constant:
P1 * V1 = P2 * V2

Where:
P1 = Initial pressure (sea level, in this case)
V1 = Initial volume (2.0 L, in this case)
P2 = Final pressure (at altitude)
V2 = Final volume (unknown, since we're trying to determine if it bursts)

3. Rearrange the equation to solve for V2:
V2 = (P1 * V1) / P2

Plug in the known values:
V2 = (1 atm * 2.0 L) / 0.658 atm ≈ 3.04 L

The calculated final volume of the balloon at an altitude with 500 mm Hg pressure is approximately 3.04 L.

Since the final volume of the balloon is less than the designed maximum volume of 2.5 L, the balloon will not burst.

To determine if the balloon will burst at the given conditions, we need to compare the pressure inside the balloon with the external pressure at the given altitude.

1. Convert the given atmospheric pressure from mm Hg to atm:
500 mm Hg = 500/760 atm (1 atm = 760 mm Hg)
= 0.6579 atm (rounded to 4 decimal places)

2. Use the ideal gas law equation to compare the pressures:
PV = nRT

Assuming the temperature remains constant, we can rewrite the equation as:
P1 / V1 = P2 / V2

Where:
P1 = initial pressure (sea level pressure in this case) = 1 atm
V1 = initial volume = 2.0 L
P2 = final pressure (pressure at altitude) = 0.6579 atm
V2 = final volume (unknown, to be determined)

3. Rearrange the equation to solve for V2:
V2 = V1 x P2 / P1

Substitute the values:
V2 = 2.0 L x 0.6579 atm / 1 atm
V2 = 1.3158 L (rounded to 4 decimal places)

4. Compare the final volume (V2) with the maximum volume allowed (2.5 L).
Since V2 (1.3158 L) is less than the maximum volume (2.5 L), we can conclude that the balloon will not burst.

Therefore, the balloon will not burst when filled with 2.0 L of helium at sea level and released to an altitude where the atmospheric pressure is 500 mm Hg.