A sealed balloon is filled with 1.00 L of helium at 23°C and 1.00 atm. The balloon rises to a point in the atmosphere where the pressure is 299 torr and the temperature is -31°C. What is the change in the volume of the balloon as it ascends from 1.00 atm to a pressure of 299 torr?

AV = ?

(p1v1/t1) = (p2v2/t2)

You have p1v1 and t1 on the ground and you have v2 and t2 in the upper atmosphere. The only unknown is the volume at it's height of ascent. Find v2, then the difference in volume is v2-v1 = ?
Watch that you keep the units the same (either all torr or all atm) and remember to change degrees C to kelvin.

To determine the change in volume of the balloon as it ascends from 1.00 atm to a pressure of 299 torr, we can use the combined gas law.

The combined gas law states that the ratio of the initial pressure (P1), initial volume (V1), and initial temperature (T1) to the final pressure (P2), final volume (V2), and final temperature (T2) of a gas sample is constant, given that the amount of gas remains constant.

The equation for the combined gas law is as follows:

(P1 * V1) / T1 = (P2 * V2) / T2

In this case, we know the initial and final pressures (P1 = 1.00 atm and P2 = 299 torr) and the initial and final temperatures (T1 = 23°C and T2 = -31°C).

However, the equation requires that all temperatures be in Kelvin, so we need to convert both temperatures from Celsius to Kelvin. To do this, we use the following formula:

T(K) = T(°C) + 273.15

Converting the temperatures:

T1 in Kelvin = 23°C + 273.15 = 296.15 K
T2 in Kelvin = -31°C + 273.15 = 242.15 K

Now we plug the values into the equation:

(P1 * V1) / T1 = (P2 * V2) / T2

(1.00 atm * 1.00 L) / 296.15 K = (299 torr * V2) / 242.15 K

To find V2, we solve for it:

V2 = (299 torr * 1.00 L * 242.15 K) / (1.00 atm * 296.15 K)

V2 ≈ 246.1

Therefore, the change in volume of the balloon as it ascends from 1.00 atm to a pressure of 299 torr is approximately 246.1 L.

To find the change in volume (ΔV) of the balloon, you can use the combined gas law equation, which relates the initial and final states of a gas:

(P1 * V1) / (T1) = (P2 * V2) / (T2)

where:
P1 = initial pressure (1 atm)
V1 = initial volume (1.00 L)
T1 = initial temperature (23°C + 273.15 K)
P2 = final pressure (299 torr)
V2 = final volume (unknown)
T2 = final temperature (-31°C + 273.15 K)

Let's plug in the values and solve for V2:

(1 atm * 1.00 L) / (23°C + 273.15 K) = (299 torr * V2) / (-31°C + 273.15 K)

Simplifying the equation:

1 L / 296.15 K = (299 torr * V2) / 242.15 K

Cross-multiplying:

1 L * 242.15 K = 296.15 K * (299 torr * V2)

242.15 K = 88901.85 torr * V2

Dividing both sides by 88901.85 torr:

V2 = 0.00272 L

Therefore, the change in volume of the balloon as it ascends is approximately 0.00272 L.