A weather balloon is filled with helium that occupies a volume of

4.39 x 10^4 L at 0.995 atm and 32.0°C. After it is released, it rises to a location where the pressure is 0.720 atm and the temperature is -14.1°C. What is the volume of the balloon at that new location?

(P1V1/T1) = (P2V2/T2)

Remember T must be in kelvin.

To find the volume of the balloon at the new location, we can use the ideal gas law equation:

PV = nRT

Where:
P = pressure in atmospheres
V = volume in liters
n = number of moles
R = ideal gas constant = 0.0821 L·atm/(mol·K)
T = temperature in Kelvin

First, let's convert the given temperatures to Kelvin:
Initial temperature (T1) = 32.0°C = 32.0 + 273.15 = 305.15 K
New temperature (T2) = -14.1°C = -14.1 + 273.15 = 259.05 K

Next, let's calculate the number of moles using the ideal gas law equation at the initial location:
P1 = 0.995 atm
V1 = 4.39 x 10^4 L
R = 0.0821 L·atm/(mol·K)
T1 = 305.15 K

Rearranging the equation to solve for n, we get:
n = (P1 * V1) / (R * T1)

Substituting the given values into the equation:
n = (0.995 atm * 4.39 x 10^4 L) / (0.0821 L·atm/(mol·K) * 305.15 K)

Calculating this gives us the number of moles (n) at the initial location.

Now, let's use the ideal gas law equation at the new location to find the volume (V2):
P2 = 0.720 atm
V2 = ?
R = 0.0821 L·atm/(mol·K)
T2 = 259.05 K

Rearranging the equation to solve for V2, we get:
V2 = (n * R * T2) / P2

Substituting the calculated value of n and the given values into the equation:
V2 = ((calculated value of n) * 0.0821 L·atm/(mol·K) * 259.05 K) / 0.720 atm

Calculating this gives us the volume (V2) of the balloon at the new location.

So, by following these steps and plugging in the appropriate values, you can calculate the volume of the balloon at the new location.