A gas-filled balloon having a volume of 1.50 L at 1.2 atm and 25°C is allowed to rise to the stratosphere (about 30 km above the surface of Earth), where the temperature and pressure are -23°C and 3.00 multiplied by 10-3 atm, respectively. Calculate the final volume of the balloon.
(P1V1)/T1=(P2V2)/T2 Don't forget to change T to Kelvin
To calculate the final volume of the balloon, we can use the combined gas law equation. The combined gas law relates the initial and final conditions of volume, pressure, and temperature of a gas.
The combined gas law equation is given by:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 is the initial pressure (1.2 atm)
V1 is the initial volume (1.50 L)
T1 is the initial temperature (25°C = 25 + 273 = 298 K)
P2 is the final pressure (3.00 x 10^-3 atm)
V2 is the final volume (we need to calculate this)
T2 is the final temperature (-23°C = -23 + 273 = 250 K)
Substituting the given values into the equation, we have:
(1.2 atm * 1.50 L) / (298 K) = (3.00 x 10^-3 atm * V2) / (250 K)
Now, let's solve for V2:
(1.2 atm * 1.50 L * 250 K) = (3.00 x 10^-3 atm * V2 * 298 K)
(1.8 L * 250) = (0.00894 V2)
450 = 0.00894 V2
V2 = 450 / 0.00894
V2 ≈ 50.33 L
Therefore, the final volume of the balloon is approximately 50.33 L when it rises to the stratosphere.