A sealed balloon is filled with 1.20 L of helium at 23°C and 1.00 atm. The balloon rises to a point in the atmosphere where the pressure is 250. torr and the temperature is -27°C. What is the change in volume of the balloon as it ascends from 1.00 atm to a pressure of 250. torr?
(P1V1/T1) = (P2V2/T2)
You must change atm to torr or torr to atm. Remember T must be in kelvin.
1.82L
To find the change in volume of the balloon, we can use the combined gas law, which relates the initial and final conditions of pressure, volume, and temperature.
The combined gas law is given by:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
where P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes, and T1 and T2 are the initial and final temperatures.
Let's start by converting the temperatures to Kelvin. The temperature in Celsius can be converted to Kelvin by adding 273.15. So, we have:
T1 = 23°C + 273.15 = 296.15 K
T2 = -27°C + 273.15 = 246.15 K
The initial pressure, P1, is given as 1.00 atm, and the final pressure, P2, is given as 250 torr. To express them in the same unit, let's convert 1.00 atm to torr. Since 1 atm = 760 torr, we have:
P1 = 1.00 atm * 760 torr/atm = 760 torr
Now we can plug in the values into the combined gas law equation:
(760 torr * V1) / (296.15 K) = (250 torr * V2) / (246.15 K)
Next, we can rearrange the equation to solve for the change in volume:
V2 = (760 torr * V1 * (246.15 K)) / (250 torr * 296.15 K)
Simplifying the equation:
V2 = (760 torr * V1 * 246.15 K) / (250 torr * 296.15 K)
Now, we can calculate the change in volume by substituting the given value of V1 as 1.20 L:
V2 = (760 torr * 1.20 L * 246.15 K) / (250 torr * 296.15 K)
Simplifying the equation further:
V2 = (1824 torr * 246.15 K) / (250 torr * 296.15 K)
Finally, we can cancel out the units and calculate the change in volume:
V2 = (1824) / (250) L
V2 = 7.296 L - 1.20 L
Therefore, the change in volume of the balloon as it ascends is 6.096 L.