A weather balloon was filled with helium to a volume of 25L at STP. What volume will it have when it rises to an altitude where the atmospheric pressure is 735 torr and the temperature is -22C?
Use (P1V1/T1) = (P2V2/T2)
Remember to convert T from C to kelvin. K = 273 + C
Post your work if you get stuck.
(P1V1/T1) = (P2V2/T2)
STP means standard temperature and pressure with standard pressure being 760 mm Hg and standard T being 0 degrees C which is 273 K. So
P1 = 760 mm Hg
V1 = 25 L
T1 = 273 K
P2 = 735 mm Hg (torr and mm Hg are the same)
V2 = ?
T2 = -22 C + 273 = 251 K
Plug those values into the formula and solve for V2 in which will be in units of Liters. Post your work if you get stuck. If you have trouble tell be what your problem is. This is not higher mathematics. It's algebra.
-22 + 273 =251K
P1= 735torr
V1= 25 L
Is the right, or how do I set up this problem?
To determine the volume of the weather balloon at an altitude where the atmospheric pressure and temperature are given, we need to apply the ideal gas law equation. The ideal gas law equation is as follows:
PV = nRT
Where:
P = pressure (in Pascals)
V = volume (in cubic meters)
n = number of moles
R = ideal gas constant (8.314 J/(mol K))
T = temperature (in Kelvin)
First, let's convert the initial volume given in liters to cubic meters, since the ideal gas law equation uses SI units (Pascals and cubic meters).
1 liter = 0.001 cubic meters
Given that the initial volume is 25L, we can convert it to cubic meters:
25L * (0.001 m³ / 1L) = 0.025 m³
Now, we can calculate the initial pressure (P1) at STP. At Standard Temperature and Pressure (STP), the temperature is 0 degrees Celsius (273.15 Kelvin), and the pressure is 1 atmosphere (atm), which is equal to 760 torr.
P1 = 760 torr
We also need to convert torr to Pascals since the ideal gas law equation uses Pascals:
1 torr = 133.32 Pascals
P1 = 760 torr * (133.32 Pa / 1 torr) = 101,325 Pa
Next, let's convert the given temperature of -22°C to Kelvin.
T = -22°C + 273.15 = 251.15 K
Now, we can calculate the final pressure (P2) using the given atmospheric pressure of 735 torr.
P2 = 735 torr * (133.32 Pa / 1 torr) = 98,047 Pa
Since we are given the number of moles (n) nor any additional information, we assume that the number of moles remains constant throughout the process. Hence, we can eliminate the n term from the equation.
Now, we can rearrange the ideal gas law equation to solve for the final volume (V2):
V2 = (P1 * V1 * T2) / (P2 * T1)
Substituting the given values:
V2 = (101,325 Pa * 0.025 m³ * 251.15 K) / (98,047 Pa * 273.15 K)
Evaluating this equation will give us the volume of the weather balloon at the given altitude and temperature.