A helium-filled weather balloon has a 0.90-m radius at liftoff where air pressure is 1.0 atm and the temperature is 298 K.When airborne,the temperature is 210 K,and its radius expands to 3.5 m.What is the pressure at the airborne location?
A) 0.50 atm
B) 0.012 atm
C) 0.019 atm
D) 0.38 atm

Question

Quizplus · Accepted Answer

We can use the ideal gas law to solve this problem:

PV = nRT

where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature.

At liftoff:

P = 1.0 atm
V = (4/3)π(0.9 m)^3 = 3.05 m^3
T = 298 K

We can solve for n:

n = PV/RT = (1.0 atm)(3.05 m^3)/(0.0821 L atm/mol K)(298 K) = 0.127 mol

Now we can use the same equation at the airborne location:

V = (4/3)π(3.5 m)^3 = 179.6 m^3
T = 210 K
n = 0.127 mol (since the number of moles of gas does not change)

Solving for P:

P = nRT/V = (0.127 mol)(0.0821 L atm/mol K)(210 K)/(179.6 m^3) = 0.012 atm

Therefore, the answer is B.

A Helium-Filled Weather Balloon Has a 0