intermolecular forces

Question

A gas‑filled weather balloon with a volume of 58.0 L is held at ground level, where the atmospheric pressure is 7.60×102 mmHg and the temperature is 24.2 ∘C . The balloon is released and rises to an altitude where the pressure is 0.0537 bar and the temperature is −7.38 ∘C . Calculate the weather balloon's volume at the higher altitude.

Answer 1

This question tests your knowledge of the combined gas law (P₁V₁/T₁=P₂V₂/T₂). Using algebra, we can create permutations of this equation to solve for each variable. Knowing this, it is just a process of deciding what information is given to us, and what information still needs to be determined. I suggest that we make a list of the given variables, and convert our temperatures from °C to K by adding 273.15:

for the variables with the subscript (1), I typically assign those to the initial conditions to help me stay organized. Therefore,

P₁ - 7.60 x 10² mmHg

V₁ - 58.0 L

T₁ - (24.2 °C + 273.15) = 297.35 k

Now, for the variables with the subscript (2), I assign the final conditions:

P₂ - 0.0537 bar

V₂ - ?

T₂ - (-7.38 °C +273.15) = 265.77 k

Organizing our known values this way allows for us to quickly determine that we are solving for the final volume (V₂) of the gas-filled weather balloon. Now we just need to convert our units to identical units of the gas constant to solve this problem. Typically, for the ideal gas law equation, we would need to convert our temperature and pressure units to match the units of R (our gas law constant given in units of atm·L/mol·k). For this problem, let's just convert 0.0537 bar and 7.60 x 10² mmHg to atm by multiplying it by the corresponding conversion factor:

(0.0537 bar)(0.987 atm/1 bar) = 0.0530 atm

(7.60 x 10² mmHg)(1 atm/760 mmHg) = 1.00 atm

Now we just plug in all of our variables into the combined gas equation:

(1.00 atm)(58.0 L)/(297.35 k) = (0.0530 atm)(V₂)/(265.77 k)

Solving for V₂ gives us:

0.195056 atm·L/k = (0.0530 atm)(V₂)/(265.77 k)

multiply both sides by 265.77 k

51.840 atm·L = (0.0530 atm)(V₂)

Now, divide both sides by 0.0530 atm

V₂ = 978.1 L, which is our final volume at the higher altitude.

It is noteworthy to mention that we change to units of R out of convention, and that the combined gas law is essentially a proportion between the three variables V, P, and T. Therefore, it is not strictly necessary to convert your units and will workout as long as your units for each measurement are identical. I hope this helps!

Jake