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? asked in Science & MathematicsChemistry · 4 weeks ago

What is the volume of the balloon at this depth?

A scuba diver takes a 2.3 L balloon from the surface, where the pressure is 1.1 atm and the temperature is 31 ∘C, to a depth of 25 m, where the pressure is 3.5 atm and the temperature is 14 ∘C.

3 Answers

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  • 4 weeks ago
    Favorite Answer

    (2.3 L) x (1.1 atm / 3.5 atm) x (14 + 273) K / (31 + 273) K = 0.68 L

  • ?
    Lv 7
    4 weeks ago

    PV=nRT <<<memorize!!

    n is moles, R is gas constant (use correct one!), T is temp in K (C+273.15)

    Since you have a before and after with the same n &R simplifies to

    PV/T initial = nR = PV/T final

    Now sub in your numbers and solve

    SI Units R values:

    8.31446261815324 J⋅K−1⋅mol−1

    8.31446261815324 m3⋅Pa⋅K−1⋅mol−1

    8.31446261815324 kg⋅m2·K−1⋅mol−1s−2

    8.31446261815324×103 L⋅Pa⋅K−1⋅mol−1

    8.31446261815324×10−2 L⋅bar⋅K−1⋅mol−1

    0.082057 L atm mol-1K-1

    62.36L·torr/mol·K = L·mmHg/mol·K

  • 4 weeks ago

    pV = nRT  -->  note n*R = constant so

    Let V0, p0, and T0 be volume, pressure and temperature at surface (respectively) and

    V1, p1, T1 be volume, pressure and temperature at depth (respectively)

    Using ideal gas equation of state  nR = p0*V0/T0

    then using it again for the balloon at depth

    p1*V1 = nRT1 = {p0*V0/T0} T1  -->  solve for V1

    V1 = {p0*V0/(p1*T0}}*T1

    Plug in values and you're finished

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