Question

Cylinders of compressed gas are typically filled to a pressure of 200 bar. For oxygen, what would be the molar volume at this pressure and 25 °C based on (i) the perfect gas equation, (ii) the van der Waals equation? For oxygen, a = 1.364 dm6 atm mol−2, b = 3.19 × 10−2 dm3 mol−1.

Answer 1

Answer:

a

 $V = 0.124 \ Liters$

b

$V = 0.112 \ Liters$

Explanation:

From the question we are told that

  The pressure of compressed gas is $P = 200 \ bar = \frac{200}{1.013}= 197.4 \ atm$

  The  temperature is  $T = 25^oC = 25 + 273 = 298 \ K$

Generally the perfect gas equation is mathematically represented as

     $PV = nRT$

substituting 0.08206 L-atm/mol-K  for R and  1 mole for n

We have that

     $V = \frac{1 * 0.08206 * 298 }{ 197.4}$

       $V = 0.124 \ Liters$

Generally the van der Waals equation is mathematically represented as

       $nRT = [P + \frac{n^2 * a }{V^2 } ][V - nb]$

=>$1 * 0.08206 *298 = [197.4 + \frac{1^2 * 1.364}{V^2 } ][V - 1 * 3.19 * 10^{-2}]$

=>    $V = 0.112 \ Liters$