Question

13. For real gases, we make a change to the ideal gas law such that it appears as below. This is known as the Van der Waals equation: (𝑃 + 𝑛^2/𝑉^2 𝑎) ∗ (𝑉 − 𝑛𝑏) = 𝑛𝑅𝑇 a) The “a” correctional factor adjusts for interparticle attractions. It is added to the observed pressure to correct for the pressure/force lost by particle attraction. The effect of interparticle attraction is most apparent at moderately high pressures and low temperatures. Why do we multiply “a” by n/V (moles over volume)? (Hint: how would a change in either parameter, or both, impact the number of interacting molecules in a given space) b) The “b” correctional factor adjusts for the space taken up by gas molecules. As discussed in class, at sufficiently high pressures (and low volumes), gas molecules take up a relatively large amount of space such that the free space they are able to explore is much less than that of the container size. This results in a much higher apparent pressure since the actual volume is much smaller (P goes up as V goes down). i. Using the ideal gas law, determine the pressure inside a 0.5 L flask containing 10 moles of gas at a temperature of 300 K. ii. Using the Van der Waals equation as shown above, determine the pressure of the system given that b = 0.005 L/mol. We will assume a = 0 for this problem.

          13. For real gases, we make a change to the ideal gas law such that it appears as below. This is
known as the Van der Waals equation:
(𝑃 + 𝑛^2/𝑉^2 𝑎) ∗ (𝑉 − 𝑛𝑏) = 𝑛𝑅𝑇
a) The “a” correctional factor adjusts for interparticle attractions. It is added to the observed
pressure to correct for the pressure/force lost by particle attraction. The effect of interparticle attraction is most apparent at moderately high pressures and low temperatures. Why do we multiply “a” by n/V (moles over volume)? (Hint: how would a change in either parameter, or
both, impact the number of interacting molecules in a given space)

b) The “b” correctional factor adjusts for the space taken up by gas molecules. As discussed in class, at sufficiently high pressures (and low volumes), gas molecules take up a relatively large amount of space such that the free space they are able to explore is much less than that of the
container size. This results in a much higher apparent pressure since the actual volume is much smaller (P goes up as V goes down).

i. Using the ideal gas law, determine the pressure inside a 0.5 L flask containing 10 moles of gas at a temperature of 300 K.

ii. Using the Van der Waals equation as shown above, determine the pressure of the system given that b = 0.005 L/mol. We will assume a = 0 for this problem.

Added by Emily D.

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