Use the van der Waals equation and the ideal gas equation to...

Use the van der Waals equation and the ideal gas equation to calculate the pressure exerted by $1.000 \mathrm{~mol}$ of $\mathrm{Cl}_{2}$ in a volume of $5.000 \mathrm{I}$. at a temperature of $2730 \mathrm{~K}$ Fxplain why the two values are different.

Key Concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in thermodynamics that relates the pressure, volume, temperature, and number of moles of a gas with the equation PV = nRT. It assumes that gas particles have negligible volume and no intermolecular forces, making it most applicable under conditions of low pressure and high temperature where gases behave ideally.

Van der Waals Equation

The Van der Waals Equation is a modified version of the Ideal Gas Law that accounts for the finite volume of gas molecules and the attractive forces between them. It introduces correction factors to better model the behavior of real gases, particularly at high pressures and low temperatures, where deviations from ideality are significant.

Real Gas Behavior

Real gas behavior refers to the deviations from the predictions of the Ideal Gas Law when intermolecular forces and the actual volume of gas molecules become significant. These deviations are captured by equations like the Van der Waals Equation, which better describe the properties of real gases under non-ideal conditions.

Transcript

00:01 Hi guys, i'm going to answer question number 94.

00:06 The question wants us to use the underwall equation and i think gas equation to calculate pressure of 1 mole of chlorine with a volume of 5 liter at temperature of 273 carbon.

00:49 And you want us to explain the different between the two follow so definitely we're going to have different value one follow from under wall equation at the other one from id gas equation let me do the act of id gas first i think gas plus p f because nrt that is the id kajar's equation because i want to calculate pressure i will make it this subject i can say p pb nrd divide by follow so i will calculate my p i have n1 more of chlorine and my r is zero point is gas constant is 0 .082 litre atmosphere per kivapermore and the temperature is 273 kivin who divide this by volume of 5 theta so we get 4 .472 atmosphere.

02:08 That is the answer with id gas law.

02:15 Now i want to use vanderwrowl.

02:23 I can call the vandahuaq equation because most gas with default from id gas behavior at a certain condition.

02:36 So the adegas, they found our whole equation is p plus a .n squared by f squared and bracket v minus np equals nrt.

03:02 So get our p, p will be nrt divided by v minus nb and minus a n square divide by v square so i will use that to solve the calculate the pressure of this chlorine gas n is 1 r is 0 .0 8 2 temperature is 273 divided by volume is 5 litre minus n is 1 and b i will look up this volume a and b for chlorine chlorine is 6 .49, liter square, atmosphere, more, the rest of b is 0 .0562, little bit of number.

04:14 So i have to put the value of b, 0 .0562, minus a is 6 .49, 10 is 1, divide by v is 5 liter square.

04:31 And that gives 4 .5 to 8096 minus this value i get 0 .2596 and everything gives 4 .2685 atmosphere.

04:56 We can see the difference now comparing this and this...

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