The ideal gas law assumes that molecules bounce around and have negligible volum

Question

The ideal gas law assumes that molecules bounce around and have negligible volume themselves. This is not always true. To compensate for the simplifying assumptions of the ideal gas law. the Dutch scientist Johannes van der Waals developed a "real" gas law that uses several factors to account for molecular volume and intermolecular attraction. He was awarded the Nobel Prize in 1910 for his work. The van der Waals equation is as follows: P, V, n, R, and T are the same quantities as found in the ideal gas law. The constant "a" is a correction for intermolecular forces [atm L 2/mol 2], and the constant "b" accounts for molecular volume [L/mol]. Each of these factors must be determined by experiment. Create a worksheet using the provided template. The molecular weight. " a, " and " b " should automatically fill in after the user selects the type of gas in cell B7. The user will also set the quantity of gas and the temperature of the system Next, create a column of volume beginning in A21 at 0.5 liters and increasing in increments of 0.1 liters to a volume of 5 liters In column B, calculate the pressure (P, in atmospheres [atm]) using the ideal gas law. In column C, calculate the pressure (P, in atmospheres [atm]) using the van der Waals equation.

Explanation / Answer

Ideal gas equation gives PV=nRT

we take room temperature T=30degree=30+273=303K

Volume V=.5l

now R= 8.314

but for Acetylene n=.0384mole using the same we get

P=nRT/V =.0384*8.314* 303/.5= 193.47Atm

again from vandarwaals equation we know that a= 4.516,b=.05220 [Acetylene

then from Vandarwaal's expression (P+an^2/V^2)(V-bn)=nRT

using values we get

(P+4.516*.0384^2/.5^2)(.5-.05220*.0384)=.0384*8.314*303

or P= 194.214Atm

In the similar way wwe can calcculate all the values wwhile increasing the volume

Now if we take V=1l

we get Pideal= .0384*8.314*303/1=96.73atm

Pvandarwaal=[ .0384*8.314*303/(1-.05220*.0384)]- 4.516*.0384^2/1^2= 96.91Atm

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