   Chapter 10, Problem 53PS

Chapter
Section
Textbook Problem

In the text, it is stated that the pressure of 4.00 mol of Cl2 in a 4.00-L tank at 100.0 °C should be 26.0 atm if calculated using the van der Waals equation. Verify this result, and compare it with the pressure predicted by the ideal gas law.

Interpretation Introduction

Interpretation:

For the gas under given conditions the pressure for the gas should be determined by van der Waals equation then it should be compared with that pressure has to be calculated using ideal gas equation.

Concept introduction:

Ideal gas Equation:

Any gas can be described by using four terms namely pressure, volume, temperature and the amount of gas.  Thus combining three laws namely Boyle’s, Charles’s Law and Avogadro’s Hypothesis the following equation could be obtained.  It is referred as ideal gas equation.

nTPV = RnTPPV = nRTwhere,n = moles of gasP = pressureT = temperatureR = gas constant

Under some conditions gases don not behave like ideal gas that is they deviate from their ideal gas properties.  At lower temperature and at high pressures the gas tends to deviate and behave like real gases.

Boyle’s Law:

At given constant temperature conditions the mass of given ideal gas in inversely proportional to its volume.

Charles’s Law:

At given constant pressure conditions the volume of ideal gas is directly proportional to the absolute temperature.

Two equal volumes of gases with same temperature and pressure conditions tend to have same number of molecules with it.

Van der Waal’s gas equation:

The van der Waal equation describes the ideal gas as it approaches to zero.  The van der Waal equation contains correction terms a and b for the intermolecular forces and molecular size respectively.

The van der Waal equation is as follows,

[P+a(nV)2](Vnb)=RT

Explanation

Given,

Volume, V = 4 LTemperature, T=100oC=373.15Kmoles = 4 moles of Cl2Gas constant, R = 0.0821 L atm mol-1K-1Pressure, P = 26 atm Prove it by using van der Waal's equation.

Using van der Waal equation the pressure for the gas is determined as follows,

[P+a(nV)2](Vnb)=RT[P+a(nV)2]=RT(Vnb)P=RT(Vnb)a(nV)2=0

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