Ch.5 - GasesSee all chapters
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Ch.1 - Intro to General Chemistry
Ch.2 - Atoms & Elements
Ch.3 - Chemical Reactions
BONUS: Lab Techniques and Procedures
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Ch.4 - Chemical Quantities & Aqueous Reactions
Ch.5 - Gases
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Ch.22 - Chemistry of the Nonmetals
Ch.23 - Transition Metals and Coordination Compounds

The Van der Waals Equation is used when dealing with real, non-ideal gases. 

Understanding the Van der Waals Equation

Concept #1: Van der Waals Equation

The Van der Waals Equation takes into consideration that real gases do not behave ideally. As a result these gases can experience attractive or repulsive forces while also having definite volumes. 

Calculations with the Van der Waals Equation

Example #1: Van der Waals Equation

Example #2: Van der Waals Equation

Example #3: Van der Waals Equation

Example #4: Van der Waals Equation

Additional Problems
Use the van der Waals equation and the ideal gas equation to calculate the pressure exerted by 1.000 mol of Cl2 in a volume of 5.000 L. at a temperature of 273.0 K. Explain why the two values are different. 
Which gas molecule do you expect to be the largest? (a and b are Van der Waals constants.) 1. Butane 2. Acetonitrile 3. Freon
Use the van der Waal's equation to calculate the pressure (in atm) exerted by 1.00 mol of chlorine gas confined to a volume of 2.00 L at 273K. The value of a = 6.49 L2 atm mol-2, and that of b = 0.0562 L mol-1 for chlorine gas. a) no given answer is close b) 9.9 c) 4.12 d) 1.54 e) 3.73
Which gas would you expect to have the largest value for the van der Waals constant “a”? 1. Ne 2. CH4 3. He 4. NH3
The constant a in the Van der Waal’s equation corrects for ________and is important at ________. a. intermolecular attraction, high temperature b. intermolecular attraction, low temperature c. lower than average energy of molecules, low temperature d. volume of molecules, low pressure e. volume of molecules, high pressure
The graph below shows the change in pressure as the temperature increases for a 1-mol sample of a gas confined to a 1-L container. The four plots correspond to an ideal gas and three real gases: CO2, N2, and Cl2. At room temperature, all three real gases have a pressure less than the ideal gas. Which van der Waals constant, a or b, accounts for the influence intermolecular forces have in lowering the pressure of a real gas?
The graph below shows the change in pressure as the temperature increases for a 1-mol sample of a gas confined to a 1-L container. The four plots correspond to an ideal gas and three real gases: CO2, N2, and Cl2. Use the van der Waals constants in the table below to match the labels in the plot (A, B, and C) with the respective gases (CO2, N2, and Cl2). Van der Waals Constants for Gas Molecules Substance a(L2-atm/mol2) b(L/mol) He 0.0341 0.02370 Ne 0.211 0.0171 Ar 1.34 0.0322 Kr 2.32 0.0398 Xe 4.19 0.0510 H2 0.244 0.0266 N2 1.39 0.0391 O2 1.36 0.0318 F2 1.06 0.0290 Cl2 6.49 0.0562 H2O 5.46 0.0305 NH3 4.17 0.0371 CH4 2.25 0.0428 CO2 3.59 0.0427 CCl4 20.4 0.1383
Assuming that the van der Waals equation predictions are accurate, account for why the pressure of He is higher than that predicted for an ideal gas.
Assuming that the van der Waals equation predictions are accurate, account for why the pressure of Ne is higher than that predicted for an ideal gas.
Assuming that the van der Waals equation predictions are accurate, account for why the pressure of H2 is higher than that predicted for an ideal gas.
Assuming that the van der Waals equation predictions are accurate, account for why the pressure of CH4 is lower than that predicted for an ideal gas.
Assuming that the van der Waals equation predictions are accurate, account for why the pressure of CO2 is lower than that predicted for an ideal gas.
The table below shows that the van der Waals b parameter has units of L/mol. Van der Waals Constants for Gas Molecules Substance a(L2-atm/mol2) b(L/mol) He 0.0341 0.02370 Ne 0.211 0.0171 Ar 1.34 0.0322 Kr 2.32 0.0398 Xe 4.19 0.0510 H2 0.244 0.0266 N2 1.39 0.0391 O2 1.36 0.0318 F2 1.06 0.0290 Cl2 6.49 0.0562 H2O 5.46 0.0305 NH3 4.17 0.0371 CH4 2.25 0.0428 CO2 3.59 0.0427 CCl4 20.4 0.1383 This means that we can calculate the sizes of atoms or molecules from the b parameter. Refer back to the discussion in Section 7.3 in the textbook.Is the van der Waals radius we calculate from the b parameter of the table above more closely associated with the bonding or nonbonding atomic radius discussed there?
You may want to reference (Pages 419 - 423)Section 10.9 while completing this problem.Calculate the pressure of a 2.975-mol sample of N2 in a 0.7500-L flask at 300.0 oC using the van der Waals equation and then repeat the calculation using the ideal-gas equation. Within the limits of the significant figures justified by these parameters, will the ideal-gas equation overestimate or underestimate the pressure, and if so by how much? For N2, a = 1.39 L2atm/mol2 and b = 0.0391 L/mol.
Based on their respective van der Waals constants, is Ar (a = 1.34, b = 0.0322) or CO2 (a = 3.59, b = 0.0427) expected to behave more nearly like an ideal gas at high pressures?
In Sample Exercise 10.16 in the textbook, we found that one mole of Cl2 confined to 22.41 L at 0 oC deviated slightly from ideal behavior. Calculate the pressure exerted by 1.00 mol  Cl2 confined to a smaller volume, 6.00 L , at 25 oC.Why is the difference between the result for an ideal gas and that calculated using van der Waals equation greater when the gas is confined to 6.00 L compared to 22.4 L?
Large amounts of nitrogen gas are used in the manufacture of ammonia, principally for use in fertilizers. Suppose 130.00 kg of N2(g) is stored in a 1400.0 L metal cylinder at 290 oC.Under the conditions of this problem, which correction dominates, the one for finite volume of gas molecules or the one for attractive interactions?
Calculate the pressure exerted by 1.00 mol of He in a box that is 0.300 L and 298 K. For He, a = 0.0342 L2 atm/mol2 and b = 0.02370 L/mol.
Calculate the pressure exerted by 1.00 mol of Ne in a box that is 0.300 L and 298 K. For Ne, a = 0.211 L2 atm/mol2 and b = 0.0171 L/mol.
Calculate the pressure exerted by 1.00 mol of H2 in a box that is 0.300 L and 298 K. For H2, a = 0.244 L2 atm/mol2 and b = 0.0266 L/mol.
Calculate the pressure exerted by 1.00 mol of CH4 in a box that is 0.300 L and 298 K. For CH4, a = 2.25 L2 atm/mol2 and b = 0.0428 L/mol.
Calculate the pressure exerted by 1.00 mol of CO2 in a box that is 0.300 L and 298 K. For CO2, a = 3.59 L2 atm/mol2 and b = 0.0427 L/mol.
You may want to reference (Pages 196 - 236) Chapter 5 while completing this problem.Use the van der Waals equation to calculate the pressure exerted by 1.255 mol of Cl2 in a volume of 5.005 L at a temperature of 273.5 K .
In Sample Exercise 10.16 in the textbook, we found that one mole of Cl2 confined to 22.41 L at 0 oC deviated slightly from ideal behavior. Calculate the pressure exerted by 1.00 mol  Cl2 confined to a smaller volume, 6.00 L , at 25 oC.Use van der Waals equation for your calculation. (Values for the van der Waals constants are a = 6.49 L2atm/mol2, b = 0.0562 L/mol.)
Calculate the pressure that CCl4 will exert at 41 oC if 1.20 mol occupies 33.6 L , assuming thatCCl4 obeys the van der Waals equation. (Values for the van der Waals constants are a=20.4, b=0.1383.)
Large amounts of nitrogen gas are used in the manufacture of ammonia, principally for use in fertilizers. Suppose 130.00 kg of N2(g) is stored in a 1400.0 L metal cylinder at 290 oC.Given that for N2, a = 1.39 L atm/mol2 and b = 0.0391 L/mol, calculate the pressure of the gas according to the van der Waals equation.
Use the van der Waals equation and the ideal gas equation to calculate the volume of 1.000 mol of neon at a pressure of 500.0 atm and a temperature of 355.0 K.
It turns out that the van der Waals constant b equals four times the total volume actually occupied by the molecules of a mole of gas. Using this figure, calculate the fraction of the volume in a container actually occupied by Ar atoms:Assume b= 0.0322 L/mol.at 210 atm pressure and 0 oC. (Assume for simplicity that the ideal-gas equation still holds.)
Use the van der Waals equation of state to calculate the pressure of 2.70 mol of Xe at 473 K in a 5.50-L vessel. Van der Waals constants can be found below. P= ______________ atm Use the ideal gas equation to calculate the pressure under the same conditions. P=_______________atm
Describe the factors responsible for the deviation of the behavior of real gases from that of an ideal gas
For which of the following gases should the correction for the molecular volume be largest: CO, CO2, H2, He, NH3, SF6?
For each of the following, which shows the greater deviation from ideal behavior at the same set of conditions? Explain.(a) Argon or xenon 
For each of the following, which shows the greater deviation from ideal behavior at the same set of conditions? Explain.(b) Water vapor or neon
For each of the following, which shows the greater deviation from ideal behavior at the same set of conditions? Explain.(c) Mercury vapor or radon 
For each of the following, which shows the greater deviation from ideal behavior at the same set of conditions? Explain.(d) Water vapor or methane
In the following table shows that the van der Waals exttip{b}{b} parameter has units of L/mol. This implies that we can calculate the size of atoms or molecules from exttip{b}{b}.Using the value of exttip{b}{b} for Xe, calculate the radius of a Xe atom. Recall that the volume of a sphere is (4/3)πr3.Table Van der Waals Constants for Gas MoleculesSubstance exttip{a}{a} (L2 - atm/mol2) exttip{b}{b} ( L/mol )He0.03410.02370Ne0.2110.0171Ar1.340.0322Kr2.320.0398Xe4.190.0510H20.2440.0266N21.390.0391O21.360.0318Cl26.490.0562H2O5.460.0305CH42.250.0428CO23.590.0427CCl420.40.1383
Many water treatment plants use chlorine gas to kill microorganisms before the water is released for residential use. A plant engineer has to maintain the chlorine pressure in a tank below the 85.0-atm rating and, to be safe, decides to fill the tank to 80.0% of this maximum pressure. (b) What is the tank pressure if she uses the van der Waals equation for this amount of gas? 
A 0.245-L flask contains 0.467 mol CO2 at 159 °C. Calculate the pressure:(b) using the van der Waals equation
To study a key fuel-cell reaction, a chemical engineer has 20.0-L tanks of H 2 and of O2 and wants to use up both tanks to form 28.0 mol of water at 23.8°C. (b) Use the van der Waals equation to find the pressure needed in each tank. 
Ammonia is essential to so many industries that, on a molar basis, it is the most heavily produced substance in the world. Calculate  PIGL and PVDW (in atm) of 51.1 g of ammonia in a 3.000-L container at 0°C and 400.°C, the industrial temperature. (See Table 5.4 for the values of the van der Waals constants.)
Calculate the pressure exerted by 0.5000 mole of N2 in a 1.0000-L container at 25.0°Cb. using the van der Waals equation.
Calculate the pressure exerted by 0.5000 mole of N2 in a 10.000-L container at 25.0°Cb. using the van der Waals equation.
Chlorine is produced from sodium chloride by the electrochemical chlor-alkali process. During the process, the chlorine is collected in a container that is isolated from the other products to prevent unwanted (and explosive) reactions. If a 15.50-L container holds 0.5950 kg of Cl2 gas at 225°C, calculate:(b) PVDW (use R = 0.08206 mol·K/(atm·L))
A slight deviation from ideal behavior exists even at normal conditions. If it behaved ideally, 1 mol of CO would occupy 22.414 L and exert 1 atm pressure at 273.15 K. Calculate PVDW for 1.000 mol of CO at 273.15 K. (Use R = 0.08206 atm·L/(mol·K))
Calculate the pressure in bar of 8.5 mol of ethanol vapor in a 12.0-L container held at 82°C:a. treating ethanol vapor as a van der Waal's gas,b. treating ethanol as an ideal gas. 
At high pressures, real gases do not behave ideally. (a) Use the van der Waals equation and data in the text to calculate the pressure exerted by 10.5 g _2 at 20 C in a 1.00 L container. (b) Repeat the calculation assuming that the gas behaves like an ideal gas. van der Waals (real) gas pressure ideal gas pressure
Calculate the pressure that CCl4 will exert at 43 C if 1.20 mol occupies 33.5 L, assuming that CCl4 obeys the ideal-gas equation: P = CCl4 obeys the van der Waals equation. (Values for the van der Waals constants are a = 20.4, b = 0.1383.)
Use the van der Waals equation to calculate the pressure exerted by 1.330 mol of Cl_2 in a volume of 5.285 L at a temperature of 303.0 K. Use the ideal gas equation to calculate the pressure exerted by 1.330 mol of Cl_2 in a volume of 5.285 L at a temperature of 303.0 K.
Use the van der Waals equation of state to calculate the pressure of 2.80 mol of NH3 at 483 K in a 5.50 L vessel.Use the ideal gas equation to calculate the pressure under the same conditions. 
Use the van der Waals equation of state to calculate the pressure of 2.20 mol of Xe at 497 K in a 4.40 L vessel. Van der Waals constants can be found here. Use the ideal gas equation to calculate the pressure under the same conditions. 
Use the van der Waals equation of state to calculate the pressure of 2.50 mol of H2O at 497 K in a 4.90 L vessel. Van der Waals constants can be found here. Use the ideal gas equation to calculate the pressure under the same conditions.
According to the ideal gas law, a 9.847 mol sample of methane gas in a 0.8237 L container at 500.0 K should exert a pressure of 490.5 atm. By what percent does the pressure calculated using the van der Waals' equation differ from the ideal pressure? For CH4 gas, a = 2.253 L2 atm/mol2 and b = 4.278 x 10-2 L/mol.
Part B If 1.00 mol of argon is placed in a 0.500-L container at 30.0°C, what is the difference between the ideal pressure (as predicted by the ideal gas law) and the real pressure (as predicted by the van der Waals equation)? For argon, a = 1.345 (L2. atm)/mol2 and b = 0.03219 L/mol.Express your answer to two significant figures and include the appropriate units. 
15.0 moles of gas are in a 8.00 L tank at 22.2°C. Calculate the difference in pressure between methane and an ideal gas under these conditions. The van der Waals constants for methane are a = 2.300 L2 • atm/mol2 and b = 0.0430 L/mol. Express your answer with the appropriate units.
At high pressures, real gases do not behave ideally. (a) Use the van der Waals equation and data in the text to calculate the pressure exerted by 21.0 g H2 at 20°C in a 1.00 L container. (b) Repeat the calculation assuming that the gas behaves like an ideal gas.