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

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.

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Which gas molecule do you expect to be the largest? (a and b are Van der Waals constants.)
1. Butane
2. Acetonitrile
3. Freon

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.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).

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.

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.

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= ______________ atmUse 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

A 0.245-L flask contains 0.467 mol CO2 at 159 °C. Calculate the pressure:(b) using the van der Waals equation

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.

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.

For which of the following gases should the correction for the molecular volume be largest: CO, CO2, H2, He, NH3, SF6?

Which statement(s) concerning the van der Waals constants a and b is true?(a) The magnitude of a relates to molecular volume, whereas b relates to attractions between molecules.(b) The magnitude of a relates to attractions between molecules, whereas b relates to molecular volume.(c) The magnitudes of a and b depend on pressure.(d) The magnitudes of a and b depend on temperature.

The ideal gas law tends to become inaccurate when a. the pressure is lowered and molecular interactions become significant. b. the pressure is raised and the temperature is lowered. c. the temperature is raised above the temperature of STP.d. large gas samples are involved.e. the volume expands beyond the standard molar volume.

In general, which of the following gases would you expect to behave the least ideally even under extreme conditions?a. N2b. COc. H2Kinetic molecular theory makes certain assumptions about gases that are, in fact, not true for real gases. Therefore, the measured properties of a gas are often slightly different from the values predicted by the ideal gas law. The van der Waals equation is a more exact way of calculating properties of real gases. The formula includes two constants, a and b, that are unique for each gas.The van der Waals equation is(P+an2V2)(V-nb)=nRTwhere P is the pressure, n the number of moles of gas, V the volume, T the temperature, and R the gas constant. All real gases possess intermolecular forces that can slightly decrease the observed pressure.In the van der Waals equation, the variable P is adjusted toP+an2V2where a is the attractive force between molecules.The volume of a gas is defined as the space in which the gas molecules can move. When using the ideal gas law we make the assumption that this space is equal to the volume of the container. However, the gas molecules themselves take up some space in the container. So in the van der Waals equation, the variable V is adjusted to be the volume of the container minus the space taken up by the moleculesV-nbwhere bb is the volume of a mole of molecules.

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?

(a) which of these gases would you expect to have the largest Van der Waals constant a?H2, HF, F2(b) which of these gases would you expect to have the largest Van der Waals constant b? H2, HCL, CL2

13.0 moles of gas are in a 5.00 L tank at 20.4 °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.Kinetic molecular theory makes certain assumptions about gases that are, in fact, not true for real gases. Therefore, the measured properties of a gas are often slightly different from the values predicted by the ideal gas law. The van der Waals equation is a more exact way of calculating properties of real gases. The formula includes two constants, a and b, that are unique for each gas.The van der Waals equation is(P+an2V2)(V-nb)=nRTwhere P is the pressure, n the number of moles of gas, V the volume, T the temperature, and R the gas constant. All real gases possess intermolecular forces that can slightly decrease the observed pressure.In the van der Waals equation, the variable P is adjusted toP+an2V2where a is the attractive force between molecules.The volume of a gas is defined as the space in which the gas molecules can move. When using the ideal gas law we make the assumption that this space is equal to the volume of the container. However, the gas molecules themselves take up some space in the container. So in the van der Waals equation, the variable V is adjusted to be the volume of the container minus the space taken up by the moleculesV-nbwhere bb is the volume of a mole of molecules.

(a) Briefly explain the significance of the constants a and b in the van der Waals equation.

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 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.

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 .

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.

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.

Consider the following gases, all at STP: Ne, SF6, N2, CH4.Which one has the highest total molecular volume relative to the space occupied by the gas?

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.)

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.

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 closeb) 9.9c) 4.12d) 1.54e) 3.73

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.

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.)

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?

To prevent tank rupture during deep-space travel, an engineering team is studying the effect of temperature on gases confined to small volumes. What is the pressure of 2.80 mol of gas D measured at 251 °C in a 1.75-L container assuming real behavior?Express your answer with the appropriate units.You may be familiar with the ideal gas equation,PV=nRTwhere n is the number of moles, P is the pressure in atmospheres, V is the volume in liters, and R is equal to 0.08206 L ⋅ atm/(mol ⋅ K).Real gases, especially under extremes of temperature and pressure, deviate from ideal behavior due to intermolecular forces and the volume occupied by the gas molecules themselves. Correction factors can be applied to the ideal gas equation to arrive at the van der Waals equation,P=nRTV-nb-n2aV2where a and b are van der Waals constants for the particular gas. The term nb corrects the volume to account for the size of the molecules and the term n2a/V2 corrects the pressure for intermolecular attraction.van der Waals constants for hypothetical gases

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 STP

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 200 atm pressure and 0 oC. (Assume for simplicity that the ideal-gas equation still holds.)

If 1.00 mol of argon is placed in a 0.500-L container at 24.0 °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.Ideal versus real behavior for gasesIn the following part you can see how the behavior of real gases deviates from the ideal behavior. You will calculate the pressure values for a gas using the ideal gas law and also the van der Waals equation. Take note of how they differ.

In general, which of the following gases would you expect to behave the most ideally even under extreme conditions?a. N2b. COc. H2Kinetic molecular theory makes certain assumptions about gases that are, in fact, not true for real gases. Therefore, the measured properties of a gas are often slightly different from the values predicted by the ideal gas law. The van der Waals equation is a more exact way of calculating properties of real gases. The formula includes two constants, a and b, that are unique for each gas.The van der Waals equation is(P+an2V2)(V-nb)=nRTwhere P is the pressure, n the number of moles of gas, V the volume, T the temperature, and R the gas constant. All real gases possess intermolecular forces that can slightly decrease the observed pressure.In the van der Waals equation, the variable P is adjusted toP+an2V2where a is the attractive force between molecules.The volume of a gas is defined as the space in which the gas molecules can move. When using the ideal gas law we make the assumption that this space is equal to the volume of the container. However, the gas molecules themselves take up some space in the container. So in the van der Waals equation, the variable V is adjusted to be the volume of the container minus the space taken up by the moleculesV-nbwhere bb is the volume of a mole of molecules.

In Part B the given conditions were 1.00 mol of argon in a 0.500-L container at 24.0 °C. You identified that the ideal pressure (Pideal) was 48.8 atm, and the real pressure (Preal) was 46.7 atm under these conditions. Complete the sentences to analyze this difference.Match the words and compounds in the left column to the appropriate blanks in the sentences on the right. Make certain each sentence is complete before submitting your answer.Ideal versus real behavior for gasesIn the following part you can see how the behavior of real gases deviates from the ideal behavior. You will calculate the pressure values for a gas using the ideal gas law and also the van der Waals equation. Take note of how they differ.

The table below shows that the van der Waals b parameter has units of L/mol.Van der Waals Constants for Gas MoleculesSubstancea(L2-atm/mol2)b(L/mol)He0.03410.02370Ne0.2110.0171Ar1.340.0322Kr2.320.0398Xe4.190.0510H20.2440.0266N21.390.0391O21.360.0318F21.060.0290Cl26.490.0562H2O5.460.0305NH34.170.0371CH42.250.0428CO23.590.0427CCl420.40.1383This 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?

The table below shows that the van der Waals b parameter has units of L/mol.Van der Waals Constants for Gas MoleculesSubstancea(L2-atm/mol2)b(L/mol)He0.03410.02370Ne0.2110.0171Ar1.340.0322Kr2.320.0398Xe4.190.0510H20.2440.0266N21.390.0391O21.360.0318F21.060.0290Cl26.490.0562H2O5.460.0305NH34.170.0371CH42.250.0428CO23.590.0427CCl420.40.1383This 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.Explain.

Based on the given van der Waals constants, arrange these hypothetical gases in order of decreasing strength of intermolecular forces. Assume that the gases have similar molar masses.Rank from strongest to weakest intermolecular attraction. To rank items as equivalent, overlap them.You may be familiar with the ideal gas equation,PV=nRTwhere n is the number of moles, P is the pressure in atmospheres, V is the volume in liters, and R is equal to 0.08206 L ⋅ atm/(mol ⋅ K).Real gases, especially under extremes of temperature and pressure, deviate from ideal behavior due to intermolecular forces and the volume occupied by the gas molecules themselves. Correction factors can be applied to the ideal gas equation to arrive at the van der Waals equation,P=nRTV-nb-n2aV2where a and b are van der Waals constants for the particular gas. The term nb corrects the volume to account for the size of the molecules and the term n2a/V2 corrects the pressure for intermolecular attraction.van der Waals constants for hypothetical gases

Consider the following gases, all at STP: Ne, SF6, N2, CH4.Which one would have the largest van der Waals b parameter?

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?

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.

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.A) The pressure is higher than the ideal gas because there are strong intermolecular forces and the atoms are large. B) The pressure is higher than the ideal gas because there are weak intermolecular forces and the atoms are small. C) The pressure is higher than the ideal gas because there are strong intermolecular forces and the atoms are small. D) The pressure is higher than the ideal gas because there are weak intermolecular forces and the atoms are large.

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.A) The pressure is lower than the ideal gas because there are stronger intermolecular forces and the atoms are smaller. B) The pressure is lower than the ideal gas because there are weaker intermolecular forces and the atoms are smaller. C) The pressure is lower than the ideal gas because there are stronger intermolecular forces and the atoms are larger. D) The pressure is lower than the ideal gas because there are weaker intermolecular forces and the atoms are larger

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.A) The pressure is lower than the ideal gas because there are stronger intermolecular forces and the atoms are smaller. B) The pressure is lower than the ideal gas because there are weaker intermolecular forces and the atoms are smaller. C) The pressure is lower than the ideal gas because there are stronger intermolecular forces and the atoms are larger. D) The pressure is lower than the ideal gas because there are weaker intermolecular forces and the atoms are larger.

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 b 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

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?

Calculate the pressure (atm) that CCl4 will exert at 43 °C if 1.20 mol occupies 33.5 L, assuming that Part A CCl4 obeys the ideal-gas equation: Part B CCl4 obeys the van der Waals equation. (Values for the van der Waals constants are a = 20.4, b = 0.1383.)

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

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.

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