Ideal Gases Contributions by: John L. Falconer & Will Medlin Department of Chemical and Biological Engineering University of Colorado Boulder, CO 80309-0424 Supported by the National Science Foundation

A rigid tank contains CO2 at 2 atm and 50°C A rigid tank contains CO2 at 2 atm and 50°C. When the tank is heated to 250°C, the pressure increases significantly and the gas density ____________. Gas increases decreases remains the same ANSWER: C. remains the same. The density does not change because the number of moles is fixed and the volume is fixed.

The pressure of an ideal gas in a fixed volume container is doubled without changing the number of moles of the gas. The average velocity of the particles should __________. not change be doubled be halved be quadrupled none of the above ANSWER: E. none of the above. The average velocity increases by the square root of 2.

An ideal gas (water) enters a compressor, and the exiting water is a real fluid. The shaft work will be ____________ that obtained if the exiting water could be considered an ideal gas. higher than lower than the same as ANSWER: B lower than

1 mol CH4 (1 bar, 50°C) is mixed with 1 mol O2 (1 bar, 50°C) to form a mixture at 2 bar and 50°C. Assume ideal gases. The Gibbs free energy change is _____________. positive negative zero Need more information ANSWER: C. zero. There is no enthalpy change when ideal gases are mixed. The entropy does not change because the partial pressures of the gases do not change and the temperature does not change.

Which system has the highest internal energy if one mole of the same ideal gas is in each piston-cylinder? A B A B Both have the same internal energy 2 atm 50°C 10 atm 50°C ANSWER: C. Both have same internal energy. Each system is at the same temperature, and internal energy is only a function of temperature for an ideal gas.

Assume ideal gases and an isothermal system. A constant-volume tank contains CO2 at 2 atm. Nitrogen is injected into the tank. If the CO2 all remains in the tank, its partial pressure ____________. Assume ideal gases and an isothermal system. N2 decreases increases stays the same ANSWER: C. stays the same. Because the system contains ideal gases, the pressure of CO2 (its partial pressure) only depends on the number of moles, temperature, and volume. None of those change, so the partial pressure stays the same. CO2

Assume ideal gases and an isothermal system. A constant-volume tanks contains 4 mol CO2 and 1 mol N2 at a total pressure of 2 atm. The N2 is removed completely through a membrane that allows only N2 to permeate. If all the CO2 remains in the tank, the partial pressure of CO2 ___________. Assume ideal gases and an isothermal system. CO2 + N2 membrane N2 decreases increases stays the same ANSWER: C. stays the same. Because they are ideal gases, the pressure of CO2 (its partial pressure) only depends on the number of moles, temperature, and volume and none of those change.

An ideal gas is at 1 atm in a piston-cylinder An ideal gas is at 1 atm in a piston-cylinder. The piston is weightless and frictionless. When the mass is removed from the piston, the gas temperature ____________. 1 kg Vacuum Gas Piston Weight Stopper increases decreases remains the same ANSWER: C. remains the same. No work is done, so no energy is removed. The internal energy, which is only a function of temperature, does not change.

1 mol CO2 and 2 mol N2 are heated at constant pressure 1 mol CO2 and 2 mol N2 are heated at constant pressure. The partial pressure of the CO2 _________. Assume ideal gases. 1 kg 1 mol CO2 2 mol N2 1 kg increases decreases stays the same ANSWER: C. stays the same. Total pressure stays the same and the mole fraction of CO2 does not change, so the partial pressures do not change. CO2 N2 Start After heating

1 mol CO2 and 2 mol N2 are in a container at 100°C 1 mol CO2 and 2 mol N2 are in a container at 100°C. The container is then placed in an ice bath at constant pressure. The partial pressure of the CO2 _________. Assume ideal gases. 1 kg Gas Piston Weight Start After cooling increases decreases stays the same ANSWER: C. stays the same. The total pressure is the same and the mole fraction of CO2 does not change so the partial pressures do not change.

A fixed volume tank has water in VLE A fixed volume tank has water in VLE. A mole of air was added to the system. All gases are ideal. The amount of liquid water ___________. increases decreases stays the same Vapor Liquid 1 mol air ANSWER: C. stays the same. The air does not change the partial pressure of the water because it is an ideal gas.

A fixed-volume tank contains CO2 and N2, both of which are ideal gases A fixed-volume tank contains CO2 and N2, both of which are ideal gases. One mole of O2, also an ideal gas, is added. The partial pressure of H2 __________. increases decreases stays the same PCO2 = 0.6 atm PN2 = 0.5 atm 1 mol O2 ANSWER: C. stays the same. Because they are all ideal gases, one gas does not affect the other gases.

A gas is heated and expands in a sealed, frictionless, piston-and cylinder arrangement, where the piston mass and the atmospheric pressure above the piston remain constant. The pressure of the gas will _________. 1 kg Gas 1 mol CO2 2 mol N2 1 kg increase   remain the same   decrease   Insufficient information   Gas ANSWER: B. remains the same. Start After heating

D A E B C Which line corresponds to an isotherm? Pressure Volume ANSWER: C

Which is the correct plot of enthalpy vs Which is the correct plot of enthalpy vs. mole fraction of one component for a binary mixture of ideal gases? yi H yi H yi H A B C yi H yi H ANSWER: B. The enthalpy of a mixture of ideal gases is a linear combination of the enthalpy of the individual components. D E

Which is the correct plot of Gibbs free energy vs Which is the correct plot of Gibbs free energy vs. yi for a binary mixture of ideal gases? yi G yi G yi G A B C yi G yi G ANSWER: C. Enthalpy for an ideal gas mixture is a linear combination. Entropy for an ideal gas mixture is greater than a linear combination of the pure component entropies. Thus, G= H-TS means that G for mixture is less than the linear combination D E

A membrane divides a rigid, well-insulated 2 m3 tank into equal parts A membrane divides a rigid, well-insulated 2 m3 tank into equal parts. The left side contains an ideal gas (Cp = 30 J/mol K) at 300 K and 10 bar and the right side is a vacuum. If the membrane ruptures, what will be the final temperature of the gas? Gas Vacuum 200 K 300 K 400 K Need more information ANSWER: B. 300 K. No work is done, so no energy is removed from the gas. For an ideal gas, the internal energy is only a function of the temperature. Membrane

A rigid isolated vessel is divided by a barrier into two chambers of equal volume. One side contains an ideal monatomic gas, the other side contains vacuum. If the barrier is removed, the temperature of the gas will __________. double be cut in half not change go to absolute zero Ideal monotomic gas Vacuum ANSWER: C. not change. No work is done, so no energy is removed from the gas. For an ideal gas, the internal energy is only a function of the temperature. Piston Remove Stoppers

A rigid vessel is divided by a barrier into two chambers of equal volume. One side contains a real gas, the other side contains vacuum. If the barrier is removed, the temperature of the gas will _____________. go to absolute zero increase decrease not change Real gas Vacuum ANSWER: C. decrease. Piston Remove Stoppers