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This print-out should have 15 questions. Multiple-choice questions may continue on the next column or page - find all choices before answering. An ideal gas is contained in a vessel of fixed volume at a temperature of 300 K and a pres­sure of 1.27 times 105 Pa. If the pressure is increased to 1.68 times 105 Pa, what is the final temperature of the gas? Answer in units of K A sealed glass bottle at. 27 degree C contains air at a pressure of 1.01 times 105 Pa and has a volume of 33.2 cm3. The bottle is tossed into an open fire. When the temperature of the air in the bottle reaches 244 degree C, what is the pressure inside the bottle? Assume the volume of the bottle is constant. Answer in units of Pa A room of volume 78 m3 contains air having an average molar mass of 23.9 g/mol. If the temperature of the room is raised from 17.1 degree C to 34 degree C, what mass of air will leave the room? Assume that the air pressure in the room is maintained at 41.1 kPa. Answer in units of kg Using multiple laser beams, physicists have been able to cool and trap sodium atoms in a small region. In one experiment the temperature of the sodium atoms was reduced to 0.00035 K. The atoms can be trapped for about 1s. The trap has linear dimensions of roughly 3.3 cm. Determine the rms speed of the sodium atoms at this temperature. The universal gas constant is 8-3H51 J/K rnol and the molar mass of sodium is 23 g/mol. Approximately how long would it take an atom to wander out of the trap region it there were no trapping action? Answer in units of s A cylinder contains a mixture of helium and argon gas in equilibrium at a temperature of 240 degree C. Boltzmann's constant is 1.38066 times 10-23 J/K, and Avogadro's number is 6.02 times 1023 mol-1. What is the average kinetic energy of each type of molecule? Answer in units of J What is the rms speed of helium? Answer in units of km/s What is the rms speed of argon? Answer in units of km/s Consider neon, a noble gas whose molecules consist of single atoms of atomic mass 0.02 kg/mol. Avogadro's number is 6.02 times 1023 mol-1, and Boltzmann's constant is 1.38 times 10-23 J/K. What is the average kinetic energy of a neon atom when the gas is at a temperature of 430 K? Answer in units of J What is the root-mean-square speed of a neon atom under such conditions? Answer in units of m/s The internal energy of a monoatomic ideal gas such as neon is simply the total kinetic energy of all its atoms. What is the internal energy of 5 liters of neon at a temperature of 430 K and pressure of 1.07 atm? Answer in units of J

Explanation / Answer

5) The time taken for an electron to wander off = d / vrms

Vrms changes from element to element so does d.

distance / Vrms = 0.033 / 0.616 = 0.0535 seconds = 53.5 milli seconds.

6) the average KE of a gas = 3/2 kT

1.5 * 1.38 * 10 ^-23 *(240 + 273) = 1.0624 * 10^-20 J for one molecule

= 6398.89 J per mole of gas

7) RMS speed of helium is sqrt (3RT / M )

T = 513 K

Vrms = sqrt ( 3 * 8.314 * 513 / 0.004) = 1788.52 m/s or 1.7885 km / s

8) Similarly for argon too we need to know the temperature.

T = 513 K ,

Vrms = sqrt ( 3 * 8.314 * 513 / 0.018)

= 843.11 m/s = 0.8431 km / s

9) Avearge Kinetic energy of neon =

3/2 kT = 1.5 * 1.38 * 10^-23 * 430 = 8.905 *10^-21 J is the KE of atom per molecule

If KE per mole is required, then it is 8.905 * 10^-21 * 6.023*10^23 = 5363.6 J

10) Vrms of neon at T = 430K

Vrms = sqrt ( 3 * 8.314 * 430 / 0.01) = 1035.61 m/ s = 1.0356 km/s

11) First we find out the number of moles of the gas:

n = PV / RT = 1.07 * 5 / (0.0821 * 430) = 0.1515 moles

Now, internal energy = fnRT / 2

f = degrees of freedom = 3 for a monoatomic gas

= 3 * 0.1515 * 8.314 * 430 / 2 = 812.66 J

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