Physics final exam question: mass density of gases

Physics 205A Final Exam, Fall Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Conceptual Question 13.10

[10 points.] Suppose there are two tanks of identical volume, one containing H2 molecules and the other He atoms. The two gases are at the same temperature and pressure. Which has the higher mass per volume density (or are they equal)? Explain your answer using the ideal gas law and properties of ideal gases.

Solution and grading rubric:

• p = 10/10:
  Correct. Identical pressures, volumes, and temperatures means that both tanks hold the same number of particles. Since an He atom has more mass than an H_2 molecule, then the He tank will have the greater mass per volume density.
  
• r = 8/10:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. May only indirectly imply that the number of particles is the same.
  
• t = 6/10:
  Nearly correct, but argument has conceptual errors, or is incomplete. Does not discuss how it is that the tanks have the same number of particles, directly arguing from greater molar mass for He atoms; or says that mass per volume will be the same due to the same number of particles for either tank.
  
• v = 4/10:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Uses equipartition (mode-counting) and/or fact that He and H_2 are monatomic and diatomic, respectively.
  
• x = 2/10:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y = 1/10:
  Irrelevant discussion/effectively blank.
  
• z = 0/10:
  Blank.
  

Grading distribution:
Sections 70854, 70855
p: 9 students
r: 4 students
t: 16 students
v: 7 students
x: 2 students
y: 0 students
z: 1 student

A sample of a "p" response (from student 0013):

A sample of a "t" response (from student 1863) confusing number density with mass density:

A sample of a "v" response (from student 1001) appealing to equipartition:

Physics quiz question: mass, moles and molar mass of He

Physics 205A Quiz 7, Fall Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 13.36

[3.0 points.] How many grams of He atoms are there in 5.0 moles?
(A) 0.80 g.
(B) 1.3 g.
(C) 6.8 g.
(D) 20 g.

Correct answer: (D)

The molar mass of He is 4.0 unified atomic mass units; that is, there are 4.0 g per mole of He atoms. Since there are 5.0 moles of He atoms, then there are 20 g of He atoms. Response (A) is 4.0/5.0; response (B) is 5.0/4.0; response (C) is 4.0*1.7 (in reference to another sample of 1.7 moles of Ne atoms discussed in a later, related question).

Student responses
Sections 70854, 70855
(A) : 6 students
(B) : 5 students
(C) : 2 students
(D) : 23 students

"Difficulty level": 63%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.49

Physics quiz question: moles of dry ice

Physics 5A Quiz 7, Fall Semester 2007
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 13.36

[Version 1]

[3.0 points.] How many moles of CO2 are there in 60.0 g of CO2? The atomic masses of carbon and of oxygen are 12.0 u and 16.0 u, respectively.
(A) 0.467 moles.
(B) 0.733 moles.
(C) 1.36 moles.
(D) 2.14 moles.

Correct answer: (C)

The mass of one mole of CO2 is 12.0 u + 2*(16.0 u) = 44.0 u. Then the number of moles of CO2 is (60.0 u)/(44.0 u) = 1.36 moles. Choice (A) is (12.0 u + 16.0 u)/(60.0 u). Choice (B) is (44.0 u)/(60.0 u). Choice (D) is (60.0 u)/(12.0 u + 16.0 u).

Student responses
Sections 0906, 0907
(A) : 3 students
(B) : 1 student
(C) : 11 students
(D) : 2 students

[Version 2]

[3.0 points.] How many moles of CO2 are there in 15.0 g of CO2? The atomic masses of carbon and of oxygen are 12.0 u and 16.0 u, respectively.
(A) 0.341 moles.
(B) 0.536 moles.
(C) 1.87 moles.
(D) 2.93 moles.

Correct answer: (A)

The mass of one mole of CO2 is 12.0 u + 2*(16.0 u) = 44.0 u. Then the number of moles of CO2 is (15.0 u)/(44.0 u) = 0.341 moles. Choice (B) is (15.0 u)/(12.0 u + 16.0 u). Choice (C) is (12.0 u + 16.0 u)/(15.0 u). Choice (C) is (44.0 u)/(15.0 u).

Student responses
Sections 0906, 0907
(A) : 7 students
(B) : 3 students
(C) : 4 students
(D) : 3 students

Physics clicker question: molecular rms speeds

Physics 5A, Fall Semester 2007
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Conceptual Question 13.1 (extended)

Students were asked the following clicker question (Classroom Performance System, einstruction.com) at the beginning of their learning cycle:

[0.6 participation points.] Which type of air molecule has the fastest rms speed at room temperature?
(A) CO2.
(B) H2O.
(C) N2.
(D) O2.
(E) (I'm lost, and don't know how to answer this.)

Sections 0906, 0907
(A) : 5 students
(B) : 9 students
(C) : 14 students
(D) : 4 students
(E) : 0 students

This question was asked again after displaying the tallied results with the lack of consensus, with the following results. No comments were made by the instructor, in order to see if students were going to be able to discuss and determine the correct answer among themselves.

Sections 0906, 0907
(A) : 5 students
(B) : 14 students
(C) : 9 students
(D) : 2 students
(E) : 0 students

Correct answer: (B)

The rms speed of a particle is given by:

v_rms = sqrt(3*k*T/m),

where k is Boltzmann's constant, T is the absolute temperature (in Kelvin), and m is the particle mass (in kg). In unified atomic mass units, the masses of these molecules are 44 u, 18 u, 28 u, and 32 u, respectively, making H2O (the lightest molecular mass in this list) the molecule with the fastest rms speed.

Physics clicker question: molar mass

Physics 5A, Fall Semester 2007
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Conceptual Question 13.11

Students were asked the following clicker question (Classroom Performance System, einstruction.com) at the beginning of their learning cycle:

[0.6 participation points.] The mass of a single aluminum atom is 27.0 u. What is the mass of one mole of aluminum atoms?
(A) (27.0/N_A) g = 4.48*10^-23 g.
(B) 27.0 g.
(C) 27.0 kg.
(D) (N_A/27.0) g = 2.23*10^22 g.
(E) (27.0*N_A) g = 1.63*10^25 g.
(F) (I'm lost, and don't know how to answer this.)

Sections 0906, 0907
(A) : 11 students
(B) : 5 students
(C) : 2 students
(D) : 4 students
(E) : 9 students
(F) : 2 students

Correct answer: (B)

The unified atomic mass unit, "u" is defined to be exactly 1/12th the mass of one mole of carbon-12 atoms (as opposed to the defunct "amu" atomic mass unit, which is either defined to be exactly 1/16th the mass of one mole of oxygen-16 atoms, or 1/16th the mass of one mole of all isotopes of oxygen as found in their naturally occurring proportions). Thus the mass of any particle, in unified atomic mass units, is exactly the mass of one mole of these particles.