### Exam 1 - Gases

##### What the Student Brings to Exams
• official UT ID card (with your picture and name on it)
• a simple scientific calculator (not a graphing calculator)
• a pencil(s) and eraser
• memorized formulas in your head - not on paper or anything else
• nothing else is allowed
##### What we provide for the Exams
• A printed copy of the exam (every exam has a unique version number on it).
• An answer sheet for the exam. This is a bubblesheet for your answers.
• A separate sheet showing a periodic table of the elements with symbols, atomic number, and atomic weights.
• Also on that separate sheet will be numerous constants, conversion factors, and common data that is needed to solve exam problems.

#### $PV=nRT$

##### Gas Laws "contained" in the IGL:

Boyle's Law:    $$P_1V_1 = P_2V_2$$    (constant n, T)

Charles' Law:    $$\displaystyle{V_1\over T_1} = {V_2\over T_2}$$    (constant n, P)

Avogadro's Law:    $$\displaystyle{V_1\over n_1} = {V_2\over n_2}$$    (constant P, T)

Gay-Lussac's Law:    $$\displaystyle{P_1\over T_1} = {P_2\over T_2}$$    (constant n, V)

Air Up Your Tires Law:    $$\displaystyle{P_1\over n_1} = {P_2\over n_2}$$    (constant V, T)

Difficult to Do This Law:    $$n_1T_1 = n_2T_2$$    (constant P, V)

(note that you will be tested on the actual relationships of the physical properties and not the scientist's names)

and because density (ρ) is m/V and molar mass (M) is m/n, then you also know the molar mass of an ideal gas via:

${M={\rho RT\over P}}$

Dalton's Law of Partial Pressures
$P_{\rm total}=P_{\rm A} + P_{\rm B} + P_{\rm C} + \cdots$

mole fraction of gas A:   $$x_{\rm A}=P_{\rm A}/P_{\rm total}$$

Van der Waal's Equation of State (Gas Model)
$\left(P+a{n^2 \over V^2}\right)(V-nb)=nRT$

The average kinetic energy of an ideal gas
$E_{\rm k} = U = {3\over 2}RT = {1\over 2}mv^2$

Root mean squared velocity of a gas
${v_{\rm rms}=\sqrt{3RT \over M}}$

Comparing rms velocities of two different gases at the same temperature
${{v_1\over v_2}=\sqrt{M_2 \over M_1}}$

##### What we provide on the exam cover page

R = 0.08206 L atm/mol K

R = 62.36 L torr/mol K

R = 0.08314 L bar/mol K

R = 8.314 J/mol K

NA = 6.022 × 1023 mol-1

1 atm = 1.01325 × 105 Pa

1 atm = 760 torr

1 atm = 14.7 psi

1 bar = 105 Pa

1 in = 2.54 cm

1 lb = 453.6 g

1 gal = 3.785 L

$$\rho_{\rm water} = 1.00$$ g/mL

$$\rho_{\rm mercury} = 13.6$$ g/mL