chem 351 multiple choice test questions/acs concepts

The partial derivative of the internal energy with respect to temperature at a constant volume (∂U/∂T)_V

heat capacity at a constant volume C_v

molar heat capacity at a constant volume (C_v) for water due to translational and rotational motions is

C_v = 3 R

E_trans = 3/2 R

E_{rot-nonlinear} = 3/2 R

molar heat capacity at a constant volume (C_v) of hydrogen gas due to translational and rotational motions is

C_v = 5/2 R

E_trans = 3/2 R

E_rot-linear = 2/2 R = R

molar heat capacity at a constant volume (C_v) for helium gas is

C_v = 3/2 R

what is the correct expression of the partial derivative (∂U/∂V)_T = T(∂p/∂T)_V - P that obeys the van der Waals equation

(∂U/∂V)_T = an² / V²

isothermal compressibility k_t  

k_t = -1/V (∂V/∂P)_T 

for an ideal gas is equal to 

1/P

how many vibrational motions are present for a linear molecule

3N - 5

where N = number of atoms

how many vibrational motions are present for a nonlinear molecule

3N - 6

where N = number of atoms

rotational levels are typically _____ to one another than electronic levels are

closer

which partial derivative is zero for an ideal gas

(∂U/∂V)_T

q = ΔU at constant ___

q = ΔH at constant ___

V , P

from Δ_rG^o = -RT ln (K) what can be said about favoring products/reactants

products are favored if Δ_rG^o < 0 and K > 1

consider reaction A ⇌ B, if the reverse is spontaneous (endergonic) at a constant temperature and pressure, 

μ_B > μ_A and Δ_rG^o > 0 

A and B form an ideal solution when mixed. Vapor pressure of A at 25^o C is 50 torr and of B is 30 torr. In an equilibrium molar mixture (x_A = x_B) what is the vapor pressure of A

25 torr

colligative properties

• vapor pressure depression

• boiling point elevation

• freezing point depression

• osmotic pressure

based on vant hoff equation

d ln (k) / dT = Δ_rH^o / RT²

for an exothermic reaction, if temperature rises, then K will

decrease and the equilibrium will shift away from the products

what is the maximum number of phases that can be in mutual equilibrium in a four-component system?

F = C - P + 2

0 = 4 - P + 2

P = 6

two phases are in equilibrium when

their chemical potentials of each component are equal at a constant temperature and pressure

what pair of substances would most likely mix to form an ideal solution

benzene/toluene

how is the enthalpy of sublimation of a substance related to its enthalpy or vaporization

enthalpy of sublimation is greater than enthalpy of vaporization

joule thomson coefficient

temperature behavior with respect to pressure in a constant enthalpy process, will predict whether a real gas heats or cools on pressure change, can be predicted by the equation of state of the real gas

a and b in van der waals equation

a = attractive forces between molecules

b = volume of gas itself

distance dependance of intermolecular forces

imf exist between real gas particles

low pressure = low attraction

high pressure = high attraction

compressibility factor of a gas (z)

how close a gas behavior is to ideal

z = 1 → ideal

compressibility factor (z) at low pressure

z < 1

reduced parameters in terms of critical parameters

reduced = parameter / critical parameter

ex: T_r = T / T_c

ideal gas law

PV = nRT

critical point

point at the highest temperature end at the liquid/vapor phase equilibrium line in a one component equilibrium diagram, liquid and gas phase become indistinguishable

enthalpy of vaporization at critical point

0

density of gas at critical point

density of gas becomes that of the liquid

pv graph - critical point

derivative is 0

approximate magnitude of molecular size

1 cm³ mol^-1

final pressure of a mixture

P_final = P₁ + P₂ + P₃ + …

internal pressure of ideal gas (partial derivative)

(∂U/∂V)_T = 0

isothermal expansion work 

w = -nRT ln (V_f/V_i)

adiabatic expansion work

w = -P_ex dV

adiabatic

no heat can enter or leave the system

q = 0

U = w

zeroth law of thermodynamics

In closed systems A,B, and C, if A and B are in thermal contact and B and C are in thermal contact, A and C will be in thermal equilibrium with each other

first law of thermodynamics

ΔU = q + w

When energy changes, it is as heat or as work

second law of thermodynamics

In an isolated system, a spontaneous change occurs with an increase in entropy of the system

third law of thermodynamics

Absolute entropy approaches 0 as the absolute temperature approaches 0

Unique property of ideal gases

Internal energy depends only on temperature, not volume or pressure (ideal gases have no volume and have an internal pressure of zero)

Definition of entropy (Boltzman)

S = R ln(ω) 

ω is number of microstates for 1 mol of material

Enthalpy as a state function / Hess law

• Δ_rH^o = ΔH_f^o_products - ΔH_f^o_reactants

• ΔH_f^o_products  and ΔH_f^o_reactants  are both multiplied by molar coefficients

• Reverse the equation = reverse the sign

Spontaneity conditions for thermodynamic properties

(ΔG)_T,P < 0 is spontaneous

Calculation of heat capacity

q = C_p ΔT

(∂G/∂P)_T = 

V

state function

not path dependent

enthalpy definition

H = U + PV

Definition of chemical potential

μ_i = (∂G/∂n_i)_T,P,nk

relationship between number of moles and in the change of enthalpy and internal energy

ΔH = ΔU + Δn_g RT

Efficiency equation

• 𝜂 = |w| / q_1hot

• 𝜂 = 1 - (t_cold - t_hot)

Max non pv work

ΔG

Max pv work

ΔA

Finding entropy as the integral from t1 to t2 on a graph

• X axis = ln (t)

• Y axis = Cp

Application of first law of thermodynamics

|q1 + q2| = |w1 + w2|

What happens to enthalpy of vaporization as you reach critical point

goes to 0, non-linear

clapeyron equation

dP/dT = ΔS/ΔV

dP/dT = ΔH/TΔV

• Increasing pressure increases melting point temperature

Raoult’s law

P_i = x_i P_i^*