Exam 1 Key Equations and Problems

c=q/m(Δt) OR q=mc(changeint)

*note the lowercase c

where:

q=heat

m=mass

t=temp

C=q/(Δt)

*note the uppercase C

where

q=heat

t=temp

1. heat changes measured under constant pressure conditions in a device open to the atmosphere

        ΔH= q_p

2. heat changes measured under constant volume conditions in a sealed container

        ΔE = q_v

*E=internal energy

H = E + p V

(enthalpy = internal energy + (pressure x volume))

(mol/liter)/second = mol l^-1s^-1 = Ms^-1

Rate of reaction = Δ[reactant] / time interval

OR rate = Δ[reactant] / Δt

* note that t in this case stands for time interval, NOT temperature

Include the stoichiometric coefficients of the reactant if the coefficients do not equal unity.

Rate of substance A = -(1/a)(Δ[A]/Δt)

*t= time interval

*note that we need a negative sign when finding the rate of a reactant

Rate of substance C = (1/c)(Δ[C]/Δt)

*t= time interval

*note that we do NOT need a negative sign when finding the rate of a product

rate = k[reactant]ⁿ

*n=determined by experiment

*k=rate constant

rate = k[A]^x[B]^Y

*X and Y are determined through experiment

*k = rate constant

[A]_t = [A]₀ - kt

*[A]_t = concentration of A at time t

*[A]₀ = concentration of A at t=0 (initial concentration of A)

*k = rate constant

*t = time

slope(y) = -k

x = t        <-- x-axis

y= [A]_t      <-- y-axis

b= [A]₀    <--how far you would move up on the y axis

y = ln([A]₀/[A]_t)

m(slope) = k

x = t

y = 1/[A]_t

m(slope) = k

x = t

b = 1/[A]₀

t_1/2 = [A]₀/2k

k = Ae^-Ea/RT

*E_a = Activation Energy

*k = rate constant

*R = gas constant

*T = temp (kelvin)

*A = frequency factor (related to collision frequency)

ln(e) = 1

ln(XY) = ln(X) + ln(Y)

ln(X/Y) = ln(X) - ln(Y)

ln(X^m) = m ln(X)

ln(e^y) = Y ln(e) = Y

lnk = ln(Ae^-Ea/RT)  , which is then written as: lnk = lnA - (E_a/RT)

y = lnk

m = -(E_a/R)

b = lnA

x = T^-1

k_c = Ae ^-Ea,c/RT

k  = Ae ^-Ea/RT

Then re-write it all as k_c/k = e^{(Ea-Ea,c)/(RT)}

reaction quotient = (concentration of products)^{product coeff.}/ (concentration of reactants)^{reactant coeff.}

OR  Q = [products]^{product coeff.}/ [reactants]^{reactant coeff.}

*Q = reaction quotient

equilibrium constant (K)

*equation is the same as the reaction quotient (Q) equation, but Q is replaced with K

Better way to write K:

K = (([C]/M)^c([D]/M)^d) / (([A]/M)^a([B]/M)^b)

*K is dimentionless!

Plug each into the ideal gas law to make:

P_A = [A]RT    and    P_B = [B]RT

Then, plug the results into the expression for K_p

n_A/V_B=[A]    and  n_B/V_B = [B]

Then, re-write as K_p = [B]^b/[A]^A x (RT)^Δn

where Δn = b-a

therefore, K_p = K_C(RT)^Δn

K_c = [CO2]

*Pure solids and liquids do not appear in the final equilibrium constant expression

K_p = p_CO2

ax² + bx + c = 0

OR

x = (-b +- (SQ ROOT OF (b² - 4ac)) / 2a

1. Concentration of molarities

2. Change Line

3. Equilibrium Line (molarity + change line)

* reactants on left, products on right