# Variables
K = 3.5 * 10 ** - 2 # Rate constant
# Solution
print "First order reaction = 0.693 / K"
t_05 = 0.693 / K
print "Time taken for half the initial concentration to react", t_05, "minutes"
# Variables
t05 = 40 # minutes
# Solution
print "Rate constant = 0.693 / t05"
K = 0.693 / t05
print "Rate constant", "{:.4f}".format(K), "/ min"
from math import log10
# Variables
t0 = 37.0 # cm^3 of KMnO4
t5 = 29.8 # cm^3 of KMnO4
t15 = 19.6 # cm^3 of KMnO4
t25 = 12.3 # cm^3 of KMnO4
t45 = 5.00 # cm^3 of KMnO4
# Solution
K5 = 2.303 / 5 * log10(t0 / t5)
K15 = 2.303 / 15 * log10(t0 / t15)
K25 = 2.303 / 25 * log10(t0 / t25)
K45 = 2.303 / 45 * log10(t0 / t45)
print "At t = 5 min, K =", "{:.3e}".format(K5), "/min"
print "At t = 15 min, K =", "{:.3e}".format(K15), "/min"
print "At t = 25 min, K =", "{:.3e}".format(K25), "/min"
print "At t = 45 min, K =", "{:.3e}".format(K45), "/min"
print "As the different values of K are nearly same, so the reaction",
print "is of first-order"
K = (K45 + K25 + K5 + K15) / 4
print "The average value of K = ", "{:.3e}".format(K), "/min"
# Variables
t = 60 # min
x = "0.5a"
K = 5.2 * 10 ** - 3 # / mol L / min
# Solution
a = 1 / (t * K)
print "Initial concentration", "{:.3f}".format(a), "mol / L"
from math import log10
# Solution
print "99.9 % / 50 % =",
times = round((2.303 * log10(100 / (100 - 99.9))) / (2.303 * log10(100 / (100 - 50))))
print times
from math import log10
# Constants
R = 1.987 # cal / K / mol
# Variables
T1 = 273.0 # K
T2 = 303.0 # K
K1 = 2.45 * 10 ** -5
K2 = 162 * 10 ** -5
# Solution
Ea = log10(K2 / K1) * R * 2.303 / ((T2 - T1) / (T1 * T2))
print "The activation energy of the reaction is", int(Ea), "cal / mol"
# Variables
t05 = 30 # minutes
a = 0.1 # M
# Solution
print "For second order reaction,"
print "t0.5 = 1 / Ka"
K = 1 / (a * t05)
print "The rate constant is", "{:.3f}".format(K), "mol / lit / min"
from math import log
# Variables
T = 500 # C
Pi = 350 # torr
r1 = 1.07 # torr / s
r2 = 0.76 # torr / s
# Solution
print "1.07 = k(0.95a)^n"
print "0.76 = k(0.80a)^n"
n = log(r1 / r2) / log(0.95 / 0.80)
print "Hence, order of reaction is", round(n)
# Solution
print "Applying steady state approximation to the concentration of NOCl2,",
print "we get"
print "d[NOCl2] / dt = 0 = k1 [NO] [Cl2] - k-1 [NOCl2] - k2 [NO] [NOCl2]"
print "[NOCl2] = k1 [NO] [Cl2] / (k-1 + k2 [NO])"
print "Now, the overall rate of reaction,"
print "d[NOCl2] / dt = k2 [NO] [NOCl2]"
print "From the above equations we get,"
print "(k1 k2 / k-1) * [NO]^2 * [Cl2], if k2[NO] << k-1"
print "k [NO]^2[Cl2], where k = k1 * k2 / k-1"
from math import log10
# Constant
R = 1.987 # cal / K / mol
# Variables
K2_K1 = 4 # factor increase
T1 = 27 # C
T2 = 47 # C
# Solution
T1 += 273.0
T2 += 273.0
Ea = log10(4) * 2.303 * R * (T1 * T2 / (T2 - T1))
print "The activation energy for the reaction is", "{:.2e}".format(Ea),
print "cal /mol"
from math import log10
# Variables
a = 1 # mole
x = 3 / 4.0 # reaction completed
# Solution
K = (2.303 / 6) * log10(1 / (1 - x))
print "The rate constant is", "{:.3f}".format(K), "/min"
from math import log10
# Solution
print "Let the initial concentration be 100, when x = 25",
print " t = 30 minutes"
a = 100
x = 25.0
t = 30 # minutes
K = 2.303 / t * log10(a / (a - x))
t05 = 0.683 / K
t = 2.303 / K * log10(a / x)
print "K =", "{:.2e}".format(K), "/ min"
print "T0.5 =", "{:.2f}".format(t05), "min"
print "t =", "{:.1f}".format(t), "min"