Answers for Chemical Kinetics Practice Problems

1. balanced equation: N2 + 3 H2 ý 2 NH3

Rate Law: Rate = k[N2]a[H2]b

Find b:

(0.0084/0.0021) = (0.20/0.10)b

4 = 2b, so b = 2

Find a:

(0.0672/0.0084) = (0.20/0.10)a(0.40/0.20)2

8 = (2a)(4) ; 2 = 2a, so a = 1

Rate Law: Rate = k[N2][H2]2

Find k with units:

0.0021 M/min = k(0.10M)(0.10M)2

k = (0.0021 M/min)/(0.0010 M3)

k = 2.1 1/(M2*min)

 
  1. Use the combined Arrhenius equation:

ln(k2/k1) = (EA/R)(1/T1 - 1/T2)

k1 = 9.3x10-5 1/M•s when T1 = 100°C or 373K

k2 = 1.0x10-3 1/M•s when T2 = 130°C or 403K

ln(1.0x10-3 /9.3x10-5 ) = (EA/8.3145 J/mol*K)(1/373K - 1/403K)
    1. = EA*(2.40x10-5 )

EA = 2.375/(2.40x10-5 ) = 99,000 J/mol, or 99 kJ/mol

 

 
  1. Half-lives are constant for first order reactions.

ln2 = kthalf

thalf = 7.21 hr, so k = ln2/7.21 hr = 0.0961 hr-1

ln(final/initial) = -kt

ln(final/0.100 mg) = -(0.0961 hr-1)(14 hr) = -1.35

(final/0.100 mg) = e^(-1.35) = 0.260

final = (0.260)(0.100 mg) = 0.026 mg astatine remaining

 

 

4. thalf = 143 seconds, so k = ln2/143 s = 0.00485 s-1