What is the overall order of the following reaction, given the rate law? NO(g) +

Question

What is the overall order of the following reaction, given the rate law? NO(g) + O_3(g) rightarrow NO_2(g) + O_2(g) Rate = k[NO][O_3] A) 1st order B) 2nd order C) 3rd order D) 1 1/2 order Carbon-14 has a half-life of 5720 years and this is a first-order reaction. If a piece of wood has converted 75% of the carbon-14, then how old is it? A) 11440 years B) 2375 years C) 4750 years D) 4290 years The rate constant for the first-order decomposition of N_2O is 3.40 s^-1. What is the half-life of the decomposition? A) 0.491 s B) 0.204 s C) 0.236 s D) 0.294 s

Explanation / Answer

The order of reaction is sum of power of concentration terms in the rate expression. Accordingly for the given reaction

the rate for NO(g)+O3(g)----->NO2(g)+ O2(g) the reaction is -r= K[NO] [O3]

sum of the powers of concentration terms are 1( for NO)+1( for O3)= 2

The order is 2nd order. ( B is correct answer)

2. for a 1st order reaction, half life and rate constant (K) are related as K=0.693/half life =0.693/5720=0.000121/yr

for a 1st order reaction ln(NA/NAO)= -Kt

NA=0.75NAO, NAO= initial activity, NA= activity at time, t

hence ln(0.75)= -0.0000121*t, where t = life of wood , t= 2375 years. ( B is correct)

3.for 1st order reaction, lnCA= lnCAO-Kt

where CAO= initial concentration and CA= Concentration at time t

at half life CA=CAO/2, K = rate constant =3.4/s

hence ln(CAO/2)= lnCA0- 3.4*t

t= half life = 0.693/3.4 = 0.2038 sec(B is correct asnwer)

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