The decomposition of nitrogen pentoxide (N2O5) to nitrogen dioxide (NO2) and oxy

Question

The decomposition of nitrogen pentoxide (N2O5) to nitrogen dioxide (NO2) and oxygen (O2) proceeds via first order kinetics at 45C, the rate constant is 4.80X10^-5s^-1. If 25.5g of N2O5 were placed in a 5.00L flask,

a. Calculate the concentration of N2O5 after 8 hours have elapsed

b. Calculate the concentration of NO2 after 8 hours have elapsed if no NO2 was initially in the flask

c. How long would it take fr the N2O5 concentration to drop to .0010M?

d. What is the half-life for the decompostion of N2O5?

Explanation / Answer

first order kinetics,

k = (1/t)ln(a/x)

a = initial concentration of N2O5 = (25.5/108)*(1/5) = 0.04722 M

x = concentration OF n2o5 after t, time = x

(4.8*10^-5) = (1/(8*60*60))ln(0.04722/x)

x = 0.012

b. N2O5 ---> 2NO2 + 1/2O2

CONCENTRATION OF NO2 produced = 2*(0.0472-0.012) = 0.0704 M

c. if x = 0.001 M

(4.8*10^-5) = (1/(t))ln(0.04722/0.001)

t = 80308.7 sec

    = 22.3 hr

d. k = 0.693/t1/2

t1/2 = 0.693/(4.8*10^-5)

   = 4 hr

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