The first-order rate constant for the decomposition of N2O5 , 2N2O5(g)4NO2(g)+O2

Question

The first-order rate constant for the decomposition of N2O5 ,

2N2O5(g)4NO2(g)+O2(g)

at 70C is 6.82×103 s1 . Suppose we start with 2.20×102 mol of N2O5(g) in a volume of 1.7 L .

1.) How many moles of N2O5 will remain after 4.0 min ? Express the amount in moles to two significant digits.

2.) How many minutes will it take for the quantity of N2O5 to drop to 1.8×102 mol ? Express your answer using two significant figures.

3.) What is the half-life of N2O5 at 70C ? Express the half-life in seconds to three significant digits.

Explanation / Answer

ln At = lnAo -kt

1]

ln At = -6.82*10^-3 *240 + ln [2.2*10^-2 /1.7]

[At] = 2.52 M

MOles = 2.52*1.7 = 4.28*10^-3

2] ln At = ln Ao - kt

ln [1.8*10^-2 / 2.2*10^-2 ] = -6.83*10^-3 *t

t = 29.42 seconds

t= 0.49 minutes

3] t1/2 = 0.693 / k = 101.613 seconds

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