Question

The specific rate constant for the first-order decomposition of N2O5(g) to NO2(g) and O2(g) is 7.48×10−3s−1 at a given temperature.

1)Find the length of time required for the total pressure in a system containing N2O5 at an initial pressure of 0.110 atm to rise to 0.150 atm .

2)Find the length of time required for the total pressure in a system containing N2O5 at an initial pressure of 0.110 atm to rise to 0.200 atm .

Answer 1

1)

given

N205 ---> 2N02 + 0.5 02 we know that

givien inital pressure of N205 = 0.11

now

total pressure of the systemm = pN205 + pN02 + p02

total pressure of the system = 0.11 - p + 2p + 0.5p

total pressure of the system = 0.11 + 1.5 p

so

0.11 + 1.5p = 0.15

so

p = 0.026666

so

pN025 = 0.11 - p

pN205 = 0.11 - 0.0266

pN205 = 0.0833

now

for a first order reaction

ln (pN205) = ln (pN205)o - kt

so

ln 0.0833 = ln 0.11 - ( 7.48 x 10-3 x t )

t = 37.17 s

so

the time taken is 37.17 s

2)

given

N205 ---> 2N02 + 0.5 02 we know that

givien inital pressure of N205 = 0.11

now

total pressure of the systemm = pN205 + pN02 + p02

total pressure of the system = 0.11 - p + 2p + 0.5p

total pressure of the system = 0.11 + 1.5 p

so

0.11 + 1.5p = 0.2

so

p = 0.06

so

pN025 = 0.11 - 0.06

pN205 = 0.05

now

for a first order reaction

ln (pN205) = ln (pN205)o - kt

so

ln 0.05 = ln 0.11 - ( 7.48 x 10-3 x t )

t = 105.41 s

so

the time taken is 105.41 s