The decomposition of Cl2O7 at 400 K in the gas phase to Cl2 and O2 is a first order reaction. After 55 seconds at 400 K the pressure of CI2O7 falls from 0.062 to 0.044 atm. The rate constant and pressure of CI2O7 after 100 sec of decomposition at this temperature are

Question

The decomposition of Cl2O7 at 400 K in the gas phase to Cl2 and O2 is a first order reaction. After 55 seconds at 400 K the pressure of CI2O7 falls from 0.062 to 0.044 atm. The rate constant and pressure of CI2O7 after 100 sec of decomposition at this temperature are (A) 5.2 × 10-4 sec-1; 0.05 atm (B) 6.2 × 10-3 sec-1; 0.05 atm (C) 5.8 × 10-3 sec-1; 0.05 atm (D) 4.6 × 10-3 sec-1; 0.05 atm

Tardigrade Admin · Accepted Answer

The equation for first order reaction is

K = \frac{2.303}{t} l o g (\frac{a}{a - x})

(i)

Here

a = 0.062, a - x = 0.044

k = \frac{2.303}{55} l o g \frac{0.062}{0.044} = 6.2 \times 1 0^{- 3} se c^{- 1}

(ii)

Here we are to find the value of

a - x

6.2 \times 1 0^{- 3} = \frac{2.303}{100} l o g \frac{0.062}{a - x}

log

\frac{0.062}{a - x} = 2.69 \times 1 0^{- 1}

\frac{0.062}{a - x} = 1.86

a - x = \frac{0.062}{1.80} = 0.033

atm

$5.2 \times 1 0^{- 4} se c^{- 1}; 0.05 a t m$

$6.2 \times 1 0^{- 3} se c^{- 1}; 0.05 a t m$

$5.8 \times 1 0^{- 3} se c^{- 1}; 0.05 a t m$

$4.6 \times 1 0^{- 3} se c^{- 1}; 0.05 a t m$

Q. The decomposition of Cl2​O7​ at 400K in the gas phase to Cl2​ and O2​ is a first order reaction. After 55 seconds at 400K the pressure of CI2​O7​ falls from 0.062 to 0.044atm. The rate constant and pressure of CI2​O7​ after 100 sec of decomposition at this temperature are

5.2×10−4sec−1;0.05atm

6.2×10−3sec−1;0.05atm

5.8×10−3sec−1;0.05atm

4.6×10−3sec−1;0.05atm

$5.2 \times 1 0^{- 4} se c^{- 1}; 0.05 a t m$

$6.2 \times 1 0^{- 3} se c^{- 1}; 0.05 a t m$

$5.8 \times 1 0^{- 3} se c^{- 1}; 0.05 a t m$

$4.6 \times 1 0^{- 3} se c^{- 1}; 0.05 a t m$