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The first order rate constant of the gas-phase decomposition of dimethyl ether, (CH3 )2O(g) --> CH4...

The first order rate constant of the gas-phase decomposition of dimethyl ether, (CH3 )2O(g) --> CH4 (g)+ H2(g)+ CO(g) is 3.2 *10-4 s-1 at 450 C . The reaction is carried out in a constant volume container. Initially, only dimethyl ether is present, and the pressure is 0.350 atm. What is the pressure after 8.0 min? Assume ideal gas behavior.

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Answer #1

Answer – Given, rate constat, k = 3.2*10-4 s-1 , Pi = 0.350 atm, time, t = 8.0 min

We need to convert the time min to s

We know,

1 min = 60 s

So, 8.0 min = ?

= 480 s

We know the formula for the first order

ln Pt / Pi = - k *t

ln Pt / 0.350 atm = - 3.2*10-4 s-1 * 480 s

                            = - 0.1536

So taking antiln form both side

Pt / 0.350 atm = 0.858

So, Pt = 0.350 atm * 0.858

           = 0.300 atm

the pressure after 8.0 min is 0.300 atm

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