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The integrated rate equation for a first order reaction, in which the reactant and the products are expressed in terms of concentration, is

Integrated rate equation: k = 2.303/t . log [A]_{0}/[A]

Where k = rate constant

[A]_{0} = Initial concentration

[A] = Concentration at time't'

The rate equation for a first order gaseous phase reaction by applying the integrated rate equation for the reaction can be attained by replacing the "concentration of A_{0}" "in the rate equation

A(g) â†’ B(g) + C(g)

1 mole of A 1 mole of B 1 mole of C

t = 0 P_{o }atm 0 atm 0 atm

At time t P_{o }- Patm _{ }P_{ }atm_{ } P_{ }atm

k = 2.303/t . log P_{0}/P_{A}

P_{A} can be calculated using total pressure of the reaction mixture.

The total pressure of the reaction mixture at constant volume and temperature is equal to the sum of the partial pressures of all the gaseous reactants and products involved in the reaction.

Total pressure (P_{t}) = Partial pressures gaseous reactants (P_{A}) + Partial pressure of gaseous products (P_{B} +P_{C})

Total pressure = PA + PB + PC

P_{t} = P_{0}- P + P + P

P_{t} = P_{0} + P

P = P_{t} - P_{0}

P_{A} = P_{0} - P

PA = P_{0} - (Pt - P_{0})

= 2P_{0} - P_{t}

Therefore rate equation can be written as,

k = 2.303/t . log P_{0}/(2P_{0 }- P_{t})

The integrated rate equation for a first order reaction, in which the reactant and the products are expressed in terms of concentration, is

Integrated rate equation: k = 2.303/t . log [A]_{0}/[A]

Where k = rate constant

[A]_{0} = Initial concentration

[A] = Concentration at time't'

The rate equation for a first order gaseous phase reaction by applying the integrated rate equation for the reaction can be attained by replacing the "concentration of A_{0}" "in the rate equation

A(g) â†’ B(g) + C(g)

1 mole of A 1 mole of B 1 mole of C

t = 0 P_{o }atm 0 atm 0 atm

At time t P_{o }- Patm _{ }P_{ }atm_{ } P_{ }atm

k = 2.303/t . log P_{0}/P_{A}

P_{A} can be calculated using total pressure of the reaction mixture.

The total pressure of the reaction mixture at constant volume and temperature is equal to the sum of the partial pressures of all the gaseous reactants and products involved in the reaction.

Total pressure (P_{t}) = Partial pressures gaseous reactants (P_{A}) + Partial pressure of gaseous products (P_{B} +P_{C})

Total pressure = PA + PB + PC

P_{t} = P_{0}- P + P + P

P_{t} = P_{0} + P

P = P_{t} - P_{0}

P_{A} = P_{0} - P

PA = P_{0} - (Pt - P_{0})

= 2P_{0} - P_{t}

Therefore rate equation can be written as,

k = 2.303/t . log P_{0}/(2P_{0 }- P_{t})