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A reaction is said to be of the third order if the rate of the reaction depends upon three concentration term.

2NO + Cl_2 \longrightarrow 2NOCL \qquad \text{ (Third Order reaction) }

2FeCl_3 + SnCl_2 \longrightarrow 2FeCl_2 + SnCl_4

Rate constant for third order reaction is given by boxed { k = frac { 1 }{ 2t } left[ frac { 2ax - { x }^{ 2 } }{ { { a }^{ 2 }left( a - x right) }^{ 2 } } right] } At half life time { t }_{ sfrac { 1 }{ 2 } } half of reactant is reacted, so x = sfrac { a }{ 2 } lets substitute these values in above equation k = frac { 1 }{ 2{ t }_{ sfrac { 1 }{ 2 } } } left[ frac { 2aleft( sfrac { a }{ 2 } right) - { left( sfrac { a }{ 2 } right) }^{ 2 } }{ { { a }^{ 2 }left( a - left( sfrac { a }{ 2 } right) right) }^{ 2 } } right] { t }_{ sfrac { 1 }{ 2 } } = frac { 1 }{ 2k } left[ frac { { a }^{ 2 } - frac { { a }^{ 2 } }{ 4 } }{ { { a }^{ 2 }left( sfrac { a }{ 2 } right) }^{ 2 } } right] { t }_{ sfrac { 1 }{ 2 } } = frac { 1 }{ 2k } left[ frac { frac { 4{ a }^{ 2 } - { a }^{ 2 } }{ 4 } }{ frac { { a }^{ 4 } }{ 4 } } right] { t }_{ sfrac { 1 }{ 2 } } = frac { 1 }{ 2k } left[ frac { 4{ a }^{ 2 } - { a }^{ 2 } }{ { a }^{ 4 } } right] { t }_{ sfrac { 1 }{ 2 } } = frac { 1 }{ 2k } left[ frac { 3{ a }^{ 2 } }{ { a }^{ 4 } } right] boxed { { t }_{ sfrac { 1 }{ 2 } } = frac { 1 }{ 2k } left[ frac { 3 }{ { a }^{ 2 } } right] } This clearly indicates that boxed { { t }_{ sfrac { 1 }{ 2 } } propto frac { 1 }{ { a }^{ 2 } } }