# Problem: Even when a mechanism is consistent with the rate law, later work may show it to be incorrect. For example, the reaction between hydrogen and iodine has this rate law: rate = k[H2][I2]. The long-accepted mechanism had a single bimolecular step; that is, the overall reaction was thought to be elementary:H2(g) + I2(g) ⟶ 2HI(g)In the 1960s, however, spectroscopic evidence showed the presence of free I atoms during the reaction. Kineticists have since proposed a three-step mechanism:(1) I2(g) ⇌ 2I(g)                            [fast](2) H2(g) + I(g) ⇌ H2I(g)              [fast](3) H2I(g) + I(g) ⟶2HI(g)            [slow]Show that this mechanism is consistent with the rate law.

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###### Problem Details

Even when a mechanism is consistent with the rate law, later work may show it to be incorrect. For example, the reaction between hydrogen and iodine has this rate law: rate = k[H2][I2]. The long-accepted mechanism had a single bimolecular step; that is, the overall reaction was thought to be elementary:

H2(g) + I2(g) ⟶ 2HI(g)

In the 1960s, however, spectroscopic evidence showed the presence of free I atoms during the reaction. Kineticists have since proposed a three-step mechanism:

(1) I2(g) ⇌ 2I(g)                            [fast]
(2) H2(g) + I(g) ⇌ H2I(g)              [fast]
(3) H2I(g) + I(g) ⟶2HI(g)            [slow]

Show that this mechanism is consistent with the rate law.