Problem

The decomposition

NH_3

gas on a heated tungsten surface gave the following results :


Initial pressure (mm of Hg)	65	105	$y$	185
Half-life (sec)	290	$x$	670	825

Calculate approximately the values of

x

and

y

. (a)

x = 410 \text{ sec}

y = 115 \text{ mm of Hg}

(b)

x = 467 \text{ sec}

y = 150 \text{ mm of Hg}

(c)

x = 490 \text{ sec}

y = 120 \text{ mm of Hg}

(d)

x = 430 \text{ sec}

y = 105 \text{ mm of Hg}

Intuitive explanation

This problem tests whether you recognize that half-life depends on reaction order. For a first-order reaction, half-life is constant regardless of initial concentration; for a second-order reaction, half-life is inversely proportional to initial pressure ( $t_{1/2} \propto 1/P_0$ ). By checking the relationship between the known pressure–half-life pairs, you can determine the reaction order, then use that relationship to find the missing values.

Intuitive explanation

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