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 the order of reaction from how half-life changes with initial concentration. For zero-order reactions, half-life is proportional to initial pressure ( $t_{1/2} \propto P_0$ ); for first-order, half-life is independent of concentration. Plot the data to see which relationship holds, then use that pattern to find the missing values. The key is realizing that the reaction order determines whether half-life scales with pressure or stays constant.

Intuitive explanation

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