It is found that a gas undergoes a first-order decomposition reaction. if the rate constant for this reaction is 8.1 x 10-2 /min, how long will it take for the concentration of the gas to change from an initial concentration of .1m to 1.0 x 10-2 m?

28.43 min

Explanation:

Using integrated rate law for first order kinetics as:

Where,  

is the concentration at time t

is the initial concentration

Given that:

The rate constant, k = min⁻¹

Initial concentration = 0.1 M

Final concentration = M

Time = ?

Applying in the above equation, we get that:-

n2(g) + 3h2-> 2nh3(g)   this is the balanced equation

note the mole ratio between n2, h2 and nh3.   it is 1 : 3 : 2   this will be important.

moles n2 present = 28.0 g n2 x 1 mole n2/28 g = 1 mole n2 present

moles h2 present = 25.0 g h2 x 1 mole h2/2 g = 12.5 moles h2 present

based on mole ratio, n2 is limiting in this situation because there is more than enough h2 but not enough n2.

moles nh3 that can be produced = 1 mole n2 x 2 moles nh3/mole n2 = 2 moles nh3 can be produced

grams of nh3 that can be produced = 2 moles nh3 x 17 g/mole = 34 grams of nh3 can be produced

note:   the key to this problem is recognizing that n2 is limiting, and therefore limits how much nh3 can be produced.

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