A student obtained the following data for the gas phase decomposition of hydroge

Question

A student obtained the following data for the gas phase decomposition of hydrogen iodide at 700 K.

HI(g)---->½ H2(g) + ½ I2(g)

(1) What is the half-life for the reaction starting at t=0 s? _______s

   What is the half-life for the reaction starting at t=1.30×103s? ________s

   Does the half-life increase, decrease or remain constant as the reaction proceeds? _________(increase/decrease/remain constant)

(2) Is the reaction zero, first, or second order? _______(zero/first/second)

(3) Based on these data, what is the rate constant for the reaction?______________ M-1s-1

Explanation / Answer

Half life means the time that is required to decrease the concentration of a reactant by 50%

so at t = 0 the concentration is 0.75M

50% of 0.75 is 0.375 M, the time taken to reach this concentration is 1.3x103 seconds

B) at time 1.3x103 seconds the concentration is 0.375 M , 50% of this is 0.188 M, the time to reach this concentration is 3.88 x 103 seconds, the half life will be

3880 - 1300 = 2580 or 2.58x103 seconds

the half life increased

since the half life from part b has almost double the half life from part a this is a second order reaction

We can apply the formula

1 / A = 1/Ao + kt

where A is the concentration of a given specie at any time

Ao is the initial concentration of a given specie

k is the rate constant

t is time so

at 9060 seconds the concentration of HI is 0.094 M so if we apply the equation this will be

1 / 0.094 = 1 / 0.75 + kt

10.63829 = 1.3333 + k(9060)

10.63829 - 1.3333 = 9.305 = k x 9060

k = 9.305 / 9060 = 0.001027 M-1s-1

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