The decomposition of SO 2 Cl 2 is first order in SO 2 Cl 2 and has a rate consta

Question

The decomposition of SO 2 Cl 2 is first order in SO 2 Cl 2 and has a rate constant of 1.48×104 s 1 at a certain temperature. Part A What is the half-life for this reaction? Answer: 4680 s Part B How long will it take for the concentration of SO 2 Cl 2 to decrease to 25% of its initial concentration? Answer: 9370 s Part C If the initial concentration of SO 2 Cl 2 is 1.00 M , how long will it take for the concentration to decrease to 0.74 M ? Part D If the initial concentration of SO 2 Cl 2 is 0.175 M , what is the concentration of SO 2 Cl 2 after 190 s ? Part E If the initial concentration of SO 2 Cl 2 is 0.175 M , what is the concentration of SO 2 Cl 2 after 500 s ? I only need help with parts c, d, and e.

Explanation / Answer

For a first order reaction we can write -

t1/2 = ln 2 / K

given

K = 1.48 x 10-4

Therefore, t1/2 = ln 2 / 1.48 x 10-4

=> t1/2 = 4683.427 s

Part C:

Apply the formula -

A= Ao e ^( -kt)

0.74 = 1 e^( -kt)

kt = ln 1.25

t = (ln 1.35) / k

t = 2.03 x 10^3 s

so the time taken is 1.5 x 10^3 sec

Part D:

A = Ao e^(-kt)

=> A = 0.175 x e ^ ( - 1.48 x 10-4 x 190 )

=> A = 0.170 M

Therefore, the concentration is 0.170 M

Part E:

A = 0.175 x e^ ( - 1.48 x 10-4 x 500 )

A = 0.162 M

Therefore, the concentration is 0.162 M

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