The gas-phase decomposition of SO_2CI_2 is first-order in SO_2CI_2. SO_2Cl_2(g)

Question

The gas-phase decomposition of SO_2CI_2 is first-order in SO_2CI_2. SO_2Cl_2(g) rightarrow SO_2(g) + Cl_2(g) At 600 K the half-life for this process is 2.3 Times 10^5 s. What is the rate constant at this temperature? At 320 C the rate constant is 2.2 Times 10^-5 s^-1. What is the half-life at this temperature? The first-order rate constant for the decomposition of N_2O_5, N_2O_5 (g) rightarrow 2NO_2 (g) + O_2 (g) at 70 C is 6.82 Times 10^-3 s^-1. Suppose we start with 0.0250 mol of N_2O_5(g) in a volume of 2.0 L. How many moles of N_2O_5 will remain after 2.5 min? How many minutes will it take for the quantity of N_2O_5 to drop to 0.010 mot? What is the half-life of N_2O_5 at 70 C?

Explanation / Answer

7.

SO2Cl2 = SO2 + Cl2

first order

lnA = lnA0 - kt

At T = 600K

HL = 2.3*10^5 s

a)

find rate constant, k

apply formula

lnA = lnA0 - kt

ln(1/2* A0) = ln(A0) - k*(2.3*10^5)

solve for k

k = ln(0.5)/(-(2.3*10^5)) = 0.00000301368 or 3.01*10^-6

b)

at T = 320°C = 593 K

k = 2.2*10^-5

find HL for this; that is, A = 1/2*A0 and A0 = A0

then

ln(1/2*A0) = ln(A0) - k*t

ln(1/2*A0) = ln(A0) - ( 2.2*10^-5 )*t

solve for t

t = ln(0.5)/(-( 2.2*10^-5 )) = 31506.69 s (half life)

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