# What is the rate constant for this first-order decomposition at 325°C? If the initial pressure of iodoethane is 894 torr at 245°C, what is the pressure of iodoethane after three half-lives?

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The decomposition of iodoethane in the gas phase proceeds according to the following equation:

#C_2H_5I(g) → C_2H_4(g) + HI(g)#

At 660.K, k = 7.2 x 10–4s–1; at 720.K, k = 1.7 x 10–2s–1.

The decomposition of iodoethane in the gas phase proceeds according to the following equation:

At 660.K, k = 7.2 x 10–4s–1; at 720.K, k = 1.7 x 10–2s–1.

##### 1 Answer

Well, apparently the second part of the question has nothing to do with the first part...

I get

Well, for this I would make an Arrhenius plot.

#ul(k("s"^(-1))" "" "" "T("K"))#

#7.2 xx 10^(-4)" "" "660#

#1.7 xx 10^(-2)" "" "720#

We would plot

where:

#overbrace(ln k)^(y) = overbrace(-E_a/R)^(m) overbrace(1/T)^(x) + overbrace(ln A)^(b)# and

#E_a# is the activation energy in#"kJ/mol"# ,#R# is the universal gas constant in#"kJ/mol"cdot"K"# , and#T# is temperature in#"K"# .

#"slope" = -"25041 K"^(-1) = -E_a/R#

#"y-int" = 30.704 = ln A#

We would find:

#ul"Activation energy"#

#E_a = -"slope"cdotR#

#= -(-"25041 K"^(-1)) cdot "0.008314472 kJ/mol"cdot"K"#

#=# #"208.20 kJ/mol"#

#ul"Frequency factor"#

#A = e^(30.704) "s"^(-1) = 2.161 xx 10^13 "s"^(-1)#

Therefore, at

- the same frequency factor and activation energy
- that the relationship between
#lnk# and#1/T# remains linear in the expanded temperature range

the **rate constant** at

#color(blue)(k_(598)) = 2.161 xx 10^13 "s"^(-1) cdot e^(-("208.20 kJ/mol")//("0.008314472 J/mol"cdot"K"//"598.15 K"))#

#= color(blue)(1.42 xx 10^(-5) "s"^(-1))#

Of course, we don't need to use this for anything... because we are asked for the partial pressure of iodoethane left at

*We know that three half-lives have passed, and that the half-life is independent of starting concentration, just like radioactive decay.*

Therefore, **3 half-lives**, so that:

#color(blue)(P_(C_2H_5I)) = 1/8("894 torr") = color(blue)("112 torr")#

is the **remaining partial pressure** of iodoethane.