# What volume flask should be used to get 0.37 moles #I# present for every mole #I_2# at equilibrium?

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For the dissociation of #I_2"(g)"# at 1200°C, #K_c=0.011# . What volume flask should we use if we want 0.37 moles of #I# to be present for every mole of #I_2# present at equilibrium?

#I_2"(g)"\rightleftharpoons2I"(g)"#

My work:

(can't see? it sets equilibrium pressures as stated below:)

#P_I=\frac{0.37*0.0821(1200+273)}{V}=\frac{0.37*121}{V}" atm"#

#P_(I_2)=\frac{1.00*0.0821(1200+273)}{V}=\frac{1.00*121}{V}=121/V" atm"#

after using those pressures for #K_p# in the formula #\color(red)(K_c=K_p(RT)^(\Deltan))# , I got #V=0.0307/0.011\approx0.279" L"#

For the dissociation of

My work:

(can't see? it sets equilibrium pressures as stated below:)

after using those pressures for

##### 1 Answer

Are we missing information? We need to be able to figure out the exact number of mols of

We begin with the **ICE table**:

#"I"_2(g) " "rightleftharpoons" " 2"I"(g)#

#"I"" "["I"_2]_i" "" "" "" "0#

#"C"" "-x" "" "" "+2x#

#"E"" "["I"_2]_i-x" "" "2x#

So we write the **mass action expression** to get:

#K_c = 0.011 = (["I"]^2)/(["I"_2])#

#= (2x)^2/(["I"_2]_i - x)#

What we apparently want is

#(2x)/(["I"_2]_i - x) = 0.37 = (["I"])/(["I"_2]) = ("mols I"//cancel"L")/("mols I"_2//cancel"L")#

We now have a system of equations:

#(2x)^2/(["I"_2]_i - x) = 0.011# #" "" "bb((1))#

(Note that#0.011# is in implied units of#"M"# .)

#(2x)/(["I"_2]_i - x) = 0.37# #" "" "bb((2))#

(Note that#0.37# is unitless.)

By inspection, we have:

#(2x)^2/(["I"_2]_i - x) = 0.011 = 0.37(2x) = 0.74x#

So,

#x = ("0.011 M")/0.74 = ul"0.0149 M"#

As a result, take

#(2 cdot "0.0149 M")/(["I"_2]_i - "0.0149 M") = 0.37#

#2 cdot "0.0149 M" = 0.37(["I"_2]_i - "0.0149 M")#

#"0.0297 M" = 0.37["I"_2]_i - "0.0055 M"#

Therefore, the **initial concentration** of

#color(blue)(["I"_2]_i) = ("0.0352 M")/(0.37) = color(blue)("0.0952 M")#

and the fraction of dissociation is

#alpha = x/(["I"_2]_i) = 0.1565#

Now we just need to know the ACTUAL mols of either

The fraction of dissociation