Question #9ef8a
1 Answer
Here;s what I got.
Explanation:
You can't really calculate the value of
You can calculate the value of
So, for the equilibrium reaction
#2"SO"_ (2(g)) + "O"_ (2(g)) rightleftharpoons 2"SO"_ (3(g))#
you have
#K_c = (["SO"_3]^2)/( ["SO"_2]^2 * ["O"_2])#
As you know, the expression of
In your case, you will have
#K_c = ("0.259 M")^2/( ("0.59 M")^2 * "0.05 M")#
#K_c = (0.259^2 color(red)(cancel(color(black)(("mol L"^(-1))^2))))/(0.59^2 color(red)(cancel(color(black)(("mol L"^(-1))^2))) * "0.05 mol L"^(-1))#
#K_c = "3.854 mol"^(-1)"L"#
Now, you should know that
#color(blue)(ul(color(black)(K_p = K_c * (RT)^(Deltan))))#
Here
#R# is the universal gas constant, equal to#0.0821("atm" * "L")/("mol" * "K")# #T# is the absolute temperature at which the reaction takes place#Deltan# is the difference between the total number of moles on the products' side and the total number of moles on the reactants' side
In your case, you have
#"2 moles SO"_2 + "1 mole O"_2 = "3 moles gas"# You have two moles of sulfur dioxide reacting with one mole of oxygen gas on the reactants' side
#"2 moles of SO"_3 = "2 moles of gas"# You have two moles of sulfur trioxide being produced on the products' side
This means that
#Deltan = n_"total products" - n_"total reactants"#
will be equal to
#Deltan = 2 - 3 = -1#
You can now say that
#K_p = K_c * (RT)^(-1)#
If you take
#K_p = "3.854 mol"^(-1)"L" * (0.0821 ("atm" * "L")/("mol" * color(red)(cancel(color(black)("K")))) * Tcolor(white)(.) color(red)(cancel(color(black)("K"))))^(-1)#
#K_p = 3.854 color(red)(cancel(color(black)("mol"^(-1)))) color(red)(cancel(color(black)("L"))) * 1/(0.0821 * T) color(red)(cancel(color(black)("mol")))/("atm" * color(red)(cancel(color(black)("L"))))#
which gets you
#color(darkgreen)(ul(color(black)(K_p = (46.9/T)color(white)(.)"atm"^(-1))))#
All you have to do to get the actual value of
Now, does this result make sense?
Notice that in this case,
#K_p = (("SO"_3)^2)/(("SO"_2)^2 * ("O"_2))#
Keep in mind that the expression for
If you measure the partial pressures of the three gases in atmospheres, you will have -- using only units
#K_p = ( color(red)(cancel(color(black)("atm"^2))))/(color(red)(cancel(color(black)("atm"^2))) * "atm") = "atm"^(-1)#
This means that, at least from a dimensional point of view, the answer makes sense.