I put my work below, but here is the question: Consider the system: A (aq) B (aq
ID: 893049 • Letter: I
Question
I put my work below, but here is the question:
Consider the system: A (aq) B (aq)
at 283 K where Goform A = -12.1 kJ/mol and Goform B = -14.1 kJ/mol. Calculate the concentration of B at equilibrium when 2.37 mol of A and 1.71 mol of B are mixed in water to form exactly one liter of solution.
After I got it wrong on my first try, here is the hint I was given:
*****Remember, something is always gaining heat and something is always losing heat. Start by determining what is gaining and losing heat and then set the appropriate q = -q expression. For qrxn, the chemical equation tells us q for one mol of salt. Do we have one mole of salt? Finally, remember that q = m c T.*****
A (aq) B (aq)
Go(reaction) = Goform(product) - Goform(reactant)
Go(reaction) = Goform(B) - Goform(A) = -14.1 - (-12.1) = -2 kJ/mol = -2000 J/mol-K
Go(reaction) = -R*T*ln(K)
R = 8.314 J/mol-K
T = 283 K
K = exp{-8.314*283/1000} = 0.095
K = [B]eq/[A]eq = 0.095
A (aq) B (aq)
Initial: 2.37 1.71
Change: -x x
Equilibrium: (2.37-x) (1.71+x)
[B]eq/[A]eq = 0.095
(1.71+x)/(2.37-x) = 0.095
(1.71+x) = 0.095*(2.37-x)
x + 0.095*x = 0.095*2.37-1.71
x = -1.3557
Equilibrium concentration:
[A]eq = 2.37-x=2.37-(-1.35) = 3.715 M
[B]eq = 1.71+x = 1.71-1.35 = 0.354 M
What did I do wrong? and please refer to the hint because maybe I skipped a step?
Explanation / Answer
Go(reaction) = -R*T*ln(K)
R = 8.314 J/mol-K
T = 283 K
K = exp{-8.314*283/1000} = 0.095
K = [B]eq/[A]eq = 0.095
this part you have done wrong
corrected one is
Go = -R*T*ln(K)
ln(K) = Go / -R*T
k = exp [Go / -R*T]
k = exp [ -2000/ -8.314*283]
k = 2.34
but you have taken 1000 instead 2000 and
you reversed also