Equilibrium Constant Question

[eforlano]

I'm a bit confused on this question :/

Upon dissolving in water, the sugar alpha-d-glucose undergoes conversion into an isomer called beta-d-glucose. This process is called mutarotation and reaches equilibrium when 63.6% of the original alpha-d-glucose has been converted. Calculate the value of the equilibrium constant for this process.

The answer says the value is 1.74... ahhh help please

[Sine]

I'm a bit confused on this question :/

Upon dissolving in water, the sugar alpha-d-glucose undergoes conversion into an isomer called beta-d-glucose. This process is called mutarotation and reaches equilibrium when 63.6% of the original alpha-d-glucose has been converted. Calculate the value of the equilibrium constant for this process.

The answer says the value is 1.74... ahhh help please

I'm just gonna call them alpha and beta for simplicity.

So Initially there is 100% alpha and 0% beta. Then isomerisation occurs converting alpha to beta.

At the end there is unknown alpha (for now) and 63.6% beta, since isomerisation is a 1 to 1 ratio we can say that the amount of beta produced was the same as alpha lost. i.e Change in concentration to alpha was 100-x and increase in beta concentration was 0+x  = 63.6
Therefore x = 63.6%
So then we can say alpha concentration is 100-63.6 = 36.4%

k=[beta]/[alpha] = (63.6)/(36.4) = 1.75

We could have also summarised this all in an ICE table
I(initial), C(change), E(equilibrium)
   alpha     beta
I  100         0
C -x           +x
E  100-x      63.6
Solved for x then calculated K