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For the delta G equation at equilibrium, you take the natural log of K. If K is less than 1 but greater than 0 (so a fraction) then the value of the natural log will be a negative number. That's why it will be negative.
delta G is positive when K is less than 1 because the equation is dG = -RTlnK. When K is less than one, lnK is negative, which cancels out the negative sign and makes delta G positive. Vice versa, when K is greater than 1, lnK is positive, which makes delta G negative.
Delta G is positive when K is less than one because the ln of a fraction is a negative number. Since there is a negative sign in the equation delta G = -RT ln K, the two negatives cancel and the overall value is positive.
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