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For one of the problems in the homework, we are supposed to take the given stoichometic coefficients which are fractions. Numbers raised to a fraction are then represented as roots. However, what confuses me is that in the solution manual it says to combine the sum of all those fractions (1 on numerator and 1/2 + 3/2 on denominator) resulting in a square root over the entire expression. I was under the impression that you could only combine roots like this if the bases were the same, but as far as i am concerned we do not know the values of the products or reactants and i did not want to assume they were all the same value. Did they [censored] these roots because they are all unknown and therefore could technically be expressed as X?
The problem you're referring to comes from Chapter 11. From pages 439 to 440, the reading will tell you the general properties of the Equilibrium constant. The general basis is that because we divided our balanced equation by a coefficient of 1/2, our equilibrium constant will be raised to a power of one half. Further information can be found about reciprocals of equilibrium constants, multiplying/dividing, and adding two equations together on those pages.
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