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HARD TBR Q
Started by SonhosDaVida
As far as the MCAT is concerned, when you are dealing with complicated equations to solve for unknown concentrations, you can safely assume x is significantly smaller than the initial concentrations and basically ignore it completely when solving for it. This is important to save time on test day.
For this problem, if you want to be exact and not want to assume x is small, you're stuck with a scary equation of:
(1-2x)^2/((2x)^2*x) = 2.1*10^4 -->
(1-2x)^2/(4x^3) = 2.1*10^4 -->
(1-2x)^2 = 2.1*10^4 * 4x^3
This is not an easy equation to solve by hand but it can be solved by using a software. This is why for MCAT purposes, you can safely reduce 1-2x expression to 1 by assuming that x will be significantly smaller than the initial concentrations at equilibrium. This makes sense because in equilibrium, you'll have a mix of both reactants and products and generally, all the reactants or all products won't be entirely consumed. Not to mention, x can't be larger than 0.5 because the ICE table in the problem would suggest the final amount of product would be negative, which is not possible.
Note that this small x approximation shortcut won't always work but you won't see this on the MCAT.
For this problem, if you want to be exact and not want to assume x is small, you're stuck with a scary equation of:
(1-2x)^2/((2x)^2*x) = 2.1*10^4 -->
(1-2x)^2/(4x^3) = 2.1*10^4 -->
(1-2x)^2 = 2.1*10^4 * 4x^3
This is not an easy equation to solve by hand but it can be solved by using a software. This is why for MCAT purposes, you can safely reduce 1-2x expression to 1 by assuming that x will be significantly smaller than the initial concentrations at equilibrium. This makes sense because in equilibrium, you'll have a mix of both reactants and products and generally, all the reactants or all products won't be entirely consumed. Not to mention, x can't be larger than 0.5 because the ICE table in the problem would suggest the final amount of product would be negative, which is not possible.
Note that this small x approximation shortcut won't always work but you won't see this on the MCAT.
