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We use ln[A] on the y-axis in order to get a linear graph. If you graph [A] vs t, you get a exponential decay. We use ln[A] to calculate the rate constant, -k, which is the slope on the line.
ln[A] is used in order to yield a graph with a straight line, because otherwise it would yield a graph showing exponential decay. A graph with a straight line can be used to easily find the slope, which is equal to -k, giving us the equilibrium constant.
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