### Find an expression for the fraction of hydrogen

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Suppose you have a box of atomic hydrogen, initially a room temperature and atmospheric pressure. You then raise the pressure keeping the volume fixed.

(a) Find an expression for the fraction of hydrogen that is ionized as a function of temperature. (You'll have to solve a quadratic equation.) Check that your expression has the expected behavior at very low and very high temperatures.

(b) At what temperature is exactly half of the hydrogen ionized?

(c) Would raising the initial pressure cause the temperature you found in part (b) to increase or decrease? Explain.

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