Question

The graph below shows the equilibrium ratio of the number of orthohydrogen molecules to the number of parahydrogen molecules, as a function of the absolute temperature. The spins of the protons are parallel in orthohydrogen and antiparallel in parahydrogen. (a) Exhibit a theoretical expression for this ratio as a function of the temperature. (b) Calculate the value of the ratio for 100 K , corresponding to the point $P$ on the graph. The separation of the protons in the hydrogen molecule is $0.7415 \AA$. FIGURE CAN'T COPY.

   The graph below shows the equilibrium ratio of the number of orthohydrogen molecules to the number of parahydrogen molecules, as a function of the absolute temperature. The spins of the protons are parallel in orthohydrogen and antiparallel in parahydrogen.
(a) Exhibit a theoretical expression for this ratio as a function of the temperature.
(b) Calculate the value of the ratio for 100 K , corresponding to the point $P$ on the graph. The separation of the protons in the hydrogen molecule is $0.7415 \AA$.
FIGURE CAN'T COPY.

Problems and Solutions on Thermodynamics and Statistical Mechanics

U.S.T. of China… 1st Edition

Chapter 2, Problem 41

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Step 1

The orthohydrogen state has three possible orientations of the spins (parallel), while the parahydrogen state has one orientation (antiparallel). The ratio $ R $ of orthohydrogen ($ N_o $) to parahydrogen ($ N_p $) can be expressed as: \[ R = Show more…

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The graph below shows the equilibrium ratio of the number of orthohydrogen molecules to the number of parahydrogen molecules, as a function of the absolute temperature. The spins of the protons are parallel in orthohydrogen and antiparallel in parahydrogen. (a) Exhibit a theoretical expression for this ratio as a function of the temperature. (b) Calculate the value of the ratio for 100 K , corresponding to the point $P$ on the graph. The separation of the protons in the hydrogen molecule is $0.7415 \AA$. FIGURE CAN'T COPY.

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