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Groupwork 12 Chemical Equilibrium - extent of reaction

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    Work in groups on these problems. You should try to answer the questions without referring to your textbook. If you get stuck, try asking another group for help.

    Consider a reaction:

    \(v_AA(g)+v_BB(g)\leftrightharpoons v_YY(g)+v_ZZ(g)\)

    For this reaction we define a quantity, \(\xi\), called the extent of the reaction.

    If we start the reaction with a certain amount of each component, for example, nA0, nB0, nC0, and nD0 then we can express the amount of each component later in time as

    nA = nA0 - nA \(\xi\)

    nY = nY0 +nY \(\xi\)

    nB = nB0 - nB \(\xi\)

    nZ = nZ0 +nZ \(\xi\)

    What are the units of nA0, nB0, nY0, and nZ0?

    What are the units of nA, nB, nY, and nZ?

    What are the units of \(\xi\)?

    Why does \(\xi\) have those units?

    Using a total differential, for example, dnA, we can express the amount that each component in the system changes as it reaches equilibrium. Write down the total differential, dG, as a function of T, P, nA, nB, nY, and nZ. Remember that \((\frac{\partial G}{\partial n_i})_{T,P,n_i\not\equiv n_j}=\mu_i\).

    Using your definition for nA, nB, nY, and nZ as a function of x, what is dnA, dnB, dnY, and dnZ?

    Now substitute this back into your expression for dG. What is dG if T and P are constant?