# 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?