# Groupwork 12 Chemical Equilibrium - extent of reaction

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- 63524

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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, *n _{A0}, n_{B0}, n_{C0}, *and

*n*then we can express the amount of each component later in time as

_{D0}
n_{A0 }- n_{A} \(\xi\) |
n_{Y0 }+n_{Y} \(\xi\) |

n_{B0 }- n_{B} \(\xi\) |
n_{Z0 }+n_{Z} \(\xi\) |

What are the units of *n _{A0}, n_{B0}, n_{Y0}, *and

*n*?

_{Z0}What are the units of *n _{A}*,

*n*,

_{B}*n*, and

_{Y}*n*?

_{Z}What are the units of \(\xi\)?

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

Using a total differential, for example, *dn _{A}*, 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*,

*n*,

_{A}*n*,

_{B}*n*, and

_{Y}*n*. Remember that \((\frac{\partial G}{\partial n_i})_{T,P,n_i\not\equiv n_j}=\mu_i\).

_{Z}Using your definition for *n _{A}*,

*n*,

_{B}*n*, and

_{Y}*n*as a function of x, what is

_{Z}*dn*,

_{A}*dn*,

_{B}*dn*, and

_{Y}*dn*?

_{Z}Now substitute this back into your expression for *dG*. What is *dG* if *T* and *P* are constant?