When R independent reactions are present, the degrees of freedom are F = C − P + 2 − R. True or false?

• A. True
• B. False
• C. F = C − P − R
• D. F = C + P − 2 − R

Answer: (A)

The concept being tested is how the Gibbs phase rule extends to reacting systems: the degrees of freedom tell you how many intensive variables you can vary independently at equilibrium. In a nonreacting system with C components in P phases, you can freely vary temperature and pressure along with the distributions of components, giving F = C − P + 2. When there are R independent chemical reactions, each reaction imposes a constraint that reduces the number of independent variables by one. Put together, the relationship becomes F = C − P + 2 − R. This is why the statement is true. The other forms omit the baseline of two independent variables or rearrange terms in a way that doesn’t reflect the constraints correctly.