The Gibbs' phase rule states that the number of degrees of freedom in a system $F = C - P + 2$ where $C$ are the number of components and $P$ are the number of phases. The term $C$ can be expanded to $C = s-r$, where $s$ are the number of species, and $r$ are the number of independent relations.
I'm trying to find number of components for two systems, but the two approaches doesn't add up. Where am I wrong?
A closed, evacuated container with $NH_4Br(s)$ is heated, and the following equilibrium takes place: $NH_4Br(s) ⇌ NH_3(g) + HBr(g)$.
I believe the number of components C to be 1, $NH_4Br(s)$, since this substance alone can produce the gas mixture phase, and the solid phase. ($NH_3(g) + HBr(g)$ can also do this, but C should be the lowest number of components needed..).
Using the species approach, $s = NH_4Br, NH_3, HBr = 3$, and $r = $ 1 equilibrium reaction. Which gives that $C = s-r=3-1=$ 2 which doesn't match what I wrote above. Why?
A saturated aqueous solution of $KCl(aq)$ with $KCl(s)$. There is also water vapor. I also assume this is an evacuated container, but the problem doesn't mention this.
I believe the number of components to be 2, $H_2O$ and $KCl$, since these substances can produce the solid phase $KCl(s)$, the gaseuous phase $H_2O(g)$, and the liquid phase $H_2O(l)+Cl^-(aq)+K^+(aq)$.
Using the species approach, $s = H_2O(aq/g), K^+(aq), Cl^-(aq), KCl(s)$, and $r =$ one phase with ion-balance + one equilibrium between water liquid and gas + one equlilibrium between $KCl(s)$ and the dissolved ions = 3. Which gives that $C = s-r = 4-3 = $ 1, which again doesn't match what I wrote above.