# template for solving equilibrium problems

# 1: provide equilibrium constants for all equilibrium reactions
Kw = 1.00e-14
Ka = 1.75e-5

# 2: provide total concentration for all mass balance equations
C = 0.1

# 3: set up master variable
pH = seq(1, 14, 0.01)

# 4: calculate concentrations for all species in system
H3O = 10^-pH
OH = Kw/H3O
A = H3O - OH
HA = H3O * A/Ka

# 5: define an error function using charge or mass balance
error = abs(C - HA - A)

# 6: find index for the minimum error (error closest to zero)
id = which.min(error)
id

# 7: report out all values
pH[id]
H3O[id]
OH[id]
HA[id]
A[id]
error[id]

# 8: plot error function (if of interest)
plot(pH, log10(error), type = "l", xlab = "pH", ylab = "error", lwd = 2, col = "blue")
abline(v = pH[id], lty = 2, col = "red", lwd = 2)