scriptThe code below can be pasted in an R Notebook file.
---
title: "Calculate the EC of a nutrient solution"
output: 
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---
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```{r Clean memory and plots, echo=FALSE, include=FALSE}
# Clean memory and plots
rm(list=ls()) #remove all the data from the memory of R
while (!is.null(dev.list()))  dev.off() # delete all the graphs

if(!require(data.table))  {install.packages("data.table"); require(data.table)}
if(!require(optimx))      {install.packages("optimx"); require(optimx)} 
```
# General information

This script is based on techniques used by:
H. Kalka, “Aqion: Manual (Electrical Conductivity).” https://www.aqion.de/site/130, accessed on 09 April 2020.

Table of diffusion coefficients: http://www.aqion.de/site/194

* Parameters are:  
    + ci=input('Concentration in mmol/L')
    + zi=input('Charge Number of Ions')
    + Ai=input('Molar Limiting Conductivity') written as ?0m,i values are obtained from [http://www.aqion.de/site/194]. However, Ai (?0m,i) values can also be calculated if the diffusion coefficient of the ion is known. 
    + E.g. for Si: H_4SiO_4 = Di 1.10e-9 [m2s-1]: Ai=zi^2 Di (F^2 R T)  
 
* where:

    + zi        charge number of ion i
    + T         in K 	absolute temperature
    + F         = 9.6485·104 Coulomb/mol 	Faraday’s constant
    + R         = 8.31446 J/(K mol) 	gas constant
    + F2/(RT)   = 3.7554·106 s · S mol^-1 	proportionality constant at 25°C
    + Di        in m^2/s 	diffusion coefficient of ion i
    + A0m,i     in S m^2/mol (= 104 S cm^2/mol) molar limiting conductivity of ion i

# Nutrient solution composition:
```{r ,echo=FALSE, include=TRUE}
# Create the ci data.table based on the nutrient solution composition
    # Unit conversion umol to mmol (fixed)
    un = 1000
    
    # Desired nutrient solution dillution / strength
    Dl = 1

#Nutrient solution concentration per ion in mmol/L for macro elements (1 - 9) and in umol/L for micro elements
    
#Hoagland and Arnon 1950

    nut_sol = data.table(
                        N_NO3	= 	14	,
                        N_NH4	=	1	,
                        P_H2PO4	=	1	,
                        K	    =	6	,
                        Ca	    =	4	,
                        Mg   	=	2	,
                        Na	    =	0	,
                        S_SO4	=	2	,
                        Cl	    =	0.02,
                        Fe	    =	40	,
                        Cu	    =	0.32,
                        Zn	    =	0.77,
                        Mn	    =	9.15,
                        B	    =	46.3,
                        Mo	    =	0.11
                        )


# Convert macro elements to mol / L      
nut_sol.macro <- nut_sol[,1:9]*Dl/1000

# Convert micro elements to umol / L
nut_sol.micro <- nut_sol[,10:15]/un/1000

ci <- data.table(nut_sol.macro, nut_sol.micro)

#Show the nutrient solution content iin mmol / L is:
print(paste("Current evaluated nutrient solution in mmol/L"))
print(t(ci*1000))
```                    


```{r ,echo=FALSE, include=FALSE}
# Parameters for zi and Ai
# Create a data.table with the ion charges
zi = data.table(
               N_NO3    = 1,
               N_NH4    = 1,
               P_H2PO4  = 1,
               K        = 1,
               Ca       = 2,
               Mg       = 2,
               Na       = 1,
               S_SO4    = 2,
               Cl       = 1,
               Fe       = 2,
               Cu       = 2,
               Zn       = 2,
               Mn       = 2,
               B        = 3,
               Mo       = 2
            )

# Create a data.table with Molar Limiting Conductivity
Ai = data.table(
               N_NO3    = 71.4,
               N_NH4    = 74.4,
               P_H2PO4  = 31.8,
               K        = 73.6,
               Ca       = 119.1,
               Mg       = 105.1,
               Na       = 50.0 ,
               S_SO4    = 160.7,
               Cl       = 76.20,
               Fe       = 108,
               Cu       = 110.1,
               Zn       = 107.4,
               Mn       = 103.4,
               B        = 100,   #not correct should be entered
               Mo       = 100
            )

```


```{r ,echo=FALSE, include=FALSE}
# A function to calculate the EC
    # ec25 calculates electrical conductivity of solutioin based on aqion method.
    # ci is the molar concentration of ion i (ci)
    # zi is charge number of ion i (zi)
    # Ai is molar limiting conductivity

EC_25 <- function(ci,zi,Ai){
        A = 0.5085          # A is constant for gamma formula
        T = 25              # T is Temperature of solution
        cn_ci = length(ci)  # Number of Measured Ions
        
        I_sub = 0.5*sum(ci*zi^2)
        I     = rep(I_sub, 1, cn_ci)
        
        ifelse(I <= 0.36*zi,
                             a <- 0.6/(zi^(0.5)),
                             a <- (I^(0.5))/zi
               )
        
        g = exp(-(log(10))*A*(zi^2)*(I^(.5)))
        y = Ai*(g^a)*ci
        
        ec=sum(y)
        
        EC =round(ec/(1+0.02*(T-25)), 3)
        
        return(EC)
}
# Calculate the final EC
paste("The final EC is", EC_25(ci,zi,Ai), "dS/m")

```


# Set a specific EC value in dS/m (for the nutrient ratio's in your nutrient solution)
```{r ,echo=FALSE}
EC_set = 0.7
paste("EC_set:",EC_set)
```

# This is how many times you have to dillute the original solution
```{r ,echo=FALSE}
#The intial dillution factor is:
D = 1
min_val <- data.frame(minV = 0)
dil_fac <- function(D, ci, zi, Ai, EC_set, EC_25){

ci_D <- data.table(ci[,1:9]*D,ci[,10:15])

min = abs(EC_set - EC_25(ci_D,zi,Ai))

return(min)
}


     Dil_factor_x <- optimize(dil_fac, c(0,10),  ci = ci, EC_set = EC_set ,EC_25 =EC_25, zi = zi, Ai = Ai)
    print(paste("By multiplying the concentration of each marco element in your start nutrient solution with", Dil_factor_x$minimum, "you will get the requested EC of ", EC_set), quote = FALSE)

```