Phenol Red : pH Indicator

Glenn Davis

2017-12-03

Phenol red is an indicator commonly used to measure pH in swimming pool test kits, see e.g. [2]. The goal of this colorSpec vignette is to reproduce the colors seen in such a test kit, for typical values of pool pH. Calculations like this one might make a good project for a college freshman chemistry class.

library( colorSpec )


Absorbance Spectra at Different pH Values

The absorbance data for phenol red has already been digitized from [1]:

path = system.file( "extdata/stains/PhenolRed-Fig7.txt", package="colorSpec" )
wave = 350:650
phenolred = readSpectra( path, wavelength=wave )
par( omi=c(0,0,0,0), mai=c(0.6,0.7,0.4,0.2) )
plot( phenolred, main='Absorbance Spectra of Phenol Red at Different pH Values' )

Compare this plot with [1], Fig. 7. Unfortunately, the concentration and optical path length are unknown, but these curves can still be used as ‘relative absorbance’.


Absorbance at Selected Wavelengths

We investigate how absorbance depends on pH for a few selected wavelengths.

wavesel = c( 365, 430, 477, 520, 560, 590 )  # 365 and 477 are 'isosbestic points'
mat = apply( as.matrix(wavesel), 1, function( lambda ) { as.numeric(lambda == wave) } )
colnames( mat ) = sprintf( "%g nm", wavesel )
mono = colorSpec( mat, wavelength=wave, quantity='power' )
RGB = product( mono, BT.709.RGB, wavelength=wave )
colvec = grDevices::rgb( DisplayRGBfromLinearRGB( RGB / max(RGB) ) )

phenolsel = resample( phenolred, wavesel )
pH = as.numeric( sub( '[^0-9]*([0-9]+)$', '\\1', specnames(phenolred) ) )
pHvec = seq(min(pH),max(pH),by=0.05)
phenolsel = interpolate( phenolsel, pH, pHvec )
mat = t( as.matrix( phenolsel ) )
par( omi=c(0,0,0,0), mai=c(0.8,0.9,0.6,0.4) )
plot( range(pH), range(mat), las=1, xlab='pH', ylab='absorbance', type='n' )
grid( lty=1 ) ; abline( h=0 )
matlines( pHvec, mat, lwd=3, col=colvec, lty=1 )
title( "Absorbance of Phenol Red at Selected Wavelengths")
legend( 'topleft', specnames(mono), col=colvec, lty=1, lwd=3, bty='n' )


Note that the curves for the isosbestic points 365 and 477 nm are approximately flat, as expected. But for 430 nm the curve is distinctly non-monotone. This indicates that the solution is not truly a mixture of the acidic and basic species (especially for pH \(\le\) 6), and there may be an undesired side reaction, see [3].


Interpolation from pH=6.8 to pH=8.2

Swimming pools should be slightly basic; a standard test kit covers the range from pH=6.8 to pH=8.2.

pHvec = seq(6.8,8.2,by=0.2)
phenolpool = interpolate( phenolred, pH, pHvec )
par( omi=c(0,0,0,0), mai=c(0.6,0.7,0.4,0.2) )
plot( phenolpool, main="Absorbance Spectra of Phenol Red at Swimming Pool pH Values" )

The rest of this section is best viewed on a display calibrated for sRGB, see [4].

# create an uncalibrated 'material responder'
testkit = product( D65.1nm, 'solution', BT.709.RGB, wave=wave )
# now calibrate, but lower the background a little, to allow more 'headroom' for indicator colors
bglin = 0.96
testkit = calibrate( testkit, response=bglin )
RGB = product( phenolpool, testkit )
class(RGB) = 'model.matrix'
df.RGB = data.frame( RGB=RGB, LEFT=1:nrow(RGB), TOP=0, WIDTH=1, HEIGHT=2 )
par( omi=c(0,0,0,0), mai=c(0.3,0,0.3,0) )
bg = rgb( DisplayRGBfromLinearRGB( t(rep(bglin,3)) ) )
plotPatchesRGB( df.RGB, labels=F, background=bg )
text( (1:nrow(RGB)) + 0.5, 2, sprintf("%.1f",pHvec), adj=c(0.5,1.2), xpd=NA )
title( main='Calculated Colors for pH from 6.8 to 8.2' )

The background graylevel bg is slightly less than 255 so that the red channel in the colors is not saturated. If the background were ‘peak white’ (255,255,255), then some of the colors would be outside the sRGB gamut.

In the first figure above, the phenol red concentration and optical path length are unknown. Compared to a real test kit, the calculated colors look a little faded. An absorbance multiplier can easily tweak the unknown concentration, as follows.

tweak = 1.2
phenolpool = multiply( phenolpool, tweak )
RGB = product( phenolpool, testkit )
class(RGB) = 'model.matrix'
df.RGB = data.frame( RGB=RGB, LEFT=1:nrow(RGB), TOP=0, WIDTH=1, HEIGHT=2 )
par( omi=c(0,0,0,0), mai=c(0.3,0,0.3,0) )
plotPatchesRGB( df.RGB, background=bg, labels=F )
text( (1:nrow(RGB)) + 0.5, 2, sprintf("%.1f",pHvec), adj=c(0.5,1.2), xpd=NA )
main = sprintf( 'Calculated Colors for pH from 6.8 to 8.2 (absorbance multiplier=%g)', tweak )
title( main=main )

These colors are a better match to those in the test kit.

References

[1] LUIGI ROVATI, Luca Ferrari, Paola Fabbri and PILATI, Francesco. Plastic Optical Fiber pH Sensor Using a Sol-Gel Sensing Matrix. In: MOH. YASIN Sulaiman W. Harun and Hamzah AROF, eds. Fiber Optic Sensors [online]. B.m.: InTech, 2012. Available at: doi:10.5772/26517

[2] TAYLOR TECHNOLOGIES, Inc. K-1000 sureCHECK Safety Test, Bromine & Chlorine (hi range), OT/pH [online]. 2017. Available at: https://www.taylortechnologies.com/en/product/test-kits/surecheck-safety-test-bromine-chlorine-hi-range-otph--K-1000

[3] WIKIPEDIA. pH indicator — Wikipedia, The Free Encyclopedia [online]. 2017. Available at: https://en.wikipedia.org/w/index.php?title=PH_indicator. [Online; accessed 10-November-2017]

[4] WIKIPEDIA. SRGB — wikipedia, the free encyclopedia [online]. 2017. Available at: https://en.wikipedia.org/w/index.php?title=SRGB. [Online; accessed 13-November-2017]



Session Information

R version 3.4.3 (2017-11-30)
Platform: i386-w64-mingw32/i386 (32-bit)
Running under: Windows 7 (build 7601) Service Pack 1

Matrix products: default

locale:
[1] LC_COLLATE=C                          
[2] LC_CTYPE=English_United States.1252   
[3] LC_MONETARY=English_United States.1252
[4] LC_NUMERIC=C                          
[5] LC_TIME=English_United States.1252    

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] colorSpec_0.6-2

loaded via a namespace (and not attached):
 [1] MASS_7.3-47     compiler_3.4.3  backports_1.1.1 magrittr_1.5   
 [5] rprojroot_1.2   htmltools_0.3.6 tools_3.4.3     yaml_2.1.14    
 [9] Rcpp_0.12.14    stringi_1.1.6   rmarkdown_1.8   knitr_1.17     
[13] stringr_1.2.0   digest_0.6.12   evaluate_0.10.1