3.2: Parts Per Hundred vs. Parts Per Million
- Page ID
- 7132
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)It is important to understand the relationship between percentage and parts per million (ppm). Most of the time, chemical concentrations are expressed in percentages (parts per hundred, pph.) However, in chemical dosage related problems, concentrations are expressed in ppm. Therefore, it shouldn’t be too difficult to convert percentage to ppm and ppm to percentage. It is simply a difference of 10,000.
If you divide 1,000,000 or 1 ppm by 100 or 100% you get the following.
1,000,000 ÷ 100 = 10,000
This translates a 1% solution concentration to 10,000 ppm.
1% = 10,000 ppm
In other words, just multiply the percent solution by 10,000 to calculate ppm. See the table below for other examples of percent concentration to ppm equivalents.
|
Percent Concentration |
ppm |
|---|---|
|
1% |
10,000 ppm |
|
2% |
20,000 ppm |
|
3% |
30,000 ppm |
|
10% |
100,000 ppm |
Another concept that needs to be addressed is the difference between ppm, parts per billion (ppb), and parts per trillion (ppt.) As water quality regulations become more stringent and laboratory analysis techniques get better and better, contaminants are being identified at lower and lower levels. Most water quality standards are expressed in ppm or milligrams per liter (mg/L), but many are expressed in ppb or micrograms per liter (ug/L), and a few are expressed in ppt or nanograms per liter (ng/L). A simple exercise can help with understanding the different ways to express the amount of contaminant in water supplies.
1,000,000 – million
1,000,000,000 – billion
1,000,000,000,000 – trillion
1 ppm = 1,000 ppb = 1,000,000 ppt
The expression above says that 1 part of a small number (ppm) equals 1,000 parts of a smaller number (ppb) which equals 1,000,000 parts of an even smaller number (ppt.)
Exercises
Solve the following problems. Think of the “%” symbol as “pph” (parts per hundred)
- A 12.5% chlorine solution has a ppm concentration of?
- What is the percent concentration of a 100 ppm solution?
- A Water Utility uses a 0.8% sodium hypochlorite solution to disinfect a well. What is the ppm concentration of the solution?
- A container of liquid chlorine has a concentration of 1,250 ppm. What is the percent concentration of the solution?
- If a 100-gallon container is ¾ full with a 5.25% solution and is then filled with freshwater, what would the resulting ppm of the water be?
- Complete the following table with the corresponding unit for the various water quality Maximum Contaminant Levels (MCL).
|
Constituent |
ppm |
ppb |
ppt |
|---|---|---|---|
|
Arsenic |
10 |
||
|
Chromium |
0.05 |
||
|
Nitrate (NO3) |
45 |
||
|
Perchlorate |
6,000 |
||
|
Vinyl chloride |
0.5 |