ASTM C871-18(2023)
(Test Method)Standard Test Methods for Chemical Analysis of Thermal Insulation Materials for Leachable Chloride, Fluoride, Silicate, and Sodium Ions
Standard Test Methods for Chemical Analysis of Thermal Insulation Materials for Leachable Chloride, Fluoride, Silicate, and Sodium Ions
SIGNIFICANCE AND USE
5.1 Research has demonstrated that in addition to the halide ion chloride; fluoride ions, when deposited and concentrated on the surface of austenitic stainless steel, can contribute to external stress corrosion cracking (ESCC) in the absence of inhibiting ions.5 Two widely used insulation specifications that are specific to ESCC allow the use of the same Test Methods C692 and C871 for evaluation of insulation materials. Both specifications require fluoride ions to be included with chloride ions when evaluating the extractable ions.
5.2 Chlorides (and fluorides) can be constituents of the insulating material or of the environment, or both. Moisture in the insulation or from the environment can cause chlorides (and fluorides) to migrate through the insulation and concentrate at the hot stainless steel surface.
5.3 The presence of sodium and silicate ions in the insulation has been found to inhibit external stress corrosion cracking caused by chloride (and fluoride) ions, whether such ions come from the insulation itself or from external sources. Furthermore, if the ratio of sodium and silicate ions to chloride (and fluoride) ions is in a certain proportion in the insulation, external stress corrosion cracking as a result of the presence of chloride (and fluoride) in the insulation will be prevented or at least mitigated (see also Specification C795).
SCOPE
1.1 These test methods cover laboratory procedures for the determination of water-leachable chloride, fluoride, silicate, and sodium ions in thermal insulation materials in the parts per million range.
1.2 Selection of one of the test methods listed for each of the ionic determinations required shall be made on the basis of laboratory capability and availability of the required equipment and appropriateness to the concentration of the ion and any possible ion interferences in the extraction solution.
1.3 The values stated in inch-pound units are to be regarded as standard. The values given in parentheses are mathematical conversions to SI units that are provided for information only and are not considered standard.
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.
1.5 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
General Information
- Status
- Published
- Publication Date
- 30-Apr-2023
- Technical Committee
- C16 - Thermal Insulation
- Drafting Committee
- C16.31 - Chemical and Physical Properties
Relations
- Effective Date
- 15-Apr-2024
- Effective Date
- 15-Apr-2018
- Effective Date
- 01-Jun-2017
- Effective Date
- 15-Oct-2015
- Effective Date
- 01-Jun-2015
- Effective Date
- 01-May-2013
- Effective Date
- 01-May-2013
- Effective Date
- 01-Apr-2013
- Effective Date
- 15-May-2011
- Effective Date
- 15-May-2011
- Effective Date
- 15-Feb-2011
- Effective Date
- 01-Jan-2010
- Effective Date
- 15-Dec-2008
- Effective Date
- 01-Dec-2008
- Effective Date
- 01-Dec-2008
Overview
ASTM C871-18(2023) is a widely recognized international standard published by ASTM for the chemical analysis of thermal insulation materials, specifically targeting the determination of water-leachable chloride, fluoride, silicate, and sodium ions. These test methods are essential for assessing the chemical composition of insulation in the parts per million (ppm) range, helping to address risks associated with external stress corrosion cracking (ESCC) of austenitic stainless steel. The standard underscores the significance of not only chloride but also fluoride ions in contributing to ESCC. It also recognizes the role of sodium and silicate ions in inhibiting corrosion, making it valuable for quality assurance in thermal insulation used in industrial and construction environments.
Key Topics
- Leachable Ion Determination: The standard specifies laboratory procedures for extracting and measuring chloride, fluoride, silicate, and sodium ions in insulation materials.
- Test Method Selection: The appropriate test method depends on laboratory capability, available equipment, and the concentration and potential interferences for each ion type.
- Test Methods Include:
- Chloride: Amperometric-coulometric titration, specific ion electrode, and ion chromatography.
- Fluoride: Specific ion electrode, SPADNS colorimetric, ion chromatography.
- Silicate: Atomic absorption spectrophotometry, colorimetric (AWWA Methods 4500-Si D/E).
- Sodium: Flame photometric method, atomic absorption spectrophotometry, sodium ion-selective electrode, ion chromatography.
- Sample and Extraction Protocols: Provides detailed guidance on sample preparation, contamination avoidance, and extraction, emphasizing the importance of using clean tools, gloves, and proper drying and blending of insulation samples.
- Calculation and Reporting: Results are calculated and reported in μg/g (ppm) for each ion, with gravimetric conversion accounting for sample and extraction volumes.
Applications
- Corrosion Prevention: Use of ASTM C871 is critical in evaluating insulation materials intended for contact with austenitic stainless steel in high-moisture or high-temperature environments such as refineries, power plants, and chemical processing facilities. Analyzing leachable halides and silicates informs decisions to prevent external stress corrosion cracking.
- Material Specification Compliance: Ensures that insulation materials meet industry and project specifications, particularly where limitations on leachable contaminants are required to protect metallic assets.
- Quality Control and Assurance: Acts as a quality control tool for insulation manufacturers, installers, and inspectors to verify chemical composition before installation or during facility audits.
- Research and Development: Supports R&D activities aiming to improve the formulation of thermal insulation products for enhanced durability and corrosion resistance.
Related Standards
- ASTM C692: Test Method for Evaluating the Influence of Thermal Insulations on External Stress Corrosion Cracking Tendency of Austenitic Stainless Steel.
- ASTM C795: Specification for Thermal Insulation for Use in Contact with Austenitic Stainless Steel, with referenced ratios of sodium and silicate to halides.
- ASTM C168: Terminology relating to thermal insulation.
- AWWA Methods 4500-Si D and 4500-Si E: Standard colorimetric techniques for silica analysis.
Practical Value
- Supports International Standards Compliance: Developed in line with World Trade Organization (WTO) principles, promoting global acceptance.
- Reduces Costly Failures: By identifying harmful leachable ions before use, the risk of premature equipment failure due to corrosion is minimized.
- Optimizes Longevity and Safety: Facilitates the selection and use of insulation materials that contribute to the safe, long-term operation of industrial facilities.
Keywords: ASTM C871, chemical analysis, thermal insulation, leachable chloride, leachable fluoride, leachable silicate, leachable sodium, corrosion prevention, stress corrosion cracking, insulation testing, material compliance.
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ASTM C871-18(2023) - Standard Test Methods for Chemical Analysis of Thermal Insulation Materials for Leachable Chloride, Fluoride, Silicate, and Sodium Ions
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Frequently Asked Questions
ASTM C871-18(2023) is a standard published by ASTM International. Its full title is "Standard Test Methods for Chemical Analysis of Thermal Insulation Materials for Leachable Chloride, Fluoride, Silicate, and Sodium Ions". This standard covers: SIGNIFICANCE AND USE 5.1 Research has demonstrated that in addition to the halide ion chloride; fluoride ions, when deposited and concentrated on the surface of austenitic stainless steel, can contribute to external stress corrosion cracking (ESCC) in the absence of inhibiting ions.5 Two widely used insulation specifications that are specific to ESCC allow the use of the same Test Methods C692 and C871 for evaluation of insulation materials. Both specifications require fluoride ions to be included with chloride ions when evaluating the extractable ions. 5.2 Chlorides (and fluorides) can be constituents of the insulating material or of the environment, or both. Moisture in the insulation or from the environment can cause chlorides (and fluorides) to migrate through the insulation and concentrate at the hot stainless steel surface. 5.3 The presence of sodium and silicate ions in the insulation has been found to inhibit external stress corrosion cracking caused by chloride (and fluoride) ions, whether such ions come from the insulation itself or from external sources. Furthermore, if the ratio of sodium and silicate ions to chloride (and fluoride) ions is in a certain proportion in the insulation, external stress corrosion cracking as a result of the presence of chloride (and fluoride) in the insulation will be prevented or at least mitigated (see also Specification C795). SCOPE 1.1 These test methods cover laboratory procedures for the determination of water-leachable chloride, fluoride, silicate, and sodium ions in thermal insulation materials in the parts per million range. 1.2 Selection of one of the test methods listed for each of the ionic determinations required shall be made on the basis of laboratory capability and availability of the required equipment and appropriateness to the concentration of the ion and any possible ion interferences in the extraction solution. 1.3 The values stated in inch-pound units are to be regarded as standard. The values given in parentheses are mathematical conversions to SI units that are provided for information only and are not considered standard. 1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use. 1.5 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
SIGNIFICANCE AND USE 5.1 Research has demonstrated that in addition to the halide ion chloride; fluoride ions, when deposited and concentrated on the surface of austenitic stainless steel, can contribute to external stress corrosion cracking (ESCC) in the absence of inhibiting ions.5 Two widely used insulation specifications that are specific to ESCC allow the use of the same Test Methods C692 and C871 for evaluation of insulation materials. Both specifications require fluoride ions to be included with chloride ions when evaluating the extractable ions. 5.2 Chlorides (and fluorides) can be constituents of the insulating material or of the environment, or both. Moisture in the insulation or from the environment can cause chlorides (and fluorides) to migrate through the insulation and concentrate at the hot stainless steel surface. 5.3 The presence of sodium and silicate ions in the insulation has been found to inhibit external stress corrosion cracking caused by chloride (and fluoride) ions, whether such ions come from the insulation itself or from external sources. Furthermore, if the ratio of sodium and silicate ions to chloride (and fluoride) ions is in a certain proportion in the insulation, external stress corrosion cracking as a result of the presence of chloride (and fluoride) in the insulation will be prevented or at least mitigated (see also Specification C795). SCOPE 1.1 These test methods cover laboratory procedures for the determination of water-leachable chloride, fluoride, silicate, and sodium ions in thermal insulation materials in the parts per million range. 1.2 Selection of one of the test methods listed for each of the ionic determinations required shall be made on the basis of laboratory capability and availability of the required equipment and appropriateness to the concentration of the ion and any possible ion interferences in the extraction solution. 1.3 The values stated in inch-pound units are to be regarded as standard. The values given in parentheses are mathematical conversions to SI units that are provided for information only and are not considered standard. 1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use. 1.5 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
ASTM C871-18(2023) is classified under the following ICS (International Classification for Standards) categories: 91.100.60 - Thermal and sound insulating materials. The ICS classification helps identify the subject area and facilitates finding related standards.
ASTM C871-18(2023) has the following relationships with other standards: It is inter standard links to ASTM C168-24, ASTM C168-18, ASTM C168-17, ASTM C168-15a, ASTM C168-15, ASTM C692-13, ASTM C795-08(2013), ASTM C168-13, ASTM C871-11, ASTM C871-11e1, ASTM C871-08ae1, ASTM C168-10, ASTM C168-08b, ASTM C871-08ae2, ASTM C871-08a. Understanding these relationships helps ensure you are using the most current and applicable version of the standard.
ASTM C871-18(2023) is available in PDF format for immediate download after purchase. The document can be added to your cart and obtained through the secure checkout process. Digital delivery ensures instant access to the complete standard document.
Standards Content (Sample)
This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: C871 − 18 (Reapproved 2023)
Standard Test Methods for
Chemical Analysis of Thermal Insulation Materials for
Leachable Chloride, Fluoride, Silicate, and Sodium Ions
This standard is issued under the fixed designation C871; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope C795 Specification for Thermal Insulation for Use in Con-
tact with Austenitic Stainless Steel
1.1 These test methods cover laboratory procedures for the
C871 Test Methods for Chemical Analysis of Thermal Insu-
determination of water-leachable chloride, fluoride, silicate,
lation Materials for Leachable Chloride, Fluoride, Silicate,
and sodium ions in thermal insulation materials in the parts per
and Sodium Ions
million range.
D1428 Test Method for Test for Sodium and Potassium In
1.2 Selection of one of the test methods listed for each of the
Water and Water-Formed Deposits by Flame Photometry
ionic determinations required shall be made on the basis of
(Withdrawn 1989)
laboratory capability and availability of the required equipment
2.2 AWWA Standards:
and appropriateness to the concentration of the ion and any 4
4500-Si D Molybdosilicate Method for Silica
possible ion interferences in the extraction solution.
4500-Si E Heteropoly Blue Method for Silica
1.3 The values stated in inch-pound units are to be regarded
3. Terminology
as standard. The values given in parentheses are mathematical
conversions to SI units that are provided for information only
3.1 Definitions—Refer to Terminology C168 for definitions
and are not considered standard.
relating to insulation.
1.4 This standard does not purport to address all of the
4. Summary of Test Methods
safety concerns, if any, associated with its use. It is the
responsibility of the user of this standard to establish appro-
4.1 Insulation specimens are leached for 30 min in boiling
priate safety, health, and environmental practices and deter-
water. Tests to determine quantitatively chloride, fluoride,
mine the applicability of regulatory limitations prior to use.
silicate, and sodium ions are performed on aliquots of the
1.5 This international standard was developed in accor-
filtered leachate solution.
dance with internationally recognized principles on standard-
4.2 Analysis for Chloride:
ization established in the Decision on Principles for the
4.2.1 Amperometric-coulometric titration test method.
Development of International Standards, Guides and Recom-
4.2.2 Titrimetric test method. This method is no longer
mendations issued by the World Trade Organization Technical
recommended as requested by ASTM International due to use
Barriers to Trade (TBT) Committee.
of a specific hazardous substance.
4.2.3 Specific ion electrode test method.
2. Referenced Documents
4.3 Analysis for Fluoride:
2.1 ASTM Standards:
4.3.1 Specific ion electrode test method.
C168 Terminology Relating to Thermal Insulation
4.3.2 SPADNS colorimetric test method.
C692 Test Method for Evaluating the Influence of Thermal
Insulations on External Stress Corrosion Cracking Ten-
4.4 Analysis for Silicate:
dency of Austenitic Stainless Steel
4.4.1 Atomic absorption spectrophotometry test method.
4.4.2 Colorimetric test methods—AWWA Methods 4500-Si
D and 4500-Si E.
These test methods are under the jurisdiction of ASTM Committee C16 on
Thermal Insulation and are the direct responsibility of Subcommittee C16.31 on
4.5 Analysis for Sodium:
Chemical and Physical Properties.
4.5.1 Flame photometric test method
Current edition approved May 1, 2023. Published June 2023. Originally
approved in 1977. Last previous edition approved in 2018 as C871 – 18. DOI:
10.1520/C0871-18R23.
2 3
For referenced ASTM standards, visit the ASTM website, www.astm.org, or The last approved version of this historical standard is referenced on
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM www.astm.org.
Standards volume information, refer to the standard’s Document Summary page on Standard Methods for the Examination of Water and Wastewater, 17th Edition,
the ASTM website. American Public Health Association, Washington, DC, 1989.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
C871 − 18 (2023)
Test Methods D1428. or saran, or materials with metallic chlorides in their formula-
4.5.2 Atomic absorption spectrophotometry test method. tions. Prior to use, rinse gloves twice, drain, and air-dry in a
4.5.3 Sodium Ion-Selective electrode. clean, halide-free environment. Store clean gloves in a closed
container or envelope.
5. Significance and Use
7.2 It is suitable to handle materials with more than 25 ppm
5.1 Research has demonstrated that in addition to the halide
chloride with clean, dry hands with no significant contamina-
ion chloride; fluoride ions, when deposited and concentrated on
tion.
the surface of austenitic stainless steel, can contribute to
external stress corrosion cracking (ESCC) in the absence of 8. Test Specimen
inhibiting ions. Two widely used insulation specifications that
8.1 Apparatus and tools used for special preparation and
are specific to ESCC allow the use of the same Test Methods
leaching shall be clean and free of chlorides, fluorides,
C692 and C871 for evaluation of insulation materials. Both
silicates, sodium, and acidic or alkaline materials that might
specifications require fluoride ions to be included with chloride
affect the chemical test. Distilled water must be used in all tests
ions when evaluating the extractable ions.
unless deionized water has been shown to be adequate.
5.2 Chlorides (and fluorides) can be constituents of the
8.1.1 For molded insulation, use a band saw or equivalent,
insulating material or of the environment, or both. Moisture in
making several cuts through the entire cross section of each
the insulation or from the environment can cause chlorides
piece of insulation to be tested. Each specimen shall be
(and fluorides) to migrate through the insulation and concen-
representative of the entire cross section of the piece, except
trate at the hot stainless steel surface.
that metal screen, or expanded metal used as a supportive
facing shall not be included. It is recommended that thin wafers
5.3 The presence of sodium and silicate ions in the insula-
1 1
of material be cut between ⁄16 in. and ⁄8 in. (1.6 mm and
tion has been found to inhibit external stress corrosion cracking
3.2 mm) thick. Cut enough material for two 20 g samples.
caused by chloride (and fluoride) ions, whether such ions come
8.1.2 Blanket fibrous materials are cut into strips across the
from the insulation itself or from external sources.
entire width of the blanket using clean, dry scissors.
Furthermore, if the ratio of sodium and silicate ions to chloride
8.1.3 Samples containing moisture are placed in a suitable
(and fluoride) ions is in a certain proportion in the insulation,
container, protected from contamination, and oven dried at
external stress corrosion cracking as a result of the presence of
230 °F 6 10 °F (100 °C 6 5 °C) ( or manufacturers recom-
chloride (and fluoride) in the insulation will be prevented or at
mended temperature) to a constant weight (60.1 g) or over-
least mitigated (see also Specification C795).
night.
6. Reagents
9. Extraction Technique
6.1 Purity of Reagents—Reagent grade chemicals shall be
9.1 Apparatus:
used in all tests. Unless otherwise indicated, it is intended that
9.1.1 Electronic Balance, capable of weighing to 2000 g
all reagents shall conform to the specifications of the Commit-
with readability to the nearest 0.1 g.
tee on Analytical Reagents of the American Chemical Society,
9.1.2 Blender, with jar-top thread preferred.
where such specifications are available. Use other grades only
9.1.3 Beaker, 1 L stainless or borosilicate.
if is first ascertained that the reagent is of sufficiently high
9.1.4 Filter, Buchner with suitable filter paper.
purity to permit its use without lessening the accuracy of the
determination.
9.2 Using a closed-top blender, such as a 1 qt Mason jar
with blender blades, blend exactly 20.0 g of sample (or other
6.2 Purity of Water—Distilled or deionized water (DI),
weight if necessary) in approximately 400 mL of DI or distilled
having maximum conductivity of 2.5 μS/cm and containing
water for 30 s. While most materials blend to a homogeneous
less than 0.1 ppm of chloride ions shall be used in all tests.
mixture in 30 s, some very hard materials require 60 s or more.
7. Sampling
9.3 Quantitatively transfer the mixture to a tared 1 L stain-
7.1 With low-chloride insulating materials, wear clean poly- less steel or borosilicate beaker, rinsing with distilled or DI
ethylene gloves while taking and handling the sample to avoid
water.
chloride contamination from perspiration. Do not use gloves
9.4 Bring to boiling and maintain at the boiling point for
made from chloride-containing compounds such as neoprene
30 min 6 5 min.
9.5 Remove from heat, and cool in a cold water bath to
Whorlow, Kenneth M., Woolridge, Edward and Hutto, Francis B., Jr., “Effect
ambient temperature.
of Halogens and Inhibitors on the External Stress Corrosion Cracking of Type 304
9.6 Remove water from the outside of the beaker and place
Austenitic Stainless Steel”; STP 1320 Insulation Materials: Testing and
Applications, Third Volume, Ronald S. Graves and Robert R. Zarr, editors, ASTM
on a balance. Add DI (or distilled) water to bring amount of
West Conshohocken, PA, 1997, page 485.
water up to exactly 500.0 mL (g) (or other weight if necessary).
ACS Reagent Chemicals, Specifications and Procedures for Reagents and
Standard-Grade Reference Materials, American Chemical Society, Washington,
9.7 Stir mixture until it is uniform and filter through filter
DC. For suggestions on the testing of reagents not listed by the American Chemical
paper to get a clear filtrate. If not clear after the first filtration,
Society, see Analar Standards for Laboratory Chemicals, BDH Ltd., Poole, Dorset,
refilter through a finer filter paper. The first small portion of
U.K., and the United States Pharmacopeia and National Formulary, U.S. Pharma-
copeial Convention, Inc. (USPC), Rockville, MD. filtrate is used to rinse the receiving flask and Solution A bottle.
C871 − 18 (2023)
Complete this filtration by putting this filtrate in the bottle tration. This potential is measured against a constant reference
labeled Solution A. Since the relationship between solids and potential with a digital pH/mV meter or specific ion meter.
liquid has been established, it is not necessary to filter all of the Operation and use follows manufacturer’s recommended
extract. DO NOT WASH THE FILTER CAKE! procedures, especially noting any corrections for interferences
to determinations. The chloride-sensitive electrode is not
9.8 Calculate the Gravimetric Conversion Factor (GCF) by
reliable for chloride levels below 2 ppm in Solution A.
dividing the weight of the water by the weight of the sample.
10.1.4 Ion Chromatography—It is suitable to use an ion
In the ideal case, this is 500/20 = 25. If weights are not exactly
chromatograph, following the manufacturers directions and
as prescribed, a correct GCF must be calculated and used.
appropriate techniques for the concentration of the ion in the
9.9 With calcium silicate insulation it has been shown that it
extraction solution.
is not necessary to pulverize the thin chips called for in 8.1.1.
10.2 Fluoride Determination—One of the following test
Equivalent results are obtained, and a lengthy filtration step is
methods shall be used on a fresh aliquot from Solution A:
avoided, by extracting the unpulverized chips.
10.2.1 Specific Ion Electrode Test Method for Fluoride—
The fluoride-sensitive electrode consists of a single-crystal
10. Test Procedures
lanthanum fluoride membrane, and an internal reference,
10.1 Chloride Determination—One of the following test
bonded into an epoxy body. The crystal is an ionic conductor
methods shall be used on a fresh aliquot from Solution A. The
in which fluoride ions are mobile. When the membrane is in
precision of the test equipment is often improved through the
contact with a fluoride solution, an electrode potential develops
use of analytical techniques involving known addition (or
across the membrane. This potential, which depends on the
sample and standard spiking) when the ion concentrations are
level of free fluoride ions in solution, is measured against an
very low. It is recommended for chloride ion concentrations
external constant reference potential with a digital pH/mV
less than 20 ppm.
meter or specific ion meter. Operation and use follows manu-
10.1.1 Amperometric-Coulometric Titration Test Method—
facturer’s recommended procedures, especially noting any
Use an apparatus in which direct current between a pair of
corrections for interferences to determinations.
silver electrodes causes electrochemical oxidation of the anode
10.2.2 SPADNS Colorimetric Test Method—This colorimet-
and produces silver ions at a constant rate. When all of the
ric test method is based on the reaction between fluoride and a
chloride ions have combined with silver ions, the appearance
zirconium-dye lake. The fluoride reacts with the dye lake,
of free silver ions causes an abrupt increase in current between
dissociating a portion of it into a colorless complex anion
a pair of indicator electrodes. Because silver ions are generated
2−
(ZrF ) and the dye. As the amount of fluoride is increased,
at a constant rate, the amount used to precipitate the chloride
the color produced becomes progressively lighter or different
ions is proportional to the elapsed time
...




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