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Gravimetric analysis
Gravimetric analysis
Gravimetric analysis
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Gravimetric analysis
Analytical balance
ClassificationGravimetric
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Gravimetric analysis describes a set of methods used in analytical chemistry for the quantitative determination of an analyte (the ion being analyzed) based on its mass. The principle of this type of analysis is that once an ion's mass has been determined as a unique compound, that known measurement can then be used to determine the same analyte's mass in a mixture, as long as the relative quantities of the other constituents are known.[1]

The four main types of this method of analysis are precipitation, volatilization, electro-analytical and miscellaneous physical method.[2] The methods involve changing the phase of the analyte to separate it in its pure form from the original mixture and are quantitative measurements.

Precipitation method

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The precipitation method is the one used for the determination of the amount of calcium in water. Using this method, an excess of oxalic acid, H2C2O4, is added to a measured, known volume of water. By adding a reagent, here ammonium oxalate, the calcium will precipitate as calcium oxalate. The proper reagent, when added to aqueous solution, will produce highly insoluble precipitates from the positive and negative ions that would otherwise be soluble with their counterparts (equation 1).[3]

The reaction is:

Formation of calcium oxalate:

Ca2+(aq) + C2O42- → CaC2O4

The precipitate is collected, dried and ignited to high (red) heat which converts it entirely to calcium oxide.

The reaction is pure calcium oxide formed

CaC2O4 → CaO(s) + CO(g)+ CO2(g)

The pure precipitate is cooled, then measured by weighing, and the difference in weights before and after reveals the mass of analyte lost, in this case calcium oxide.[4][5] That number can then be used to calculate the amount, or the percent concentration, of it in the original mix.[2][4][5]

Volatilization methods

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Volatilization methods can be either direct or indirect. Water eliminated in a quantitative manner from many inorganic substances by ignition is an example of a direct determination. It is collected on a solid desiccant and its mass determined by the gain in mass of the desiccant.

Another direct volatilization method involves carbonates which generally decompose to release carbon dioxide when acids are used. Because carbon dioxide is easily evolved when heat is applied, its mass is directly established by the measured increase in the mass of the absorbent solid used.[6][7]

Determination of the amount of water by measuring the loss in mass of the sample during heating is an example of an indirect method. It is well known that changes in mass occur due to decomposition of many substances when heat is applied, regardless of the presence or absence of water. Because one must make the assumption that water was the only component lost, this method is less satisfactory than direct methods.

This often faulty and misleading assumption has proven to be wrong on more than a few occasions. There are many substances other than water loss that can lead to loss of mass with the addition of heat, as well as a number of other factors that may contribute to it. The widened margin of error created by this all-too-often false assumption is not one to be lightly disregarded as the consequences could be far-reaching.

Nevertheless, the indirect method, although less reliable than direct, is still widely used in commerce. For example, it's used to measure the moisture content of cereals, where a number of imprecise and inaccurate instruments are available for this purpose.

Types of volatilization methods

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In volatilization methods, removal of the analyte involves separation by heating or chemically decomposing a volatile sample at a suitable temperature.[2][8] In other words, thermal or chemical energy is used to precipitate a volatile species.[9] For example, the water content of a compound can be determined by vaporizing the water using thermal energy (heat). Heat can also be used, if oxygen is present, for combustion to isolate the suspect species and obtain the desired results.

The two most common gravimetric methods using volatilization are those for water and carbon dioxide.[2] An example of this method is the isolation of sodium hydrogen bicarbonate (the main ingredient in most antacid tablets) from a mixture of carbonate and bicarbonate.[2] The total amount of this analyte, in whatever form, is obtained by addition of an excess of dilute sulfuric acid to the analyte in solution.

In this reaction, nitrogen gas is introduced through a tube into the flask which contains the solution. As it passes through, it gently bubbles. The gas then exits, first passing a drying agent (here CaSO4, the common desiccant Drierite). It then passes a mixture of the drying agent and sodium hydroxide which lies on asbestos or Ascarite II, a non-fibrous silicate containing sodium hydroxide.[10] The mass of the carbon dioxide is obtained by measuring the increase in mass of this absorbent.[2] This is performed by measuring the difference in weight of the tube in which the ascarite contained before and after the procedure.

The calcium sulfate (CaSO4) in the tube retains carbon dioxide selectively as it's heated, and thereby, removed from the solution. The drying agent absorbs any aerosolized water and/or water vapor (reaction 3.). The mix of the drying agent and NaOH absorbs the CO2 and any water that may have been produced as a result of the absorption of the NaOH (reaction 4.).[11]

The reactions are:

Reaction 3 - absorption of water

NaHCO3(aq) + H2SO4(aq) → CO2(g) + H2O(l) + NaHSO4(aq).[11]

Reaction 4. Absorption of CO2 and residual water

CO2(g) + 2 NaOH(s) → Na2CO3(s) + H2O(l).[11]

Example

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A chunk of ore is to be analyzed for sulfur content. It is treated with concentrated nitric acid and potassium chlorate to convert all of the sulfur to sulfate (SO2−
4). The nitrate and chlorate are removed by treating the solution with concentrated HCl. The sulfate is precipitated with barium (Ba2+) and weighed as BaSO4.

Advantages

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Gravimetric analysis, if methods are followed carefully, provides for exceedingly precise analysis. In fact, gravimetric analysis was used to determine the atomic masses of many elements in the periodic table to six figure accuracy. Gravimetry provides very little room for instrumental error and does not require a series of standards for calculation of an unknown. Also, methods often do not require expensive equipment. Gravimetric analysis, due to its high degree of accuracy, when performed correctly, can also be used to calibrate other instruments in lieu of reference standards. Gravimetric analysis is currently used to allow undergraduate chemistry/Biochemistry students to experience a grad level laboratory and it is a highly effective teaching tool to those who want to attend medical school or any research graduate school.

Disadvantages

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Gravimetric analysis usually only provides for the analysis of a single element, or a limited group of elements, at a time. Comparing modern dynamic flash combustion coupled with gas chromatography with traditional combustion analysis will show that the former is both faster and allows for simultaneous determination of multiple elements while traditional determination allowed only for the determination of carbon and hydrogen. Methods are often convoluted and a slight mis-step in a procedure can often mean disaster for the analysis (colloid formation in precipitation gravimetry, for example). Compare this with hardy methods such as spectrophotometry and one will find that analysis by these methods is much more efficient.

Solubility in the presence of diverse ions

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Diverse ions have a screening effect on dissociated ions which leads to extra dissociation. Solubility will show a clear increase in presence of diverse ions as the solubility product will increase. Look at the following example:

Find the solubility of AgCl (Ksp = 1.0 x 10−10) in 0.1 M NaNO3. The activity coefficients for silver and chloride are 0.75 and 0.76, respectively.

AgCl(s) = Ag+ + Cl−

We can no longer use the thermodynamic equilibrium constant (i.e. in absence of diverse ions) and we have to consider the concentration equilibrium constant or use activities instead of concentration if we use Kth:

Ksp = aAg+ aCl−
Ksp = [Ag+] fAg+ [Cl−] fCl−
1.0 x 10−10 = s x 0.75 x s x 0.76
s = 1.3 x 10−5 M

We have calculated the solubility of AgCl in pure water to be 1.0 x 10−5 M, if we compare this value to that obtained in presence of diverse ions we see % increase in solubility = {(1.3 x 10−5 – 1.0 x 10−5) / 1.0 x 10−5} x 100 = 30% Therefore, once again we have an evidence for an increase in dissociation or a shift of equilibrium to right in presence of diverse ions.

References

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Gravimetric analysis

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Gravimetric analysis is a quantitative technique that determines the amount of an in a sample by measuring the of a pure compound formed from that , typically through , volatilization, or particulate separation methods. This method relies on the principle of conservation, where the measured of the isolated product is stoichiometrically related to the analyte's concentration, providing high precision often on the order of 1–2 parts per thousand. Developed in the by chemists such as , who introduced systematic gravimetric procedures for elements like silica, and Sigismund Marggraf, who quantified silver via chloride , the technique was further refined by through precise balance measurements and by Carl Remigius Fresenius in his 1846 textbook on quantitative analysis. The core principles of gravimetric analysis emphasize the formation of a compound with known composition and minimal to ensure complete recovery and purity, followed by accurate weighing under controlled conditions to avoid errors from impurities, losses, or incomplete reactions. Precipitation , the most common variant, involves adding a to form an insoluble precipitate (e.g., for ions), digesting it to enhance particle size and purity, filtering, washing, drying or igniting to constant mass, and calculating the content using the formula's molecular weights. Other methods include volatilization , where the or its derivative is converted to a gas (e.g., as SiF₄) and the mass loss is measured, and particulate , used for environmental samples like by direct filtration and weighing. Gravimetric analysis offers advantages such as traceability to the SI unit of , from calibration standards in many cases, and applicability to a wide range of analytes at concentrations above 1%, making it a foundational tool in fields like , pharmaceuticals, and . However, it can be labor-intensive and time-consuming due to the need for careful handling to minimize sources of error, such as of impurities or volatilization during ignition, and is less suitable for trace-level or volatile analytes compared to methods. Notable advancements, including Theodore Richards' application of principles that earned him the 1914 , have enhanced its accuracy, while modern uses extend to standard reference materials certified by organizations like NIST.

Overview

Definition and Principles

Gravimetric analysis is a quantitative technique in used to determine the amount of an in a sample by measuring the mass of a pure compound derived from that analyte. This method involves converting the analyte into a stable, isolable form, such as a precipitate or volatile product, whose mass is directly related to the analyte's quantity through stoichiometric relationships. The core principles of gravimetric analysis rely on precise measurements following a complete that quantitatively isolates the as a compound of known composition. It assumes that the reaction goes to completion, producing a pure product free from contaminants, allowing the analyte's to be calculated from the product's using the of the reaction. The basic equation for determining the percentage composition of the analyte is derived from this stoichiometric relationship: % analyte=(mass of analytemass of sample)×100\% \text{ analyte} = \left( \frac{\text{mass of analyte}}{\text{mass of sample}} \right) \times 100 where the mass of the analyte is obtained by multiplying the measured mass of the product by the appropriate gravimetric factor (the mass ratio of analyte to product). This approach ensures high reliability when mass is accurately determined, typically using analytical balances. Gravimetric analysis applies to a wide scope of analytes, including elements, ions, and , in diverse matrices such as ores, alloys, environmental samples, and aqueous solutions. Unlike volumetric methods, which rely on volume measurements of , gravimetric techniques emphasize direct mass quantification for absolute determinations without needing calibration curves. The two primary approaches are , where an insoluble compound forms, and volatilization, where the analyte or its derivative is converted to a gas and measured indirectly through mass loss. Results are typically expressed in percentages, concentrations (e.g., g/L), or absolute masses, achieving high accuracy with relative errors of 0.1% to 0.01% under ideal conditions due to the method's minimal instrumental variability.

Historical Context

Gravimetric analysis emerged as a cornerstone of classical analytical chemistry during the 18th and 19th centuries, building on early quantitative methods for elemental determination. In the late 18th century, Swedish chemist Torbern Bergman developed the first systematic gravimetric procedures, such as for silica determination, while Sigismund Marggraf quantified silver via chloride precipitation, and Antoine Lavoisier refined precise balance measurements. These foundations were further advanced in the early 1800s by Jöns Jacob Berzelius, who applied gravimetric techniques to analyze stoichiometric compounds and establish atomic weights with high accuracy. By focusing on complete reactions involving elements like oxygen, hydrogen, chlorine, bromine, and silver—often scaling weights relative to hydrogen (1) or oxygen (16)—Berzelius advanced the field through rigorous mass measurements of compounds such as water to determine oxygen-to-hydrogen ratios. In the late 19th century, the method evolved with the introduction of more systematic gravimetric procedures, influenced by leading physical chemists including , who in 1894 published foundational work on the scientific principles of that emphasized gravimetric and titrimetric approaches for accurate quantification. These developments facilitated broader adoption in chemical analysis, particularly for major and minor constituents in materials like ores and rocks. By the early , gravimetric methods were integrated into pharmacopeias and official standards, with organizations like the Association of Official Analytical Chemists (AOAC) approving them for pharmaceutical preparations between 1915 and 1950 to ensure reproducible drug assays. The technique's evolution continued into the mid-, transitioning from purely manual processes to enhanced support, such as high-precision balances that improved sensitivity for complex analyses. Gravimetric methods played a pivotal role in solidifying chemical and atomic weight tables; from the mid-19th century through the first half of the 20th century, they dominated quantitative studies by enabling mass ratio determinations in stoichiometric compounds, like silver halides in the "Harvard Method," which contributed to the periodic table's refinement until isotopic effects were understood. Despite the rise of instrumental techniques, gravimetric analysis remains foundational in , valued for its and precision in establishing reference standards. Post-2000 updates, such as ISO 6142-1:2015, have refined gravimetric protocols for preparing calibration gas mixtures and trace-level analyses, ensuring compliance with modern quality requirements for amount-of-substance concentrations in cylinders.

Fundamental Concepts

Stoichiometry and Calculations

In gravimetric analysis, the stoichiometric basis for quantifying the relies on the and the known forming the weighed species, such as a precipitate or volatile product. The mass of the analyte (mAm_A) is derived from the measured mass of the precipitate (mPm_P) using the gravimetric factor (GF), defined as GF = MA×nAMP×nP\frac{M_A \times n_A}{M_P \times n_P}, where MAM_A and MPM_P are the molar masses of the analyte and precipitate, respectively, and nAn_A and nPn_P are their stoichiometric coefficients in the balanced reaction. This factor arises from equating the moles of analyte to the moles of precipitate via the : moles of AA = nA/nPn_A / n_P × moles of PP, so mA=mP×(MA/MP)×(nA/nP)m_A = m_P \times (M_A / M_P) \times (n_A / n_P)./08%3A_Gravimetric_Methods) For application, consider the determination of chloride ion (Cl⁻) by precipitation as silver chloride (AgCl). The reaction is Ag⁺ + Cl⁻ → AgCl(s), with nA=nP=1n_A = n_P = 1, so GF = 35.45 g/mol / 143.32 g/mol ≈ 0.2474. To calculate the mass of Cl⁻ in a sample, first weigh the dried AgCl precipitate, then compute m\ceCl−=m\ceAgCl×0.2474m_{\ce{Cl^-}} = m_{\ce{AgCl}} \times 0.2474. For percentage purity in a 0.5000 g sample yielding 0.4327 g AgCl, the steps are: m\ceCl−=0.4327×(35.45/143.32)=0.1071m_{\ce{Cl^-}} = 0.4327 \times (35.45 / 143.32) = 0.1071 g, then % Cl⁻ = (0.1071 / 0.5000) × 100 = 21.42%. This method assumes complete reaction and pure precipitate, with the GF incorporating atomic masses from standard tables. In older contexts, particularly for redox-based gravimetric methods like those involving electrodeposition, the concept was employed to simplify calculations before precise atomic weights were established. The (EW) of a is EW = M/nM / n, where nn is the n-factor (number of electrons transferred per mole in the reaction). For example, in determining by electrodeposition as Cu metal, n=2n = 2 for Cu²⁺ + 2e⁻ → Cu, so EW = 63.55 / 2 = 31.78 g/equiv. The mass of was then related to the deposited mass using equivalents rather than moles, with gravimetric factors adjusted accordingly: mass Cu = mass deposit × (EW_Cu / EW_deposit). This approach, rooted in 19th-century analytical practices, facilitated computations without full stoichiometric balancing but has largely been supplanted by molar-based methods. Uncertainty in gravimetric calculations propagates primarily from measurements, as the GF is a constant with negligible relative error from atomic es. For a product like mA=mP×m_A = m_P \times GF, the relative standard deviation (RSD) of mAm_A approximates the RSD of mPm_P, since σmAmA≈σmPmP\frac{\sigma_{m_A}}{m_A} \approx \frac{\sigma_{m_P}}{m_P} for by a precise constant (using the propagation rule σy/y=(σx/x)2\sigma_y / y = \sqrt{ (\sigma_x / x)^2 }
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