Gravimetric Yield Calculator
Compute gravimetric yield using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
Formula
Mass(analyte) = Mass(precipitate) x GF, where GF = (a x M_analyte) / (b x M_precipitate)
The gravimetric factor (GF) converts precipitate mass to analyte mass using the ratio of molar masses adjusted for stoichiometric coefficients. a and b are the stoichiometric coefficients of the analyte and precipitate respectively. Percent analyte = (Mass analyte / Sample mass) x 100.
Worked Examples
Example 1: Barium Determination via BaSO4 Precipitation
Problem: A 1.2000 g sample yields 0.5124 g of BaSO4 precipitate after drying. Calculate the mass and percentage of barium in the sample.
Solution: Gravimetric Factor = M(Ba) / M(BaSO4) = 137.33 / 233.39 = 0.5884\nMass of Ba = 0.5124 x 0.5884 = 0.3015 g\nPercent Ba = (0.3015 / 1.2000) x 100 = 25.125%\n\nMoles BaSO4 = 0.5124 / 233.39 = 0.002196 mol\nMoles Ba = 0.002196 mol (1:1 ratio)
Result: Ba mass: 0.3015 g | 25.125% Ba in sample
Example 2: Chloride Determination via AgCl Precipitation
Problem: A 0.8500 g sample produces 0.3742 g of AgCl (M = 143.32 g/mol). Calculate the percent chloride (M = 35.45 g/mol).
Solution: Gravimetric Factor = M(Cl) / M(AgCl) = 35.45 / 143.32 = 0.2474\nMass of Cl = 0.3742 x 0.2474 = 0.09258 g\nPercent Cl = (0.09258 / 0.8500) x 100 = 10.892%\n\nMoles AgCl = 0.3742 / 143.32 = 0.002611 mol\nMoles Cl = 0.002611 mol
Result: Cl mass: 0.09258 g | 10.892% Cl in sample
Frequently Asked Questions
What is gravimetric analysis and how does it determine the amount of a substance?
Gravimetric analysis is one of the most accurate and precise quantitative analytical chemistry techniques, where the amount of an analyte (the substance being measured) is determined by measuring the mass of a solid product. The general procedure involves dissolving the sample, selectively precipitating the analyte as an insoluble compound with known composition, filtering and washing the precipitate, drying or igniting it to a constant mass, and then calculating the amount of analyte using stoichiometric relationships. The beauty of gravimetric analysis lies in its directness: mass can be measured with extremely high precision using analytical balances, often to four or five decimal places, making this method inherently more accurate than many instrumental techniques when performed correctly.
What is the gravimetric factor and how is it calculated?
The gravimetric factor (also called the gravimetric conversion factor) is the ratio that converts the mass of the precipitate to the mass of the analyte. It is calculated as the molar mass of the analyte multiplied by its stoichiometric coefficient, divided by the molar mass of the precipitate multiplied by its stoichiometric coefficient. For example, when determining barium as BaSO4, the gravimetric factor is the molar mass of Ba (137.33 g/mol) divided by the molar mass of BaSO4 (233.39 g/mol), giving 0.5884. This means every gram of BaSO4 precipitate corresponds to 0.5884 grams of barium. The gravimetric factor must always be less than 1 when the precipitate is heavier than the analyte, and greater than 1 when multiple analyte units are present per formula unit of precipitate.
What are the key sources of error in gravimetric analysis?
Several critical sources of error can affect gravimetric results. Coprecipitation occurs when impurities are trapped within or adsorbed onto the precipitate, causing positive errors by increasing the apparent mass. Post-precipitation happens when other substances crystallize onto the precipitate during digestion. Incomplete precipitation leads to negative errors because not all the analyte is captured. Loss of precipitate during filtration and transfer also causes negative errors. Improper drying or ignition temperature can leave volatile impurities or cause decomposition of the precipitate. Hygroscopic precipitates may absorb moisture from the air during weighing. To minimize these errors, analysts use digestion (heating the slurry), careful washing with appropriate solutions, proper ignition temperatures, and cooling in desiccators before weighing.
What are common precipitating agents used in gravimetric analysis?
Different precipitating agents are selected based on the analyte being determined and the desired precipitate properties. Silver nitrate (AgNO3) precipitates chloride as AgCl for halide determination. Barium chloride (BaCl2) precipitates sulfate as BaSO4 for sulfate analysis. Dimethylglyoxime (DMG) selectively precipitates nickel as a bright red chelate complex, making it highly specific. Oxalic acid precipitates calcium as calcium oxalate, which is then ignited to calcium oxide or calcium carbonate. Ammonium hydroxide precipitates metal hydroxides like iron(III) hydroxide and aluminum hydroxide for their determination. 8-Hydroxyquinoline (oxine) is a versatile organic precipitant that forms chelates with many metals. The ideal precipitating agent produces a pure, filterable precipitate with known, stable composition.
How does gravimetric analysis compare to other quantitative analytical methods?
Gravimetric analysis has several distinct advantages and disadvantages compared to other quantitative methods. Its primary advantage is accuracy: when properly performed, gravimetric results are accurate to 0.1 percent or better, making it a reference method against which instrumental techniques are often calibrated. It requires no calibration curves or reference standards, since results are based on fundamental mass measurements and stoichiometry. However, gravimetric analysis is time-consuming, often requiring several hours to complete one determination due to precipitation, digestion, filtration, drying, and ignition steps. It requires relatively large sample sizes (typically 0.1 to 1 gram) compared to instrumental methods that can analyze micrograms. Modern instrumental techniques like ICP-OES and AAS are faster and can analyze multiple elements simultaneously, but they require calibration and may have higher uncertainty.
What is APY vs APR in crypto yield?
APR is the simple annual rate without compounding. APY includes the effect of compounding. A 10% APR compounded daily equals roughly 10.52% APY. Always compare APY to APY for accurate yield comparisons.