Solid-State Synthesis Calculator
Weigh precursors from target mass, ratios, and stoichiometry.
Learn more
What it does
This calculator tells you exactly how much of each precursor to weigh for a solid-state reaction, given the target product mass, the precursor formulas, and their molar ratios. It solves the elemental mass balance so you do not have to balance equations by hand. It is built for ceramic, battery-cathode, and inorganic synthesis labs planning a mixed-powder calcination.
How it works
The tool parses each precursor formula into molar mass and elemental composition, then solves the stoichiometric balance A x = b, where A maps precursors to elements and b is the target product's elemental content per mole. Crucially only the non-volatile elements are balanced: carbon, hydrogen, nitrogen, oxygen, sulfur and the halogens are excluded, because carbonates, oxalates, hydroxides and ammonium salts release CO2, H2O or NH3 during calcination while oxygen is simultaneously taken up from the furnace atmosphere, so those elements are simply not conserved between precursor and product. The solution is scaled by target moles = target mass / product molar mass, and each precursor is reported as a mass and a mass percent of the batch.
Worked example
To make 10 g of LiCoO2 (M = 97.87) from Li2CO3 (M = 73.89) and Co3O4 (M = 240.80), balancing the lithium and cobalt gives 0.5 mol of Li2CO3 and 1/3 mol of Co3O4 per mole of product. 10 g of LiCoO2 is 0.1022 mol, so weigh 0.0511 x 73.89 = 3.78 g of Li2CO3 and 0.0341 x 240.80 = 8.20 g of Co3O4. That is an 11.98 g batch for 10 g of product: the 1.98 g difference leaves the crucible mainly as CO2, partly offset by oxygen absorbed from the air. In practice lithium carbonate is added a few percent in excess to compensate for lithium loss at high temperature.
When to use it
Use this before a calcination to pre-weigh a homogeneous precursor mix, to scale a literature recipe to your batch size, or to check a recipe's total mass. Practical pitfalls: volatile lithium salts are often added 5-10% in excess to offset loss during sintering, carbonates release CO2 so the precursor batch is lighter than the product, and you must list enough precursors to supply every element or the balance has no solution.
Step by step
- 1
Enter precursor formulas
List each starting material's chemical formula (for example Li2CO3 and Co3O4). The calculator reads its molar mass and elemental composition automatically, so you do not need to look them up.
- 2
Set the target mass
Type the amount of final product you want to make, in grams. All precursor masses scale linearly with this value, so scaling a recipe up or down is a single edit.
- 3
Read each precursor mass
The table shows, per precursor, the required moles, the mass to weigh in grams, and its share of the total batch. These are the stoichiometric amounts for 100% yield.
- 4
Check totals and export
Confirm the summed precursor mass and the theoretical product mass, then export the table as CSV for your lab notebook or balance printout.
FAQ
- How does the calculator decide the precursor ratios?
- It builds an element-by-precursor matrix from the formulas you enter and solves the stoichiometric balance so the mix supplies the elemental ratios of the target product. Only non-volatile elements are balanced: C, H, N, O, S and the halogens are skipped because they escape as CO2, H2O, NH3 or SOx during calcination, and oxygen is also absorbed from the furnace atmosphere. Least squares is used when the precursors are not perfectly independent, giving the closest stoichiometric fit. You must supply at least one precursor for every non-volatile element in the product.
- Why add lithium salts in excess?
- Lithium compounds such as Li2CO3 partially volatilize or react with the crucible during high-temperature calcination, so the final product ends up lithium-deficient. Adding 5-10% excess lithium precursor compensates for this loss and improves phase purity. The calculator reports the exact stoichiometric amount; add the excess on top manually.
- Why is the weighed precursor batch heavier than the final product?
- Because carbonates, oxalates and ammonium salts lose CO2, H2O and NH3 on heating. Making 10 g of LiCoO2 needs an 11.98 g batch of Li2CO3 plus Co3O4, and the 1.98 g difference leaves the crucible as gas, partly offset by oxygen taken up from the air. The tool reports the stoichiometric precursor masses, so the batch is normally heavier than the oxide you collect. If a batch comes out lighter than the product, an element in the target is not covered by any precursor - check your formula list.
- How do I account for a precursor that is not 100 percent pure?
- Divide the required mass by the purity expressed as a fraction. If the stoichiometric calculation asks for 4.00 g of a carbonate that is 98 percent pure, weigh 4.00 / 0.98 = 4.08 g. Hygroscopic precursors such as LiOH or NaOH need the same correction for absorbed water, which is why they are often dried and weighed quickly, or standardised by titration before a large batch is made.