Is it possible to start with 5g of one chemical and 10g of another chemical and make 15g of a third chemical?

Answer : No

Explanation: The chemical compounds are formed from their elements in a fixed ratio of masses, for example, in water (H2O), always Hydrogen and oxygen are combined in 1:8 by mass, i.e. with 1 g Hydrogen the Oxygen is 8 g, with 2 g Hydrogen the oxygen would be 16 g. So, there is a fixed ratio by masses.

If we were to react hydrogen with oxygen then it would again combine in 1:8 always. If we use 1 g Hydrogen with 10 g oxygen, all of the 1 g hydrogen would still react with 8 g oxygen and the third chemical formed water is 1+8 = 9 g and not 1+10 =11 g.

So, its generally not possible.

Also not all chemical reactions proceed to completion, i.e. there are always few reactant molecules left unreacted, for example the burning of candle is a chemical process where some of the lower part of wax is left behind. so, not always all of the reactants get converted to products.

Only if we have a special case where reactants react completely and you chose the masses of reactant exactly in the ratio they combine, then only the third chemica will have mass exactly equal to the sum of masses of all reactants taken at the start, like if we take hydogen 2g and oxygen 16 g then water is 2+16 = 18, because 2 will combine exactly with 16.

Hope the answer helps.