What is correct ratio of coefficients to balance this chemical equation

The key in the balancing of chemical reaction is to make sure that you got the exact chemical formula of the substance that is reacting and the yielded product. After getting the formula, identify first the hardest element/atom to be balanced such as Na, Zn, Cl, etc. Then proceed to the easier ones such as O, H. Make sure to not the atoms present in the molecule of the substance. For example Al(s) + HCl(aq) à AlCl3(aq) + H2(g). the hardest element here is the Cl. Observe that there are 3Cls in the product side so add 3 to the HCl. However, it would not balance the H2 in the product side so you increase the addition to AlCl3, add 2. Now you have 6 atoms of Cl, add this to the reactant side, you get 6HCl. Since you have 6Hs, add 3 to H2 (3 multiplied by 2 gives 6).  Then Al has 2 atoms in the product side, add 2 to the reactant side. The balance chemical reaction is 2Al(s) + 6HCl(aq) à 2AlCl3(aq) + 3H2(g).

the dissolution of polymer can be thermodynamically described in 2 steps.