An engineer has the job to optimize (make better) a tube of toothpaste. What step by step process would they need to take?

Answer is: the equilibrium  shifts toward the reactants, to the left side of chemical reaction.it is because lead(ii) nitrate dissociates in water: pb(no₃)₂ → pb²⁺(aq) + 2no₃⁻(aq).according to lechatelier's principle, the position of equilibrium moves to counteract thechange (more lead cations, common ion), the position of equilibrium will move so that the concentration ofproducts decrease and concentration of reactants of chemical reaction increase.read more on -

Answer is:     molar solubility of  yttrium fluorid is 4.23·10⁻⁶ m. balanced chemical reaction: yf₃(s)  → y³⁺(aq) + 3f⁻(aq). ksp = 8.62·10⁻²¹. ksp = [y³⁺]  · [f⁻]³.[y³⁺] = [yf₃] = s.[f⁻] = 3[yf₃] = 3s.ksp(yf₃)  = s  · (3s)³.8.62·10⁻²¹ = 27s⁴.s(yf₃)  =  ⁴√(8.62·10⁻²¹  ÷ 27).s(yf₃)  = 0.00000423 m.s(yf₃) = 4.23·10⁻⁶ m.