If a strong acid or base is dissolved in water, will all of its parts have the concentration?

For example in
Ca(OH)2 = Ca + 2OH
if the concentration of Ca(OH)2 is 8.11x10^-3 M, would the concentrations of Ca and 2OH be the same? or in the case of OH, the concentration has to be multiplied by 2 because of the proportion in the equation?

The latter. Ca is Ca(OH)2 and OH is twice that.

Remember that is true ONLY for strong acids or bases. If weak acid or weak base you must use Ka and Kb.

When a strong acid or base, such as Ca(OH)2, is dissolved in water, it dissociates completely into its constituent ions. In the case of Ca(OH)2, it dissociates into Ca2+ ions and 2 OH- ions.

The concentration of Ca(OH)2 is given as 8.11x10^-3 M. Since the compound dissociates completely, the concentration of both Ca2+ ions and OH- ions will be the same as the concentration of Ca(OH)2.

Therefore, the concentration of Ca2+ ions will also be 8.11x10^-3 M, and the concentration of OH- ions will be 2 times the concentration of Ca(OH)2, which is 2*(8.11x10^-3 M) = 1.622x10^-2 M.

So, to answer your question, the concentrations of Ca and 2OH in the given equation are not the same. The concentration of Ca is equal to the concentration of Ca(OH)2, while the concentration of OH is twice the concentration of Ca(OH)2, as per the stoichiometry of the balanced equation.