If 15.0 mL of a 1.5M HCl solution at 22.5 degrees C is mixed with 25.0mL of a 1.5M NaOH solution at 21.5 degrees C that is in a calorimeter, and the final mixed solution temperature ends up at 28.5 degrees C, what is the balanced equation for this reaction?

What kind of a balanced equation are you talking about? You can have the balanced CHEMICAL equation, you can have the balanced MATH equation, or the balanced HEAT equation. I'll assume you want the chemical equation; I also assume that this is the first of several questions.

NaOH + HCl ==> NaCl + H2O

To find the balanced equation for the reaction, we need to consider the reactants and the products involved. In this case, the reactants are the HCl solution and the NaOH solution. When these two solutions are mixed, they will undergo a neutralization reaction.

The neutralization reaction between HCl and NaOH can be represented by the following balanced equation:

HCl + NaOH → NaCl + H2O

In this equation, HCl reacts with NaOH to produce NaCl (sodium chloride) and H2O (water). The reaction results in the formation of a salt (NaCl) and water.

Therefore, the balanced equation for the reaction is:

2HCl + 2NaOH → 2NaCl + 2H2O