What the h**l happened here?!? jk but seriously.....?

Question

My AP Chem teacher took a 500 mL solution of 2.0 M hydrochloric acid (HCl) and 500 mL solution of 2.0 M sodium hydroxide and mixed them together. The reaction generated put off heat because the beaker got hot. The mixture was then measured and it was 1016.2 mL. Why did this happen?

I know the Equation is

HCl(aq) + NaOH(aq) => H2O(l) + NaCl(aq)

There was no error in the calculations!

The beaker is supposed to have more volume, but the question is why?

The beaker still contained the extra 16.2 mL after 24 hours and had been cooled down to room temperature.

Answer 1

Water molecules pack closely around ionic solutes such as HCl, NaOH, and HCl.  Thus, the addition of these compounds to water does not make much of a difference in the volume of solution present.  In other words, pretty much the only compound contributing to the volume is the water.

Now look at your equation.  We take 4 ions dissolved in water (H+, Cl-, Na+, OH-), and make two ions and one water molecule.  We can assume that the ions take up negligible volume, but you can see that additional water is produced.  This water makes up the extra volume.

To calculate how much water should have been produced, calculate how many moles of each reactant was present and calculate the moles of water produced.  Turn this to a mass, and use the density of water to find the volume increase.

From the equation, we can see that 1 mol of each reactant is present, so we can make 1 mol of water.  1 mol of water is about 18g, which is about 18mL, and this is close to the observed increase.