Standard Deviation of the Mean

Question

In a fictitious lab experiment, a class studied two acid base reactions and recorded the temperature change. class averages were reported:

1) 30 ml of 3 molar HCl with 30 ml of 1.5 NAOH change in temp was

12.2±1.3∘C

2) 30 ml of 1.5 molar HCl with 30 ml of 3 molar NAOH change in temp was

13.7±1.7∘C

Can we conclude from these data that

ΔT1 and ΔT2 are significantly different?

Answer 1

In both reactions, 1.5 M * 0.03L = 0.045 mol of HCl and NaOH react with each other to produce water and NaCl (aq), which is a neutralization reaction.

In reaction 1), NaOH was the limiting reagent and we will have 0.045 mol of unreacted HCl, whereas in reaction 2), HCl was the limiting reagent and we will have 0.45 mol of unreacted NaOH.

After the neutralization reaction, the excessive HCl will be dissociated into H+ and Cl- in reaction 1, and the excessive NaOH will be dissociated into Na+ and OH- in reaction 2.

The enthalpy of dissociation is -74.9 kJ/mol for HCl, and -44.5 kJ/mol for NaOH. So in general, HCl should release more heat than NaOH does when dissociating, thus resulting in more temperature increase. This is contrary to what was measured, but since the difference is not that large, it is probably statistically insignificant.