# Titrations

A titration is a methodical way to carefully combine two reactants in solution until they have reached their perfect reaction stoichiometric ratio. For most acid/base reactions this ratio is the simplest, 1-to-1 (1:1). Most titrations have a chemical indicator of some sort to visually clue in the analyst that they have reached the endpoint - which ideally will match the stoichiometric point (aka: equivalence point) for the reaction. This is almost always a color change of some sort to signal the end point.

On the right is an animated gif (from Wikipedia) showing a typical titration setup. Unfortunately, the animation does not stop at the endpoint, but goes right through it dispensing all the titrant. Ideally, one would stop at the first appearance of persistant color - this corresponds to the volume at the vertical red line on the pH/vol plot which is also animated.

#### Quantitative Analysis 101 - volume by difference

Believe it or not, there can be unintended bias (user error) when taking scientific readings/measurements. A common one is the way in which a technician reads the volume off of a buret. You are taught to read "the bottom of the meniscus". Different people might see that differently. There is also parallax error where the angle of view can lead to different readings. This is where technique comes in and also experience with the equipment. One way to somewhat cancel out these type of random errors is is to take two readings and take the difference. A person would first take a starting volume reading, then do the titration and take the end point reading. So you start the titration on an arbitrary volume on the buret. You do not try to make it be 0.00 mL because that could introduce a bias (error). To do this, you allow the buret to run past the 0.00 mark and then just stop it within a mL or two. Now you take a reading... for example you read to the best ±0.01 mL and you get 1.63 mL for initial reading. Now you do your titration and stick the endpoint. Now take the endpoint reading... say it is 31.08 mL. Now you take the difference to get the actual titrant volume that was used. In this case: 31.08 – 1.63 = 29.45 mL.

Random errors also tend to canel each other out the more times you repeat the experiment and log the data. So typically in the lab a titration is run at least three times and the results are averaged. We generally don't have time in class or especially on an exam for you to do three or more calculations and then average. So we will stick to one really good titration and pretend like it is really very accurate.

#### A Classic Exam Titration Question

Question: A titration on 50.00 mL of a strong acid solution (HCl) is carried out with a standardized 0.0255 M NaOH solution as the base titrant. The initial reading on the buret was 2.74 mL. The endpoint was reached (phenolphthalein color change) and found to be 38.11 mL. What is the concentration (mol/L) of the HCl solution?

HCl + NaOH → H2O + NaCl

So a simple ratio of 1:1. This means that number of moles of NaOH will equal the number of moles of HCl. Molarity times volume equals moles, so the formula to solve for is:

CHClVHCl = CNaOHVNaOH
CHCl(50) = (0.0255)(38.11 – 2.74)
CHCl = (0.0255)(35.37)/(50)
CHCl = 0.0180387

So the answer is that the concentration of the HCl is 0.0180 M. This answer only shows 3 significant figures because the original concentration of the NaOH only had 3 - we can't be more accurate than that.

Check out those external links! Go ahead and click those external links over in the margin. There is a lot of good stuff in those linked pages. OpenStax has titrations under the more broad subject of quantitative analysis - this means you collect data (measurements, numbers) and then calculate your answers. You are "quantifying" which is a really big deal for us science types.