Concentration with Uncertainty

Question

Timothy has 1 gallon of 6% bleach, assume 94% is water.
Timothy decides to dilute the bleach separately. Timothy
pours 10mL+0.1, 9mL+0.1, 8mL+0.1, 7mL+0.1, 6mL+0.1, and 1mL+0.1, of the bleach
into 6 different containers and then fills the difference
to 10mL with water. Calculate the new concentration, in moles per decimeter cubed, of the
bleach in each container.

Answer 1

If he uses 10 mL of the original 6% bleach, with density of 1.11 g/mL, then he is using 11.1 g of this starting bleach.

6% means that it is 6% by weight of sodium hypochlorite (NaClOl) per 100 g of the solution (6% bleach in water). Therefore we can say that 100 g of "bleach" contains 6 g of NaClO

11.1 g bleach x 6 g NaClO/100 g bleach = 0.666 g NaClO

Convert that to moles using formula weight.

0.1 mL error out of a 10 mL aliquot is +/- 1%, so now you have the spread for the error in moles of NaClO in the 10 mL (+/- 0.1 mL) aliquot.

On this one, you aren't doing any dilution, so take the moles and divide it by 0.010 L, and you have molarity.

For the other smaller aliquots, you have to do these calculations, and then you also have to calculate the dilution to 0.010 dm3 (0.010 L). But if you are doing this in a graduated cylinder, then you have the error measuring there also! If it's a decent 10 mL graduated cylinder, the error is probably +/- 0.1 mL, so the final volume range would be 9.9-10.1 mL

 

Additionally, when finding the % error on the original measured value, note that the smaller the volume, the greater your % error is going to be with this.  Your error is +/- 0.1 mL, out of 10 mL that was 1% but out of 1 mL that is 10% error!!!  So your original moles are going to be +/- 10% for this sample...

 

I can't walk through all of these calculations, it would take another hour. Hopefully my hints help you get the rest of the way.  Good luck!