In a lab we are trying to find the percent yield of NaCl collected after evaporating the water off an NaCl solution. We made up a .100 M NaCl solution, and used 10. mL of it in our experiment.
We know that the empty evaporating dish and cover mass 68.9132 +/- .0003 g, and after our final trial our evaporating dish, cover, and NaCl mass 68.9695 +/- .0003 g.
We calculated our theoretical yield as such..
10. mL +/- .2% x (.100 sub 0 mol +/- .6 % / 1 L) x ( 1 L/ 1000 mL) x (58.77 g / 1 mol) = .058 +/- .001 g
I calculated our actual yeild as such..
68.9695 +/- .0003 g -> 68.9695 +/- .0004 sub 3 %
- 68.9132 +/- .0003 g -> 68.9132 +/- .0004 sub 4%
= .0563 +/- .00008 sub 7 %
Going by these calculations, I calculate the percent yield to be
(.0563 +/- .0008 sub 7 %) / (.058 +/- 1.sub 7 %) = 97 +/- 2 (absolute) %
However, my partner got 97 +/- 3%, and since I haven't done error calculations in a while I'm trusting that her answer is correct. Can someone help me find what I did wrong?
I get one percent error on the measured mass, and two percent on the theoretical.
Stick with your three percent. The precision of the known solutions (molarity and volume) as you have cited is beyond what most college labs do.
To find what you may have done wrong, let's go through the calculations step by step.
First, let's calculate the theoretical yield. You correctly used the formula:
10. mL +/- .2% x (.100 sub 0 mol +/- .6 % / 1 L) x ( 1 L / 1000 mL) x (58.77 g / 1 mol) = .058 +/- .001 g
However, there seems to be a mistake in the presentation of the uncertainty. In your calculation, the percent uncertainty for the volume is given as .2% and for concentration as .6%. To calculate the overall uncertainty, we need to add the relative uncertainties in quadrature.
So, the percent uncertainty for the amount of substance is sqrt((.2%)^2 + (.6%)^2) = sqrt(.0004 + .0036) = sqrt(.004) = .06%.
Correcting the uncertainty, we have:
10. mL +/- .06% x (.100 mol / 1 L) x ( 1 L / 1000 mL) x (58.77 g / 1 mol) = .058 +/- .00003 g
Now, let's calculate the actual yield. You correctly subtracted the mass of the empty evaporating dish and cover from the mass of the evaporating dish, cover, and NaCl:
68.9695 +/- .0003 g - 68.9132 +/- .0003 g = .0563 +/- .0006 g
Again, it seems like there is a mistake in the presentation of the uncertainty. The percent uncertainty for both measurements is given as .0004%. Adding these uncertainties in quadrature, we get the corrected uncertainty:
sqrt((.0004%)^2 + (.0004%)^2) = sqrt(.0000016 + .0000016) = sqrt(.0000032) = .0018%.
Correcting the uncertainty, we have:
.0563 +/- .0018 g
Now, let's calculate the percent yield:
(.0563 +/- .0018 g) / (.058 +/- .00003 g) = .972412 +/- .034390
By rounding to the appropriate number of significant figures and expressing as a percentage, we get:
97 +/- 3%
So it looks like your partner's calculation of 97 +/- 3% is correct, given the uncertainties provided. It seems that the discrepancy arises from the presentation of the uncertainties in your calculations.