Remember to include units, and pay attention to significant figures. 12.104g of
ID: 480651 • Letter: R
Question
Remember to include units, and pay attention to significant figures.
12.104g of KCl is weighed out using an analytical balance, placed in a 100 mL volumetric flask, and Dl water added to bring the solution volume to 100mL. This solution is labeled Solution 1. In a second experiment, 6.054g of KCl is weighed out using the same analytical balance, placed into a graduated cylinder, and Dl water added until the meniscus has reached the 50 mL mark. This solution is labeled Solution 2. The measurement uncertainty (standard deviation of the measured value) of the analytical balance used is +/- 0.001 g. The measurement uncertainty of the volumetric flask is +/- 0.06mL. The measurement uncertainty of the graduated cylinder is +/- 0-5 mL. Calculate the Molarity of Solution 1 and the uncertainty in the Molarity. Calculate the Molarity of Solution 2 and the uncertainty in the Molarity. Which is the better choice of glassware to use to in making calibration standards?Explanation / Answer
Molar mass of KCl = 74.5513 g/mol.
Solution 1
Moles of KCl = (12.104 g)*(1 mole/74.5513 g) = 0.162358 mole.
Molar concentration = number of moles/volume in L = (0.162358 mole)/[(100 mL)*(1 L/1000 mL)] = 1.62358 mol/L 1.623 M (ans).
Uncertainty in mass measured by the balance, u(m)/m = (0.001 g)/(12.104 g) = 8.2617*10-5
Uncertainty in volume measured by the volumetric flask, u(V)/V = (0.06 mL)/(100 mL) = 6.0*10-4.
Uncertainty in molar concentration, u(C)/C = [u(m)/m]2 + [u(V)/V]2 = (8.2617*10-5)2 + (6.0*10-4)2 6.0*10-4
===> u(C) = C*(6.0*10-4) = (1.623 M)*(6.0*10-4) = 0.0009738 M 0.00097 M
The uncertainty in the measured molar concentration is 0.00097 M and the measured molar concentration is 1.623 0.00097 M (ans).
Solution 2
Moles of KCl = (6.054 g)*(1 mole/74.5513 g) = 0.0812 mole.
Molar concentration = number of moles/volume in L = (0.0812 mole)/[(50 mL)*(1 L/1000 mL)] = 1.624 mol/L = 1.624 M (ans).
Uncertainty in mass measured by the balance, u(m)/m = (0.001 g)/(6.054 g) = 1.6518*10-4
Uncertainty in volume measured by the graduated cylinder, u(V’)/V’ = (0.5 mL)/(50 mL) = 0.01
Uncertainty in the measured molar concentration, u(C’)/C’ = [u(m)/m]2 + [u(V’)/V’]2 = (1.6518*10-4)2 + (0.01)2 0.01
====> u(C’) = C’*(0.01) = (1.624 M)*(0.01) = 0.01624 M
The uncertainty in the measurement of molar concentration by the graduated cylinder is 0.01624 M and the measured molar concentration is 1.624 0.01624 M (ans).
Offcourse, the graduated cylinder produces a much higher uncertainty in the measured concentration (0.01624 >> 0.00097) and hence the volumetric flask is a better glassware to measure the molar concentration (ans).