[6 points] You need to make a solution of Ca(NO3)2 for a class demonstration. First, you measure a quantity of the solid Ca(NO3)2 by weighing the reagent container before obtaining the sample (4.2540 ± 0.0003 g) and after taking some reagent (3.9440 ± 0.0003 g). You were about to transfer the Ca(NO3)2 into a 100- ml volumetric flask, but notice that you forgot to wash it the previous week and there is something green growing in it. So rather than cleaning the volumetric flask, you instead decide to just use a beaker and fill it to a final volume of 0.100 ± 0.005 L. The molar mass of Ca(NO3)2 is 164.10 g/mol, and its uncertainty is negligible (i.e. treat it as a constant).
a. Calculate the concentration of nitrate ions in the resulting solution (don’t forget about the stoichiometry), and determine the uncertainty in that value. What is the primary contribution to the uncertainty?
b. A typical 100-ml volumetric flask has an uncertainty of ± 0.12 ml. If you had made the above solution in a volumetric flask instead of the beaker, what would have been the resulting concentration and uncertainty?
To calculate the concentration of nitrate ions in the resulting solution, we need to follow the given information and perform some calculations.
a. First, we need to calculate the mass of Ca(NO3)2 used in the solution:
Mass of Ca(NO3)2 = (Weight of container before - Weight of container after) = (4.2540 g - 3.9440 g) = 0.3100 g
Next, we need to calculate the number of moles of Ca(NO3)2 used:
Number of moles of Ca(NO3)2 = (Mass of Ca(NO3)2) / (Molar mass of Ca(NO3)2) = (0.3100 g) / (164.10 g/mol) = 0.001885 mol
Since the stoichiometry of Ca(NO3)2 is 1:2 between calcium ions (Ca2+) and nitrate ions (NO3-), the number of moles of nitrate ions will be twice the number of moles of Ca(NO3)2:
Number of moles of NO3- = 2 * (Number of moles of Ca(NO3)2) = 2 * 0.001885 mol = 0.00377 mol
Now, we calculate the volume of the solution:
Volume of the solution = 0.100 L ± 0.005 L
Next, we calculate the concentration of nitrate ions:
Concentration of NO3- = (Number of moles of NO3-) / (Volume of the solution) = 0.00377 mol / 0.100 L = 0.0377 mol/L
To determine the uncertainty in the concentration value, we need to consider the primary contribution to the uncertainty. In this case, the primary contribution is the uncertainty in the volume measurement.
The uncertainty in concentration will be propagated from the volume uncertainty:
Uncertainty in concentration = (Uncertainty in volume of the solution) * (Number of moles of NO3-) / (Volume of the solution) = 0.005 L * 0.00377 mol / 0.100 L = 0.0001885 mol/L
Therefore, the concentration of nitrate ions in the resulting solution is 0.0377 mol/L ± 0.0001885 mol/L, and the primary contribution to the uncertainty is the volume measurement.
b. If the solution were made in a 100-ml volumetric flask instead of the beaker, we need to recalculate the concentration using the new volume and its uncertainty.
The new volume of the solution in a 100-ml volumetric flask is 100 ml ± 0.12 ml.
The new concentration of nitrate ions can be calculated as:
Concentration of NO3- = (Number of moles of NO3-) / (Volume of the solution) = 0.00377 mol / 0.100 L = 0.0377 mol/L
The uncertainty in the concentration calculation can be obtained by propagating the uncertainty from the volume measurement:
Uncertainty in concentration = (Uncertainty in volume of the solution) * (Number of moles of NO3-) / (Volume of the solution)
= 0.12 ml * 0.00377 mol / 0.100 L = 0.004524 mol/L
Therefore, if the solution were made in a 100-ml volumetric flask instead of the beaker, the resulting concentration of nitrate ions would be 0.0377 mol/L ± 0.004524 mol/L.
To calculate the concentration of nitrate ions in the resulting solution, we need to use the formula:
Concentration (mol/L) = (Amount of solute (mol)) / (Volume of solution (L))
a. Firstly, let's calculate the amount of Ca(NO3)2 used by finding the difference in weight before and after taking the reagent:
Amount of Ca(NO3)2 (mol) = (Weight before - Weight after) / Molar mass
Weight before = 4.2540 g
Weight after = 3.9440 g
Molar mass of Ca(NO3)2 = 164.10 g/mol
Amount of Ca(NO3)2 (mol) = (4.2540 g - 3.9440 g) / 164.10 g/mol
Next, we need to consider the stoichiometry of Ca(NO3)2. From the chemical formula, we can see that there are two nitrate ions (NO3-) for every one Ca(NO3)2 molecule. So, the amount of nitrate ions is twice the amount of Ca(NO3)2:
Amount of NO3- (mol) = 2 * Amount of Ca(NO3)2 (mol)
Now, we calculate the concentration by dividing the amount of nitrate ions by the final volume of the solution:
Concentration of NO3- (mol/L) = Amount of NO3- (mol) / Volume of solution (L)
Finding the uncertainty in the concentration is a bit more involved. The primary contribution to the uncertainty in this case is the uncertainty in the weight measurements.
To determine the uncertainty in the amount of Ca(NO3)2, we use the formula:
Uncertainty in amount of Ca(NO3)2 (mol) = ((Uncertainty in weight before)^2 + (Uncertainty in weight after)^2)^(1/2) / Molar mass
Uncertainty in weight before = 0.0003 g
Uncertainty in weight after = 0.0003 g
Uncertainty in amount of Ca(NO3)2 (mol) = ((0.0003 g)^2 + (0.0003 g)^2)^(1/2) / 164.10 g/mol
To find the uncertainty in the amount of NO3- ions, we multiply the uncertainty in the amount of Ca(NO3)2 by the stoichiometric factor of 2:
Uncertainty in amount of NO3- (mol) = 2 * Uncertainty in amount of Ca(NO3)2 (mol)
Finally, to determine the uncertainty in the concentration, we use the formula:
Uncertainty in concentration (mol/L) = Uncertainty in amount of NO3- (mol) / Volume of solution (L)
b. If the solution was made in a 100-ml volumetric flask, we need to consider the uncertainty in the volume of solution.
Uncertainty in concentration is calculated by using the formula:
Uncertainty in concentration (mol/L) = Uncertainty in amount of NO3- (mol) / Volume of solution with uncertainty (L)
Volume of solution with uncertainty = Volume of solution + Uncertainty in volume of solution
Now, use this information to calculate the resulting concentration and uncertainty in both cases.