The capacity of a large irregularly shaped vessel cannot be computed from geometric data. As a result, it is decided that the volume be established from analytical data. The vessel is filled to its capacity mark with calcium-free water. A known small amount of a concentrated calcium solution is added, and a homogeneous solution is obtained by stirring. The volume of the solution added is insignificant with respect to volume of the vessel.
In the experiment, 350 mL of a solution 0.735 M in Ca are added to the vessel. A 50.00 mL portion of the liquid in the vessel is removed after stirring and titrated with 0.001000 M EDTA. What is the capacity of the vessel in gallons if 32.21 mL of EDTA were required to reach the endpoint? One gallon is 3.78 liters.
mols added to vessel = M x L = 0.735 x 0.350 = 0.25725
mols titrated in 50.00 mL = M x L = 0.001 x 0.03221 = 3.221 x 10^-5 which is
3.221 x 10^-5 mols/0.05 L = 6.442 x 10^-4 mols/L.
L in vessel = 0.25725 mols x L/6.442 x 10^-4 = ?? Liters in vessel.
Convert to gallons. Check my thinking. Check my work.
volume of vessel =
6.442 L
6.442 L in mL
0.00057 mL
To find the capacity of the vessel in gallons, we need to use the information provided in the experiment.
First, let's calculate the number of moles of calcium (Ca) in the 350 mL solution added to the vessel. We can use the formula:
moles of Ca = concentration of Ca x volume of solution (in liters)
Converting the volume from mL to liters:
350 mL = 350 mL x 1 L / 1000 mL = 0.35 L
Now we can calculate the moles of Ca:
moles of Ca = 0.735 M x 0.35 L = 0.25725 moles of Ca
Next, we need to determine the number of moles of calcium present in the 50 mL portion of the liquid removed from the vessel and titrated with EDTA.
Since the volume of the EDTA used is given in mL, we need to convert it to liters:
32.21 mL = 32.21 mL x 1 L / 1000 mL = 0.03221 L
Now we can calculate the moles of Ca removed:
moles of Ca removed = concentration of EDTA x volume of EDTA (in liters)
Converting the concentration of EDTA from Molarity (mol/L) to moles of Ca per L:
Moles of Ca per L = 1 mole of EDTA / 6 moles of Ca
moles of Ca removed = 0.001000 M x 0.03221 L x (1 mole of EDTA / 6 moles of Ca) = 0.0000053683 moles of Ca removed
Since the volume of the solution added is insignificant compared to the volume of the vessel, we can assume that the moles of Ca removed represent the moles of Ca originally in the vessel.
Now we can find the ratio between the moles of Ca in the 50 mL portion and the total volume of the vessel:
moles of Ca in the vessel = (moles of Ca removed / volume of liquid removed) x total volume of vessel
Converting the volume of the liquid removed from mL to liters:
50 mL = 50 mL x 1 L / 1000 mL = 0.05 L
Calculating the moles of Ca in the vessel:
moles of Ca in the vessel = (0.0000053683 moles of Ca / 0.05 L) x total volume of vessel
Now we can solve for the total volume of the vessel:
total volume of vessel = (moles of Ca in the vessel / 0.0000053683 moles of Ca) x 0.05 L
Substituting the values:
total volume of vessel = (0.00025725 moles of Ca / 0.0000053683 moles of Ca) x 0.05 L = 2.42325 L
Finally, we convert the total volume of the vessel from liters to gallons:
total volume of vessel = 2.42325 L x (1 gallon / 3.78 L) = 0.6402 gallons
Therefore, the capacity of the vessel is approximately 0.6402 gallons.