The concentration of calcium ions in hard water can be determined by titration with reagent X,which forms a complex with Ca2+(aq), giving a change of color. Three moles of X combine with one mole of Ca2+(aq). Since the color change in this titration is sensitive to pH, the titration has to be carried out in an alkaline buffer. A 25cm3 sample of hard water reacted with 24.0 cm3 of 1.00 x 10-4cm3 X(aq)
(a) What is the concentration, in moldm-3, of calcium ions in the hard water?
(b)The structure of X is similar to that of an amino acid. The way X acts as a ligand can be understood by considering how aminoethanoic acid, H2NCH2CO2H, forms coordinate(dative covalent) bonds with cations
(c)Explain why the complex formed betwwen aminoethanoic acid and aqueous calcium ions is more stable at pH10 than at pH4
I think you have a typo here. I believe the 1.00 x 10^-4 cc X should be 1.00 x 10^-4 mol/dm^3 of X.
24.0 cc X * 1.00E-4 mol/dm^3 = 0.0024 mmols X.
Divide by 3 to obtain mmols Ca^2+ = 0.0008.
a. (Ca^2+) = mmols/cc.
b. no question.
c.
(a) To find the concentration of calcium ions in the hard water, we can start by determining the number of moles of X that reacted with the calcium ions.
From the given information, we know that three moles of X combine with one mole of Ca2+(aq). Therefore, the number of moles of X that reacted can be calculated as follows:
Number of moles of X = Volume of X(aq) used (in dm3) x Concentration of X(aq) (in mol/dm3)
The volume of X(aq) used is given as 24.0 cm3, which is equivalent to 24.0/1000 = 0.024 dm3.
The concentration of X(aq) is given as 1.00 x 10-4 mol/cm3, which is equivalent to 1.00 x 10-4/1000 = 1.00 x 10-7 mol/dm3.
Number of moles of X = 0.024 dm3 x 1.00 x 10-7 mol/dm3
= 2.40 x 10-9 mol
Since three moles of X combine with one mole of Ca2+(aq), we can determine the number of moles of Ca2+(aq) present in the hard water sample as follows:
Number of moles of Ca2+(aq) = (2.40 x 10-9 mol X) / 3
= 8.00 x 10-10 mol
Now, to find the concentration of calcium ions in the hard water, we divide the number of moles of Ca2+(aq) by the volume of the water sample.
Volume of water sample = 25 cm3 = 25/1000 dm3 = 0.025 dm3
Concentration of Ca2+(aq) = Number of moles of Ca2+(aq) / Volume of water sample
= 8.00 x 10-10 mol / 0.025 dm3
= 3.20 x 10-8 mol/dm3
Therefore, the concentration of calcium ions in the hard water is 3.20 x 10-8 moldm-3.
(b) The ligand X, which forms a complex with Ca2+(aq), has a structure similar to an amino acid. This suggests that X can act as a ligand by donating a lone pair of electrons from a functional group (e.g., amino or carboxylate group) to form coordinate (dative covalent) bonds with cations like calcium ions.
(c) The complex formed between aminoethanoic acid and aqueous calcium ions is more stable at pH 10 than at pH 4 due to the effect of pH on the ionization of aminoethanoic acid.
At low pH (e.g., pH 4), aminoethanoic acid exists primarily in its protonated form, with the amino group protonated (–NH3+) and the carboxylate group uncharged (–COOH). In this form, the lone pair of electrons on the amino group is less available for bond formation with the calcium ions, resulting in a weaker complex.
At higher pH (e.g., pH 10), the aminoethanoic acid becomes deprotonated, with the amino group in its uncharged form (–NH2) and the carboxylate group negatively charged (–COO-). In this form, the lone pair of electrons on the amino group is more available for bond formation with the calcium ions, resulting in a stronger complex. The increased availability of the lone pair of electrons and the negative charge on the carboxylate group enhance the stability of the complex formed between aminoethanoic acid and aqueous calcium ions at pH 10.
(a) To determine the concentration of calcium ions in the hard water, we can use the information given in the question. It states that three moles of reagent X combine with one mole of Ca^2+ ions.
First, let's calculate the number of moles of X used in the titration:
Volume of X(aq) = 24.0 cm^3
Concentration of X(aq) = 1.00 x 10^-4 moldm^-3
Using the formula:
Number of moles of X = (concentration of X) x (volume of X)
Number of moles of X = (1.00 x 10^-4 moldm^-3) x (24.0 cm^3 / 1000 cm^3/dm^3)
= 2.40 x 10^-6 moles
Since the ratio of X to Ca^2+ ions is 3:1, we can calculate the number of moles of Ca^2+ ions:
Number of moles of Ca^2+ ions = (number of moles of X) / 3
= (2.40 x 10^-6 moles) / 3
= 8.00 x 10^-7 moles
Given that the volume of the sample of hard water used in the titration is 25 cm^3, we can calculate the concentration of calcium ions:
Concentration of Ca^2+ ions = (number of moles of Ca^2+ ions) / (volume of sample)
Concentration of Ca^2+ ions = (8.00 x 10^-7 moles) / (25 cm^3 / 1000 cm^3/dm^3)
= 3.20 x 10^-5 moldm^-3
Therefore, the concentration of calcium ions in the hard water is 3.20 x 10^-5 moldm^-3.
(b) Reagent X is described to have a structure similar to that of an amino acid. Ligands, including amino acids, can form coordinate (dative covalent) bonds with cations.
In the case of aminoethanoic acid (H2NCH2CO2H), the amino group (NH2) and the carboxylic acid group (CO2H) can both donate a lone pair of electrons to bond with metal cations, including calcium ions (Ca^2+).
The amino group's lone pair can form a coordinate bond with the calcium ion, resulting in a dative covalent bond. Similarly, the carboxylic acid group can also form a coordinate bond.
This coordination or bonding occurs because the metal cation, in this case, the calcium ion, is electron-deficient and can accept a lone pair of electrons from the ligand, X.
(c) The stability of a complex formed between aminoethanoic acid and aqueous calcium ions can be influenced by the pH of the solution.
At pH 10, the solution is alkaline. In an alkaline environment, the concentration of hydroxide ions (OH-) is high. The presence of hydroxide ions can react with the carboxylic acid group of aminoethanoic acid, deprotonating it. This results in the formation of a carboxylate ion (CO2-) which is a stronger ligand.
The carboxylate ion (CO2-) can form a more stable complex with the calcium ion because it has a greater negative charge compared to the undeprotonated carboxylic acid group. This facilitates the formation of stronger coordinate bonds between the ligand and the calcium ion.
In contrast, at pH 4, the solution is acidic. The lower concentration of hydroxide ions means that there is less deprotonation of the carboxylic acid group. Consequently, the undeprotonated carboxylic acid group is present, which is a weaker ligand.
Therefore, the complex formed between aminoethanoic acid and aqueous calcium ions is more stable at pH 10 than at pH 4 due to the presence of a stronger ligand, the carboxylate ion, formed in an alkaline environment.