The total concentration of Ca^2+ and Mg^2+ in a sample of hard water was determined by titrating

The total concentration of Ca^2+ and Mg^2+ in a sample of...

The total concentration of $\mathrm{Ca}^{2+}$ and $\mathrm{Mg}^{2+}$ in a sample of hard water was determined by titrating a $0.100-\mathrm{L}$ sample of the water with a solution of EDTA $^{4-}$. The EDTA $^{4-}$ chelates the two cations: $$ \begin{array}{r} \mathrm{Mg}^{2+}+[\mathrm{EDTA}]^{4-}--\rightarrow[\mathrm{Mg}(\mathrm{EDTA})]^{2-} \\ \mathrm{Ca}^{2+}+[\mathrm{EDTA}]^{--}--\rightarrow[\mathrm{Ca}(\mathrm{EDTA})]^{2-} \end{array} $$ It requires $31.5 \mathrm{~mL}$ of $0.0104 M[\mathrm{EDTA}]^{4-}$ solution to reach the end point in the titration. A second $0.100-\mathrm{L}$ sample was then treated with sulfate ion to precipitate $\mathrm{Ca}^{2+}$ as calcium sulfate. The $\mathrm{Mg}^{2+}$ was then titrated with $18.7 \mathrm{~mL}$ of $0.0104 \mathrm{M}[\mathrm{EDTA}]^{4-}$. Calculate the concentrations of $\mathrm{Mg}^{2+}$ and $\mathrm{Ca}^{2+}$ in the hard water in $\mathrm{mg} / \mathrm{L}$.

The total concentration of $\mathrm{Ca}^{2+}$ and $\mathrm{Mg}^{2+}$ in a sample of hard water was determined by titrating a $0.100-\mathrm{L}$ sample of the water with a solution of EDTA $^{4-}$. The EDTA $^{4-}$ chelates the two cations:
$$
\begin{array}{r}
\mathrm{Mg}^{2+}+[\mathrm{EDTA}]^{4-}--\rightarrow[\mathrm{Mg}(\mathrm{EDTA})]^{2-} \\
\mathrm{Ca}^{2+}+[\mathrm{EDTA}]^{--}--\rightarrow[\mathrm{Ca}(\mathrm{EDTA})]^{2-}
\end{array}
$$
It requires $31.5 \mathrm{~mL}$ of $0.0104 M[\mathrm{EDTA}]^{4-}$ solution to reach the end point in the titration. A second $0.100-\mathrm{L}$ sample was then treated with sulfate ion to precipitate $\mathrm{Ca}^{2+}$ as calcium sulfate. The $\mathrm{Mg}^{2+}$ was then titrated with $18.7 \mathrm{~mL}$ of $0.0104 \mathrm{M}[\mathrm{EDTA}]^{4-}$. Calculate the concentrations of $\mathrm{Mg}^{2+}$ and $\mathrm{Ca}^{2+}$ in the hard water in $\mathrm{mg} / \mathrm{L}$.

Key Concepts

Unit Conversions in Analytical Chemistry

Converting the calculated quantities from the titration (such as moles) into mass concentration units (like mg/L) is critical. This process involves using the molar mass of the analytes and adjusting for the sample volume to present the final results in standard and interpretable units.

Stoichiometric Calculations in Titration

These calculations involve using the known concentration and volume of a titrant to determine the number of moles of reactants in the solution. This essential quantitative relationship underpins titrimetric analyses by linking the titrant consumption to the analyte concentration.

Precipitation in Selective Separations

Precipitation reactions are used to separate specific ions from a mixture by converting them into an insoluble form. In analytical chemistry, the selective precipitation of one ion (for example, precipitating calcium as an insoluble sulfate) enables the separate quantification of other ions present in the solution.

Chelation

Chelation is the process wherein a ligand, such as EDTA, binds to a metal ion at multiple coordination sites, creating a ring-like complex. This enhanced binding specificity and stability allow for accurate quantitative analysis of metal ions in complex mixtures.

Complexometric Titration

This is an analytical technique used to determine the concentration of metal ions in solution by forming a stable complex with a chelating agent. In this method, EDTA is commonly employed as the titrant due to its ability to form strong, stable complexes with metals like calcium and magnesium, making it invaluable for water hardness analysis.

Water Hardness

Water hardness refers to the concentration of multivalent metal ions, chiefly calcium and magnesium, present in water. High levels of these ions can lead to scaling and other issues in water systems, which is why determining their concentration through titrimetric methods is important in both environmental and industrial applications.

Transcript

00:02 We are asked to calculate the concentration of the calcium ion and magnesium ion in a sample of hard water.

00:09 We're given the following information.

00:14 We titrated a 0 .10 -0 -0 -liter sample of hard water with edta 4 -minus.

00:32 The edta culates two cations.

00:49 Here are the reactions.

01:35 Okay, and then we're given two additional pieces of intradients.

01:38 We require 31 .5 milliliters of 0 .0104 molar of our titrant to reach the endpoint.

02:00 And that's everything.

02:02 That's both ions.

02:12 And then we precipitate out the, we precipitate all the calcium ion from the same size sample, same sample size as calcium sulfate.

02:48 Then we titrate the magnesium, and that's titrated with 18 .7 milliliters of the same titrant.

03:15 And then we're going to calculate the percentage of each as milligrams per liter.

03:32 Concentration of each in milligrams per liter.

03:36 I'm going to go ahead to the next page.

03:41 So for our first calculation, i'm going to do the full calculation first with 31 .5 millilators.

03:51 Of 0 .0104 molar.

03:55 And i'm going to calculate the number of moles of this by taking 0 .315 liters times 0 .0104 moles per liter.

04:11 And we're going to divide that by the liters of solution, which is this.

04:23 And for this, i get 3 .000.....

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