The equilibrium constant for the following reaction is }\\\ 1.0 \times 10^{23}\\\ \mathrm{Cr}^{3+}(a q)+\mathrm{H}_{2} \mathrm{EDTA}^{2-}(a q) \rightleftharpoons \operatorname{CrEDTA}^{-}(a q)+2 \mathrm{H}^{+}(a q) \end{array} $$ EDTA is used as a complexing agent in chemical analysis. Solutions of EDTA, usually containing the disodium salt \(\mathrm{Na}_{2} \mathrm{H}_{2} \mathrm{EDTA}\), are used to treat heavy metal poisoning. Calculate \(\left[\mathrm{Cr}^{3+}\right]\) at equilibrium in a solution originally \(0.0010 \mathrm{M}\) in \(\mathrm{Cr}^{3+}\) and \(0.050 \mathrm{M}\) in \(\mathrm{H}_{2} \mathrm{EDTA}^{2-}\) and buffered at \(\mathrm{pH}=6.00 .\)

Understanding chemical equilibrium is crucial in predicting the extent of a chemical reaction under specific conditions. At equilibrium, the rate of the forward reaction equals the rate of the reverse reaction, and the concentrations of the reactants and products remain constant over time.

The equilibrium constant (\(K\textsubscript{eq}\)) is a numerical value derived from the equilibrium concentrations of the reactants and products. It provides insight into the position of equilibrium; a large constant suggests a product-favored reaction, while a smaller constant indicates a reactant-favored process.

When calculating the equilibrium constant, it’s important to account for the reaction’s stoichiometry, as each species' concentration is raised to the power of its coefficient in the balanced chemical equation. Any change in the system, like temperature, concentration, or pressure, can potentially shift the equilibrium according to Le Chatelier’s Principle.

In the world of analytical chemistry, EDTA, ethylenediaminetetraacetic acid, plays a vital role as a complexing or chelating agent. This means EDTA has the ability to form stable complexes with metal ions, which is invaluable during the process of titration to determine metal concentrations.

EDTA usually exists as a disodium salt and is revered for its high affinity for metal ions like \(\mathrm{Cr}^{3+}\), which was observed in the given exercise. The \(\mathrm{H}_2\mathrm{EDTA}^{2-}\) can bind to metals, forming a one-to-one complex, causing a change in the equilibrium of metal ion concentration.

EDTA is also used medically for treating heavy metal poisoning, as it can bind with toxic metals in the bloodstream, rendering them inert and allowing their excretion from the body.

pH is a scale used to quantify the acidity or basicity of an aqueous solution. It is crucial in chemical equilibrium calculations, as it affects the concentration of \(\mathrm{H}^+\) ions in a solution. In the given exercise, the pH of the solution is buffered at 6.00, which is within the acidic range.

By using the pH, we can calculate the concentration of \(\mathrm{H}^+\) ions using the relation \(\mathrm{pH}= -\log{[\mathrm{H}^+]}\). For equilibrium involving species affected by pH, like \(\mathrm{H}_2\mathrm{EDTA}^{2-}\), the pH can influence the degree of deprotonation and subsequently the equilibrium concentrations.

Ensuring the pH remains constant is essential in our calculations since it determines the availability of \(\mathrm{H}^+\) ions, which can shift the equilibrium if their concentration changes.

Stoichiometry is the section of chemistry that involves the quantitative relationship between reactants and products in a chemical reaction. It is based on the conservation of mass and the law of definite proportions.

In the context of equilibrium calculations, it helps us predict how changes in one substance's concentration affect others involved in the reaction. This is exemplified in the exercise problem where the stoichiometry of the reaction indicates that for every \(\mathrm{Cr}^{3+}\) ion that reacts, one \(\mathrm{H}_2\mathrm{EDTA}^{2-}\) molecule reacts, and conversely one \(\mathrm{H}^+\) ion is produced for every \(\mathrm{CrEDTA}^{-}\) complex formed.

Understanding stoichiometry allows us to express changes in concentration with a single variable (\(x\textsubscript{i}\) which simplifies the process of finding equilibrium concentrations. It’s a fundamental concept for solving chemical equilibrium problems effectively.