To 100.0 mL of a solution that contains 0.120 M Cr(NO3)2 and 0.500 M HNO3 is added to 20.0 mL of 0.250 M K2Cr2O7. The dichromate and chromium(II) ions react to give chromium(III) ions. (a) Write a balanced net ionic equation for the reaction.

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Identify the reactants and products in the reaction: Cr(NO_3)_2 provides Cr^{2+} ions, K_2Cr_2O_7 provides Cr_2O_7^{2-} ions, and the reaction produces Cr^{3+} ions.

Write the unbalanced net ionic equation: Cr_2O_7^{2-} + Cr^{2+} \rightarrow Cr^{3+}.

Balance the chromium atoms: There are 2 chromium atoms in Cr_2O_7^{2-}, so you need 2 Cr^{3+} ions on the product side.

Balance the charges: The total charge on the reactant side is 2- from Cr_2O_7^{2-} and 2+ from Cr^{2+}, which sums to 0. The product side has 2 Cr^{3+} ions, which is 6+. To balance, add 6 electrons to the product side.

The balanced net ionic equation is: Cr_2O_7^{2-} + 6 Cr^{2+} + 14 H^+ \rightarrow 7 Cr^{3+} + 7 H_2O.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Net Ionic Equations

A net ionic equation represents the chemical species that are involved in a reaction, excluding spectator ions that do not participate. It focuses on the actual chemical change occurring in the solution, providing a clearer picture of the reaction. To write a net ionic equation, one must first write the complete ionic equation and then remove the ions that appear unchanged on both sides.

Oxidation States

Oxidation states (or oxidation numbers) indicate the degree of oxidation of an atom in a compound. They help in identifying which species are oxidized and reduced during a chemical reaction. In the context of the given reaction, understanding the oxidation states of chromium in Cr(NO3)2, K2Cr2O7, and the resulting chromium(III) ions is essential for balancing the equation correctly.

Stoichiometry of Reactions

Stoichiometry involves the calculation of reactants and products in chemical reactions based on the balanced equation. It allows chemists to predict the amounts of substances consumed and produced. In this question, stoichiometry is crucial for determining the molar ratios of chromium(II) ions and dichromate ions that react to form chromium(III) ions, which is necessary for writing the balanced net ionic equation.

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