A sample of impure tin of mass 0.535 g is dissolved in strong acid to give a solution of Sn²⁺. The solution is then titrated with a 0.0448 M solution of NO₃^–, which is reduced to NO(g). The equivalence point is reached upon the addition of 0.0344 L of the NO₃^– solution. Find the percent by mass of tin in the original sample, assuming that it contains no other reducing agents.

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Identify the balanced chemical equation for the reaction between Sn^{2+} and NO_3^-: Sn^{2+} + 2 NO_3^- + 4 H^+ \(\rightarrow\) Sn^{4+} + 2 NO + 2 H_2O.

Calculate the moles of NO_3^- used in the titration using the formula: \(\text{moles of NO}\)_3^- = \(\text{molarity}\) \(\times\) \(\text{volume in liters}\).

Use the stoichiometry of the balanced equation to find the moles of Sn^{2+} that reacted. According to the equation, 1 mole of Sn^{2+} reacts with 2 moles of NO_3^-.

Calculate the mass of tin (Sn) that reacted using the moles of Sn^{2+} and the molar mass of tin (118.71 \(\text{ g/mol}\)).

Determine the percent by mass of tin in the original sample using the formula: \(\text{percent by mass}\) = \(\left\)( \(\frac{\text{mass of tin}\)}{\(\text{mass of sample}\)} \(\right\)) \(\times\) 100.

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Key Concepts

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

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It involves using balanced chemical equations to determine the relationships between the amounts of substances consumed and produced. In this question, stoichiometry is essential for relating the moles of tin (Sn) to the moles of nitrate (NO3-) used in the titration, allowing for the determination of the mass of tin in the sample.

Titration

Titration is a quantitative analytical technique used to determine the concentration of a solute in a solution. It involves the gradual addition of a titrant to a solution until the reaction reaches its equivalence point, where stoichiometrically equivalent amounts of reactants have reacted. In this scenario, the titration of Sn2+ with NO3- allows for the calculation of the amount of tin present based on the volume and concentration of the nitrate solution used.

Percent by Mass

Percent by mass is a way to express the concentration of a component in a mixture or solution, calculated as the mass of the component divided by the total mass of the mixture, multiplied by 100. In this problem, after determining the mass of tin from the titration data, calculating the percent by mass involves comparing the mass of tin to the original mass of the impure sample, providing insight into the purity of the tin.

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