Question

The impure \(6 \mathrm{~g}\) of \(\mathrm{NaCl}\) is dissolved in water and then treated with excess of silver nitrate solution. The weight of precipitate of silver chloride is found to be \(14 \mathrm{~g}\). The \% purity of \(\mathrm{NaCl}\) solution would be: (a) \(95 \%\) (b) \(85 \%\) (c) \(75 \%\) (d) \(65 \%\)

Short answer

The percentage purity of the NaCl solution is approximately 85%.

Step-by-step solution

Write the chemical equation for the reaction

Identify the reaction between sodium chloride (NaCl) and silver nitrate (AgNO3) that will give silver chloride (AgCl) as the precipitate. The balanced chemical equation for the reaction is: \[\mathrm{NaCl_{(aq)} + AgNO3_{(aq)} \rightarrow AgCl_{(s)} + NaNO3_{(aq)}}\].

Calculate the number of moles of AgCl precipitate

Use the given mass of AgCl to determine the moles of AgCl using the molar mass of AgCl (143.32 g/mol). The moles of AgCl can be calculated as: \[\text{moles of AgCl} = \frac{\text{mass of AgCl}}{\text{molar mass of AgCl}}\] \[\text{moles of AgCl} = \frac{14 \mathrm{~g}}{143.32 \mathrm{~g/mol}}\].

Determine moles of NaCl that reacted

From the stoichiometry of the balanced chemical equation, 1 mole of NaCl reacts with 1 mole of AgNO3 to produce 1 mole of AgCl. Therefore, the moles of NaCl that reacted will be equal to moles of AgCl.

Calculate the theoretical mass of NaCl that reacted

Calculate the theoretical mass of NaCl using its molar mass (58.44 g/mol) and the moles of NaCl. \[\text{mass of NaCl} = \text{moles of NaCl} \times \text{molar mass of NaCl}\].

Calculate the percentage purity of NaCl

Finally, calculate the percentage purity of NaCl as \[\text{percentage purity} = \left( \frac{\text{actual mass of NaCl that reacted}}{\text{total mass of impure NaCl}} \right) \times 100\%.\] Use the mass of NaCl that reacted (theoretical mass from step 4) and the total mass of impure NaCl given as 6 g.

Key concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that involves the calculation of the quantities of reactants and products in chemical reactions. It is based on the balanced chemical equation, which shows the ratio in which substances react and form products.

Consider the equation from the given problem, \(\text{NaCl}_{(aq)} + \text{AgNO}_3_{(aq)} \rightarrow \text{AgCl}_{(s)} + \text{NaNO}_3_{(aq)}\). This equation indicates that 1 mole of sodium chloride reacts with 1 mole of silver nitrate to produce 1 mole of silver chloride and 1 mole of sodium nitrate. Stoichiometry allows us to understand this 1:1:1:1 ratio and apply it to calculate the amount of reactants needed or products formed.

To help students grasp the concept, drawing a 'mole map' or a diagram linking moles of each substance can serve as a powerful visual aid. Moreover, practice problems involving various stoichiometric calculations can reinforce the concept and enhance problem-solving skills.

Chemical Reactions

Chemical reactions involve the transformation of one or more substances into new substances. The reactants undergo a chemical change to form the products. Each chemical reaction is represented by a balanced chemical equation which respects the law of conservation of mass — meaning the number of atoms of each element is the same on both sides of the equation.

In the context of the provided exercise, the reaction between sodium chloride and silver nitrate to form silver chloride exemplifies a precipitation reaction, where an insoluble product, silver chloride (AgCl), forms and settles out of the solution. Introducing students to different types of chemical reactions, like synthesis, decomposition, single replacement, and double replacement, along with practical examples, can bolster their understanding and retention. Hands-on experiments where they can witness the formation of precipitates can also solidify their grasp of these concepts.

Molar Mass

Molar mass is the weight of one mole of a substance, typically expressed in grams per mole (g/mol). It is essentially the mass of the number of atoms found in 12 grams of carbon-12, about \(\text{6.022} \times \text{10}^{23}\) atoms (Avogadro's number). The molar mass allows chemists to convert between the mass of a substance and the number of moles.

To find the molar mass, you sum the atomic masses of all the atoms in a molecule. For instance, in the compound sodium chloride (NaCl), the molar mass is 58.44 g/mol, calculated by adding the atomic mass of sodium (Na, approximately 22.99 g/mol) with that of chlorine (Cl, approximately 35.45 g/mol). Teaching students to calculate molar mass in a step-by-step fashion can be achieved through practice problems that involve calculating the molar mass of different compounds. Ensuring that they understand it's not just a random number but correlated to the number of particles involved in the substance will make the topic less abstract and more concrete.