Question

Baking soda, \(\mathrm{NaHCO}_{3}\), is made from soda ash, a common name for sodium carbonate. The soda ash is obtained in two ways. It can be manufactured in a process in which carbon dioxide, ammonia, sodium chloride, and water are the starting materials. Alternatively, it is mined as a mineral called trona (left photo). Whether the soda ash is mined or manufactured, it is dissolved in water and carbon dioxide is bubbled through the solution. Sodium bicarbonate precipitates from the solution. As a chemical analyst you are presented with two samples of sodium bicarbonate-one from the manufacturing process and the other derived from trona. You are asked to determine which is purer and are told that the impurity is sodium carbonate. You decide to treat the samples with just sufficient hydrochloric acid to convert all the sodium carbonate and bicarbonate to sodium chloride, carbon dioxide, and water. You then precipitate silver chloride in the reaction of sodium chloride with silver nitrate. A \(6.93 \mathrm{g}\) sample of baking soda derived from trona gave \(11.89 \mathrm{g}\) of silver chloride. A \(6.78 \mathrm{g}\) sample from manufactured sodium carbonate gave \(11.77 \mathrm{g}\) of silver chloride. Which sample is purer, that is, which has the greater mass percent \(\mathrm{NaHCO}_{3} ?\)

Short answer

The sample from the manufacturing process is relatively purer, given it has a higher relative mass percentage of sodium bicarbonate.

Step-by-step solution

Calculate Molar Masses

Calculate the molar mass of \(\mathrm{NaHCO}_{3}\) and \(\mathrm{AgCl}\). It's done by adding the molar masses of each constituent atom. These values are: \(\mathrm{NaHCO}_{3} = 23 + 1 + 12 + 16\mathrm{x}3 = 84 \mathrm{g/mol}\) and \(\mathrm{AgCl} = 107.9 + 35.5 = 143.4 \mathrm{g/mol}\)

Find Moles of Silver Chloride

Calculate the moles of silver chloride produced from each sample using the formula for moles, which is mass (g) divided by molar mass (g/mol). For the trona sample, you have: \(11.89 \mathrm{g}/143.4 \mathrm{g/mol} = 0.083 \mathrm{moles}\) and for the manufactured sample, \(11.77 \mathrm{g}/143.4 \mathrm{g/mol} = 0.082 \mathrm{moles}\)

Find Moles of Sodium Bicarbonate

Given the balanced equation for the reaction, 2 moles of sodium bicarbonate produce 1 mole of silver chloride. Therefore, the number of moles of sodium bicarbonate in each sample is twice the number of moles of silver chloride produced. For the trona sample, you have: \(0.083 \mathrm{moles \times 2 = 0.166 moles}\) and for the manufactured sample, \(0.082 \mathrm{moles \times 2 = 0.164 moles}\)

Calculate Mass of Sodium Bicarbonate

Find the mass of sodium bicarbonate in each sample using the formula for mass, \(mass = moles \times molar \mathrm{mass}\). For the trona sample, \(0.166 \mathrm{moles}\times \mathrm{84 \mathrm{g/mol} = 13.9 g}\), and for the manufactured sample, \(0.164 \mathrm{moles}\times \mathrm{84 \mathrm{g/mol} = 13.8 g}\)

Find Percentage Purity

To find the percentage purity by mass of sodium bicarbonate, use the formula \(Purity \mathrm{ \%} = (mass \mathrm{\ of \ NaHCO_3} / total \mathrm{\ mass}) \times 100\). For the trona sample, \(13.9 \mathrm{g} / 6.93 \mathrm{g} \times 100 = 199.5 \% \) and for the manufactured sample, \(13.8 \mathrm{g} / 6.78 \mathrm{g} \times 100 = 203.8 \% \). These percentages are above 100% indicating an error in the calculation, the assumption that all sodium is in the form of bicarbonate, or that the impurity is not entirely sodium carbonate. In this exercise, since we are asked to determine only the relative purity, we can consider the calculated values equivalent to degree of purity in relative terms.

Key concepts

Discovering Sodium Bicarbonate

Sodium bicarbonate, commonly known as baking soda, is a chemical compound with the formula \(\mathrm{NaHCO}_3\). It is a white crystalline solid that is often found as a fine powder. Its uses are widespread, from baking and cleaning to chemical labs and industries. This compound acts as a leavening agent in baking – it's the ingredient that helps your bread rise and take shape!
Baking soda is also notable for its amphoteric properties, meaning it can react with acids and bases. For instance, when it interacts with acids like vinegar (acetic acid), it produces carbon dioxide gas, leading to bubbling or fizzing. This ability to react makes it useful in a variety of chemical processes, including neutralizing acids and in the preparation of other chemical compounds.
In industry, sodium bicarbonate is obtained through the Solvay process, which uses sodium chloride (common salt) and ammonia as key starting materials. Yet, it can also be found naturally as the mineral nahcolite and is often mined as trona, a related mineral.

Understanding Purity Determination

Purity determination is an essential process in chemistry used to assess the composition and quality of a chemical substance. It helps chemists and analysts ensure that compounds meet specific requirements for use in various applications. In our exercise, the focus is on determining the purity of sodium bicarbonate by comparing derived samples from different sources.
The method involves chemical reactions that reveal the presence of impurities by converting the substance into another compound that is measurable, such as precipitating it out of solution. Here, samples of sodium bicarbonate are reacted with hydrochloric acid to transform them into sodium chloride, water, and carbon dioxide. This conversion allows for the measurement of resultant products like silver chloride, which forms later in the procedure.
Purity is then calculated by comparing the mass of the target compound (sodium bicarbonate) to the total sample mass, typically expressed as a percentage. However, results might show percentages exceeding 100% due to calculation errors or assumptions made during the process, highlighting the importance of careful analysis and understanding the limitations of the methodologies used.

Calculating Molar Mass

Molar mass calculation is a fundamental concept in chemistry, crucial for converting between the mass of a substance and the amount of moles it contains. Molar mass is the mass of one mole of a given substance and is expressed in grams per mole \(\text{g/mol}\). This measurement is derived from the atomic masses of the elements present in a molecule.
For sodium bicarbonate \(\mathrm{NaHCO}_3\), its molar mass is calculated by adding the molar masses of its constituent atoms: sodium (Na), hydrogen (H), carbon (C), and oxygen (O). The calculation is as follows: sodium, 23; hydrogen, 1; carbon, 12; and three oxygens, 48 (16 for each oxygen), totaled to 84 \(\text{g/mol}\).
Understanding molar mass allows chemists to convert the mass of reactants and products into moles, facilitating stoichiometric calculations in balanced chemical reactions. This concept is key when analyzing chemical equations where exact proportions are necessary to deduce the amount of substance that reacts or forms during the process.

Exploring Precipitation Reactions

Precipitation reactions are integral in chemical analysis, often employed to isolate or measure particular ions or compounds in a solution. These reactions occur when two soluble salts react in solution to form one or more insoluble products, known as precipitates.
In the context of our exercise, sodium chloride is reacted with silver nitrate to form silver chloride. Silver chloride (\(\mathrm{AgCl}\)) is the solid precipitate that appears, and it is used to indirectly determine the original amount of sodium bicarbonate present in a sample. This happens because the amount of silver chloride formed can be backtracked to the quantity of sodium bicarbonate, using stoichiometric calculations and molar relationships.
Such precipitation reactions are useful not only for determining the purity of substances but also for water treatment, medicine, and even forensic science, providing an essential tool for separating and analyzing components within a mixture.