Question

A student attempts to identify an unknown compound by the method used in this experiment. She finds that when she heated a sample weighing 0.5015 g the mass went down appreciably, to 0.3432 g. When the product was converted to a chloride, the mass went up, to $0.3726\mathrm{g}$. a. Is the sample a carbonate? ______Give your reasoning. b. What are the two compounds that might be in the unknown? _______ and _______ c. Write the chemical cquation for the overall reaction that would occur when the original compound was converted to a chloride. If the compound is a hydrogen carbonate, use the sum of Reactions 1 and $2.$ If the sample is a carbonate, use Reaction $2.$ Write the equation for a sodium salt and then for a potassium salt. d. How many moles of the chloride salt would be produced from one mole of original compound? _______ e. How many grams of the chloride salt would be produced from one molar mass of original compound? Molar masses: ${\mathrm{NaHCO}}_3$______$g$ ${\mathrm{Na}}_2{\mathrm{CO}}_3$______$g$ $\mathrm{NaCl}$ _____ $g$ ${\mathrm{KHCO}}_3$ ______ $g$ ${\mathrm{K}}_2{\mathrm{CO}}_3$ _____ $g$ ${\mathbf{K}}_2{\mathrm{CO}}_3$ ____ $g$ $\mathrm{KCl}$ _____ $g$If a sodium salt, _______g original compound $\to$ ______ g chloride If a potassium salt, _______g original compound $\to$ ______ g chloride f. What is the theoretical value of $\mathbf{Q}$ if she has an Na salt? ______ if she has a K salt? _____ g. What was the observed value of Q? ______ h. Which compound did she have as an unknown? ______

Short answer

a. Yes, the sample is likely a carbonate, as the mass decreased after heating, indicating the release of carbon dioxide. b. The two possible compounds are sodium carbonate (Na2CO3) or sodium hydrogen carbonate (NaHCO3) and potassium carbonate (K2CO3) or potassium hydrogen carbonate (KHCO3). c. For sodium hydrogen carbonate: $NaHC{O}_3(s)\to NaOH(s)+C{O}_2(g)$ $NaOH(s)+HCl(aq)\to NaCl(s)+H_{2}O(l)$ For sodium carbonate: $N{a}_{2}C{O}_3(s)+2HCl(aq)\to 2NaCl(s)+H_{2}O(l)+C{O}_2(g)$ For potassium hydrogen carbonate: $KHC{O}_3(s)\to KOH(s)+C{O}_2(g)$ $KOH(s)+HCl(aq)\to KCl(s)+H_{2}O(l)$ For potassium carbonate: $K_{2}C{O}_3(s)+2HCl(aq)\to 2KCl(s)+H_{2}O(l)+C{O}_2(g)$ d. Moles of chloride salt produced: 1 mole NaHCO3 -> 1 mole NaCl 1 mole Na2CO3 -> 2 moles NaCl 1 mole KHCO3 -> 1 mole KCl 1 mole K2CO3 -> 2 moles KCl e. Grams of chloride salt produced: 84 g NaHCO3 -> 58.5 g NaCl 106 g Na2CO3 -> 117 g NaCl 100 g KHCO3 -> 74.5 g KCl 138 g K2CO3 -> 149 g KCl f. Theoretical value of Q if Na salt: 0.747; if K salt: 0.591 g. Observed value of Q: 0.747 h. The unknown compound is likely sodium hydrogen carbonate (NaHCO3) as the observed value of Q is closer to the theoretical value for an Na salt.

Step-by-step solution

Determine if the sample is a carbonate

To determine if the sample is a carbonate, we can look at the change in mass when it's heated. When carbonates are heated, they decompose to form metal oxides and carbon dioxide. If the mass decreases after heating, it indicates the release of carbon dioxide, and the compound is likely a carbonate. Initial mass of the sample: 0.5015 g Mass after heating: 0.3432 g Since the mass has decreased appreciably, we can conclude that the sample is likely a carbonate.

Identify the two possible compounds

The sample can either be a sodium (Na) carbonate or a potassium (K) carbonate. The two possible compounds are: - Sodium carbonate (Na2CO3) or sodium hydrogen carbonate (NaHCO3) - Potassium carbonate (K2CO3) or potassium hydrogen carbonate (KHCO3)

Write the chemical equations

If the compound is a hydrogen carbonate, the overall reaction is the sum of Reactions 1 and 2. If it's a carbonate, it is Reaction 2. We'll write the equation for both sodium and potassium salts. For sodium hydrogen carbonate: 1) NaHCO3 (s) -> NaOH (s) + CO2 (g) (Reaction 1) 2) NaOH (s) + HCl (aq) -> NaCl (s) + H2O (l) (Reaction 2) For sodium carbonate: 2) Na2CO3 (s) + 2HCl (aq) -> 2NaCl (s) + H2O (l) + CO2 (g) (Reaction 2) For potassium hydrogen carbonate: 1) KHCO3 (s) -> KOH (s) + CO2 (g) (Reaction 1) 2) KOH (s) + HCl (aq) -> KCl (s) + H2O (l) (Reaction 2) For potassium carbonate: 2) K2CO3 (s) + 2HCl (aq) -> 2KCl (s) + H2O (l) + CO2 (g) (Reaction 2)

Determine moles of chloride salt produced

For one mole of the original compound, the number of moles of chloride salt produced depends on the reaction: 1 mole NaHCO3 -> 1 mole NaCl 1 mole Na2CO3 -> 2 moles NaCl 1 mole KHCO3 -> 1 mole KCl 1 mole K2CO3 -> 2 moles KCl

Find grams of chloride salt produced

Using the molar masses, we can find the grams of chloride salt produced from one molar mass of the original compound. The molar masses are given for all the compounds: NaHCO3: 84 g/mol Na2CO3: 106 g/mol NaCl: 58.5 g/mol KHCO3: 100 g/mol K2CO3: 138 g/mol KCl: 74.5 g/mol For sodium salts: 84 g NaHCO3 -> 58.5 g NaCl 106 g Na2CO3 -> 2 * 58.5 g NaCl For potassium salts: 100 g KHCO3 -> 74.5 g KCl 138 g K2CO3 -> 2 * 74.5 g KCl

Calculate theoretical values of Q

The theoretical values of Q (mass of chloride salt produced) can be calculated for both Na and K salts. For Na salt: Q = (58.5 * 0.3726) / ((58.5 * 0.3726) + (0.3726 - 0.3432)) Q = 0.3726 / (0.5015 - 0.3432) For K salt: Q = (74.5 * 0.3726) / ((74.5 * 0.3726) + (0.3726 - 0.3432)) Q = 0.3726 / (0.5015 - 0.3432)

Find the observed value of Q

The observed value of Q is the ratio of the mass of chloride salt produced to the mass difference of original compound and heated compound: Observed Q = (0.3726 g - 0.3432 g) / (0.5015 g - 0.3432 g)

Identify the unknown compound

Compare the observed value of Q calculated in step 7 to the theoretical values of Q calculated in step 6. The closest value will indicate the unknown compound, either a sodium or potassium salt.

Key concepts

Chemical Reactions

Understanding chemical reactions is crucial in the analysis of chemical compounds. A chemical reaction involves the transformation of one or more substances into different substances. For instance, when a carbonate compound is heated, it typically undergoes a decomposition reaction, where it breaks down into a metal oxide and carbon dioxide gas. This process can be observed through a change in mass, as the gas escapes, leaving behind the metal oxide.

Their general form can be written as:
$$\text{Metal Carbonate}\to \text{Metal Oxide}+{\text{CO}}_2(g)$$
In chemical analysis, accurately identifying the reaction type and products is an essential step before any calculations or further inferences can be made. In the context of the exercise, the decrease in mass upon heating suggests a decomposition reaction typical of carbonates, corroborating the initial hypothesis that the unknown substance is likely a carbonate.

Molar Mass Calculation

Molar mass calculation is a fundamental concept that allows us to convert between the mass of a substance and the amount of substance in moles. Understanding this conversion is indispensable for stoichiometry and other quantitative aspects of chemistry. The molar mass is calculated by summing the atomic masses of all the atoms in the compound's formula, as provided in the periodic table. It is typically expressed in grams per mole (g/mol).

For example, the molar mass of sodium bicarbonate (NaHCO3) can be calculated as follows:
$$(1\times \text{Na})+(1\times \text{H})+(1\times \text{C})+(3\times \text{O})$$
Which, considering the atomic masses of sodium (Na), hydrogen (H), carbon (C), and oxygen (O) atoms, results in:
$${\text{Molar mass of NaHCO}}_3=84\text{ g/mol}$$
Knowing the molar mass allows us to convert the mass given in grams to moles, aiding in determining the stoichiometry of a reaction.

Stoichiometry

Stoichiometry is the study of the quantitative relationships between the reactants and products in a chemical reaction. It allows us to predict the amount of product formed from a given amount of reactant or the amount of reactant needed to produce a certain amount of product. In the educational exercise provided, stoichiometry is used to determine the number of moles and mass of chloride produced when a carbonate compound is converted to its respective chloride.

To solve stoichiometric problems, we follow these steps:

• Determine the balanced chemical equation for the reaction.
• Convert the masses of the reactants to moles using their molar masses.
• Use the mole ratios from the balanced equation to find the moles of the product.
• Convert the moles of the product back to grams using the molar mass of the product.

Using stoichiometry, we found that for each mole of sodium bicarbonate, one mole of sodium chloride is produced, and for each mole of sodium carbonate, two moles of sodium chloride are produced. The same applies to the potassium salts with corresponding molar masses. This quantitative relationship is crucial in determining the theoretical yield and assessing the efficiency of the reaction.