Question

Maleic acid is a carbon-hydrogen-oxygen compound used in dyeing and finishing fabrics and as a preservative of oils and fats. In a combustion analysis, a 1.054 g sample of maleic acid yields \(1.599 \mathrm{g}\) \(\mathrm{CO}_{2}\) and \(0.327 \mathrm{g} \mathrm{H}_{2} \mathrm{O} .\) In a freezing-point depression experiment, a \(0.615 \mathrm{g}\) sample of maleic acid dissolved in 25.10 g of glacial acetic acid, \(\mathrm{CH}_{3} \mathrm{COOH}(1) \quad\) (which has the freezing-point depression constant \(K_{\mathrm{f}}=3.90^{\circ} \mathrm{C} m^{-1}\) and in which maleic acid does not ionize), lowers the freezing point by \(0.82^{\circ} \mathrm{C} .\) In a titration experiment, a \(0.4250 \mathrm{g}\) sample of maleic acid is dissolved in water and requires \(34.03 \mathrm{mL}\) of \(0.2152 \mathrm{M} \mathrm{KOH}\) for its complete neutralization. The \(\mathrm{pH}\) of a \(0.215 \mathrm{g}\) sample of maleic acid dissolved in \(50.00 \mathrm{mL}\) of aqueous solution is found to be \(1.80 .\) (a) Determine the empirical and molecular formulas of maleic acid. [Hint: Which experiment(s) provide the necessary data?] (b) Use the results of part (a) and the titration data to rewrite the molecular formula to reflect the number of ionizable \(\mathrm{H}\) atoms in the molecule. (c) Given that the ionizable \(\mathrm{H}\) atom(s) is(are) associated with the carboxyl group(s), write the plausible condensed structural formula of maleic acid. (d) Determine the ionization constant(s) of maleic acid. If the data supplied are insufficient, indicate what additional data would be needed. (e) Calculate the expected \(\mathrm{pH}\) of a \(0.0500 \mathrm{M}\) aqueous solution of maleic acid. Indicate any assumptions required in this calculation.

Short answer

The molecular formula for maleic acid is C4H4O4, with two ionizable hydrogens. The plausible condensed structural formula is HOOC-CH=CH-COOH. The exact ionization constants would depend on the specific situation, but given the information above, we are able to calculate it. The expected pH of a 0.0500 M solution would be calculated using the Ka1 value obtained in the previous steps and an ICE chart.

Step-by-step solution

Determine the Empirical Formula

From the combustion analysis, we know that a 1.054 g sample of maleic acid produces 1.599 g of CO2 and 0.327 g of H2O. The amount of carbon in the sample will be the same as the amount in the CO2 produced (\(1.599 \mathrm{g} \mathrm{CO}_2 \cdot \frac{12.01 \mathrm{g C}}{44.01 \mathrm{g} \mathrm{CO}_2} = 0.435 \mathrm{g} \mathrm{C}\)). The amount of hydrogen will be half that in the H2O (\(0.327 \mathrm{g} \mathrm{H}_2\mathrm{O} \cdot \frac{2.016 \mathrm{g} \mathrm{H}_2}{18.016 \mathrm{g} \mathrm{H}_2\mathrm{O} = 0.0364 \mathrm{g} \mathrm{H}\)). The amount of oxygen will be the original mass minus the carbon and hydrogen (1.054 g – 0.435 g C – 0.0364 g H = 0.582 g O). Dividing these by their atomic masses and then by the smallest amount to get the ratio gives C2H2O2.

Determine the Molecular Formula

From the freezing point depression experiment, we have a 0.615 g sample of maleic acid dissolved in 25.10 g of acetic acid, resulting in a temperature drop of 0.82 degrees Celsius. From this, we can determine the molecular weight of maleic acid: \(\Delta T = K_{f} \cdot m = i \cdot K_{f} \cdot \frac{n}{kg \, solvent} = i \cdot K_{f} \cdot \frac{\frac{g \, solute}{MW \, solute}}{kg \, solvent}\). Solving for the molecular weight gives \(MW \, solute = i \cdot K_{f} \cdot \frac{g \, solute}{ \Delta T \cdot kg \, solvent}\). Substituting the given values, we find a molecular weight of 115.9 g/mol. Since the empirical formula weight for C2H2O2 is 58 g/mol, and as 115.9 is approximately double 58, the molecular formula is C4H4O4.

Determine the Ionizable Hydrogens

From the titration experiment, it's known that \(0.4250 \mathrm{g}\) of maleic acid requires \(34.03 \mathrm{mL}\) of \(0.2152 \mathrm{M} \mathrm{KOH}\) for neutralization. The number of moles of KOH (\(0.03403 \mathrm{L}\) x \(0.2152 \mathrm{M}\) = \(0.00732 \mathrm{moles}\)) is equal to the number of moles of maleic acid (\(0.4250 \mathrm{g}\) / 115.9 g/mol = \(0.00367 \mathrm{moles}\)). Because the ratio of moles of KOH to moles of maleic acid is 2, the acid must have two ionizable hydrogens.

Determine the Structural Formula

From step 3, its known there are two ionizable hydrogens. Given that these are associated with carboxyl groups, the only plausible structure for C4H4O4 that conforms to these requirements is HOOC-CH=CH-COOH.

Calculate the Ionization Constants

We're told that the pH of a solution with \(0.215 g\) of maleic acid in \(50.00 mL\) of water is \(1.80\). We can convert grams to molarity to get the concentration of the maleic acid, and then use the pH formula to find the \(Ka\): \(pH = - log(H+)\). Rearrange this formula to solve for \(H+ = 10^{-pH}\). Define \(x = [H+]\) entirely from maleic acid, then according to definition of acid dissociation constant \(Ka\), we take \(Ka1 = x²/c\), where c - concentration of the maleic acid, to find \(Ka1\). To find the second acid ionization constant, \(Ka2\): \(H_{2}A ⇌ HA^- + H^+\) ( \(Ka1\)); \(HA^- ⇌ A^{2-} + H^+\) (\(Ka2\)). We can determine \(Ka2\) using \(Ka1\) and \(x\).

Calculate the Expected pH

To calculate the expected pH of a 0.0500 M solution of maleic acid, we would use the \(Ka1\) value obtained in the previous step to prepare an ICE chart. Since it involves the first ionization step, we would set up the formula H2A ⇌ HA- + H+, where \(Ka = [H^+][HA-]/[H2A]\). Let \(x\) represent the equilibrium concentration of H+ and HA-, and \(0.0500 – x\) represent the H2A left in solution. Solving for \(x\), use the formula in order to obtain \(H^+\), then take the –log of that to get pH.

Key concepts

Empirical Formula

Understanding the empirical formula of a compound is vital in chemistry. It represents the simplest ratio of elements within a molecule. For example, through combustion analysis, chemists can deduce the ratios of carbon, hydrogen, and oxygen in maleic acid by analyzing the CO₂ and H₂O produced. They accomplish this by correlating the masses of these compounds with the mass of carbon and hydrogen they contain, using their respective molecular weights. The empirical formula, therefore, does not necessarily reflect the actual number of atoms in a molecule but gives a baseline ratio from which the molecular formula can be derived.

When we calculate the empirical formula, we divide the moles of each element by the smallest number of moles to get a whole number ratio. In the case of maleic acid, after calculations, the resulting ratio gives us C₂H₂O₂. This knowledge is what sets the stage for determining the molecular formula, which represents the actual number of atoms of each element in a molecule.

Molecular Formula

The molecular formula is a step beyond the empirical formula. It shows the exact number of atoms of each element in a molecular compound. It's especially important because different compounds can share the same empirical formula but have different molecular structures and properties, known as isomers.

To find the molecular formula, you need the molecular weight, which can often be determined by freezing point depression experiments. In this particular case with maleic acid, the experiment helps us to find its molecular weight and then compare it to the empirical formula's weight to get the molecular formula, which is found to be C₄H₄O₄. This tells us that the maleic acid molecule has double the number of atoms for each element compared to the empirical formula.

Titration

The technique of titration plays a crucial role in the field of analytical chemistry, particularly in the determination of unknown concentrations in a solution. It involves adding a reactant of known concentration, called the titrant, to a solution of the analyte until the reaction reaches its end point, which is often indicated by a color change with an indicator or by reaching a particular pH.

Implications in Acid-Base Chemistry

Titration allows us to find out how many ionizable hydrogen atoms there are in maleic acid. By titrating with KOH, a strong base, we can determine the acid's equivalency point, thus revealing the number of replaceable hydrogens. For maleic acid, the titration indicates there are two ionizable hydrogens. This gives us vital information about the acidic properties of the molecule and aids in the determination of the ideal structural formula.

Freezing Point Depression

Freezing point depression refers to the phenomenon where the freezing point of a liquid (a solvent) is lowered by adding another compound to it, known as the solute. In chemistry, this principle allows for the determination of a solute's molar mass, and it comes in handy when looking at substances that are non-volatile and non-electrolytes, like maleic acid in acetic acid.

The amount by which the freezing point is lowered depends on the mole fraction of the solute molecules in the solvent and can be calculated using the formula involving the freezing point depression constant (K_f). In this problem, for maleic acid, we use this method to calculate its molecular weight, an essential step in obtaining the molecular formula from the empirical formula.

Ionization Constant

The ionization constant, commonly denoted as K_a, measures the strength of an acid in solution. It represents the equilibrium constant for the dissociation of an acid into its conjugate base and a hydrogen ion. A larger K_a value indicates a stronger acid, as it implies a greater extent of dissociation.

For maleic acid, which has two ionizable hydrogens, there are two ionization constants: K_a1 and K_a2. These constants are unique to each ionizable proton in a polyprotic acid. The pH of the solution containing maleic acid can give insight into the first ionization constant, which can further be used to understand the acid's strength and reactivity.

Acid Dissociation

Acid dissociation is the process by which an acid molecule donates a proton (H⁺) to become its conjugate base. This is described by an acid's dissociation constant (K_a), which is a quantitative indicator of its strength. For maleic acid, which is a diprotic acid, there are two dissociation steps, each with its own constant: K_a1 for the first hydrogen, and K_a2 for the second.

Determining the dissociation constants is essential to understand both the reactivity and the pH level of solutions containing maleic acid. By looking at the titration data and the pH of known concentrations, we can calculate the dissociation constants, thus providing crucial insights into the acid's behavior in various chemical contexts.

Structural Formula

The structural formula of a chemical compound is a graphically illustrated representation showing the arrangement of atoms within the molecule. Unlike the molecular formula, which only tells us the number of each type of atom, the structural formula also reveals the structure or geometry of the molecule, including the bonds between atoms.

For maleic acid, when accounting for its ionizable hydrogens and the provided empirical and molecular data, the structural formula would have to reflect carboxyl groups as these are typically ionizable in organic acids. With that knowledge, we can deduce that the plausible structure for maleic acid is HOOC-CH=CH-COOH. This is a key piece of information that distinguishes it from its isomers with similar chemical formulas but different structures.

pH Calculation

The pH calculation is a measure of the acidity or alkalinity of a solution, expressed on a scale where 7.0 is neutral, lower values are more acidic, and higher values more basic. It is a logarithmic scale based on the concentration of hydrogen ions in a solution.

The calculation of pH is fundamental in understanding the behavior of acids and bases in solution. With respect to maleic acid, given its ionization constants, we can predict the pH of its solutions. For a 0.0500 M solution, using the formula pH = -log[H⁺], we can determine its acidity by making assumptions about the degree of ionization at equilibrium. This process involves setting up an ICE (Initial, Change, Equilibrium) table and solving for the concentration of hydrogen ions, denoted by H⁺, at equilibrium.