Problem 98 - Chemistry and Chemical Reactivity

Question

You have a \(4.554-\mathrm{g}\) sample that is a mixture of oxalic acid, \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4},\) and another solid that does not react with sodium hydroxide. If \(29.58 \mathrm{mL}\) of \(0.550 \mathrm{M} \mathrm{NaOH}\) is required to titrate the oxalic acid in the 4.554 -g sample to the equivalence point, what is the weight percent of oxalic acid in the mixture? Oxalic acid and NaOH react according to the equation $$\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(\mathrm{aq})+2 \mathrm{NaOH}(\mathrm{aq}) \longrightarrow \mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\ell)$$

Step-by-Step Solution

Answer

The weight percent of oxalic acid in the sample is 16.08%.

Step 1: Determine Moles of Sodium Hydroxide

First, find the number of moles of NaOH used in the titration. Use the formula: \[ \text{moles of NaOH} = \text{Molarity} \times \text{Volume (L)} \]Substituting the given values, convert milliliters to liters (29.58 mL = 0.02958 L):\[ \text{moles of NaOH} = 0.550 \, \text{M} \times 0.02958 \, \text{L} = 0.016269 \, \text{moles} \]

Step 2: Relate Moles of NaOH to Moles of Oxalic Acid

From the balanced chemical equation, 1 mole of \( \text{H}_2\text{C}_2\text{O}_4 \) reacts with 2 moles of NaOH. Therefore, calculate the moles of oxalic acid:\[ \text{moles of } \text{H}_2\text{C}_2\text{O}_4 = \frac{0.016269 \, \text{moles of NaOH}}{2} = 0.0081345 \, \text{moles} \]

Step 3: Calculate Mass of Oxalic Acid

Next, calculate the mass of oxalic acid using its molar mass. The molar mass of \( \text{H}_2\text{C}_2\text{O}_4 \) is approximately 90.03 g/mol:\[ \text{mass of } \text{H}_2\text{C}_2\text{O}_4 = 0.0081345 \, \text{moles} \times 90.03 \, \text{g/mol} = 0.7321 \, \text{g} \]

Step 4: Calculate Weight Percent of Oxalic Acid

Finally, calculate the weight percent of oxalic acid in the mixture:\[ \text{Weight Percent} = \left( \frac{\text{mass of } \text{H}_2\text{C}_2\text{O}_4}{\text{mass of the sample}} \right) \times 100 \%\]Substitute the values:\[ \text{Weight Percent} = \left( \frac{0.7321 \, \text{g}}{4.554 \, \text{g}} \right) \times 100 \% = 16.08 \% \]

Key Concepts

Understanding Oxalic Acid

Oxalic acid, with the formula \( \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \), is a type of organic acid found naturally in plants like spinach and rhubarb.
It is a diprotic acid, meaning it can donate two hydrogen ions. This quality makes it particularly interesting in acid-base titration reactions.
In its solid form, oxalic acid is often used as a cleaning or bleaching agent, owing to its ability to react with calcium, iron, and other metals.In this context, oxalic acid plays a crucial role as the reactant in the titration process.
During titration, it reacts with sodium hydroxide, making it possible to determine its quantity in a sample.
Understanding how oxalic acid interacts with other substances can give you insights into both its chemical properties and practical uses.

Sodium Hydroxide in Titration

Sodium hydroxide \( (\mathrm{NaOH}) \) is a strong base widely used in titrations because it dissociates completely into its ions in solution.
In a titration, sodium hydroxide serves as the titrant, which is the solution of known concentration added to another solution to determine the concentration of an analyte.
When titrating with NaOH, it is crucial to monitor the process until reaching the equivalence point, where the amount of base exactly neutralizes the acid.In our example, sodium hydroxide reacts with oxalic acid. The balanced chemical equation shows that 2 moles of \( \mathrm{NaOH} \) react with 1 mole of oxalic acid.
This 2:1 molar ratio is key for calculating the unknown quantity of oxalic acid in the sample, a concept known as stoichiometry.
Proper understanding and calculation of this ratio is essential to successfully conducting a titration and interpreting its results.

Basics of Mole Calculations

Mole calculations are fundamental in solving chemistry problems like titrations.
The mole is a unit that measures the amount of a substance, based on Avogadro's number, which is approximately \( 6.022 \times 10^{23} \) molecules or atoms per mole.
This unit links the macroscopic world of grams and liters with the microscopic world of atoms and molecules.In our exercise, mole calculations help determine how much oxalic acid is present.
You first calculated the moles of NaOH using the formula: \[ \text{Moles} = \text{Concentration (M)} \times \text{Volume (L)} \]
Knowing the relationship between NaOH and oxalic acid from the chemical equation, you can relate the moles of titrant used to the analyte.
Such conversions are central in figuring out the quantity and thus solving the chemistry problem efficiently.

Understanding Weight Percent

Weight percent is a way of expressing the concentration of a component in a mixture.
It is calculated as the ratio of the mass of the component to the total mass of the mixture, multiplied by 100 to convert it to a percentage.
This expression is often used in chemistry to convey the composition of a solution or mixture.The step-by-step solution of titration reveals how to calculate the weight percent of oxalic acid in a mixture.
Once the mass of the oxalic acid is known from mole calculations, it is divided by the total mass of the sample:\[ \text{Weight Percent} = \left( \frac{\text{mass of component}}{\text{total mass of mixture}} \right) \times 100 \% \]
By performing this calculation, you can gauge the proportion of one component relative to the entire mixture, providing important insights for practical and experimental purposes.