Problem 95 - Chemistry The Molecular Science

Question

A sample of a mixture of oxalic acid, \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4},\) and sodium chloride, \(\mathrm{NaCl}\), has a mass of \(4.554 \mathrm{~g}\). If a volume of \(29.58 \mathrm{~mL}\) of \(0.550-\mathrm{M} \mathrm{NaOH}\) is required to neutralize all the \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4},\) calculate the mass percent of oxalic acid in the mixture. Oxalic acid and \(\mathrm{NaOH}\) react according to this 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 mass percent of oxalic acid in the mixture is 16.07%.

Step 1: Calculate Moles of NaOH Used

To begin, we need to calculate the number of moles of NaOH that reacted with the oxalic acid. Use the formula for moles, \[ \text{moles} = M \times V \]where \( M \) is the molarity (0.550 M) and \( V \) is the volume in liters (29.58 mL = 0.02958 L): \[\text{moles of } \mathrm{NaOH} = 0.550 \times 0.02958 = 0.016269 \text{ mol}\]

Step 2: Calculate Moles of Oxalic Acid Reacted

Using the balanced chemical equation, we observe that oxalic acid reacts with NaOH in a 1:2 ratio. Therefore, for every mole of oxalic acid, two moles of NaOH are needed. Calculate the moles of oxalic acid:\[\text{moles of } \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} = \frac{0.016269}{2} = 0.0081345 \text{ mol} \]

Step 3: Calculate Mass of Oxalic Acid

Next, convert the moles of oxalic acid to grams using its molar mass. The molar mass of \( \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \) is approximately 90.03 g/mol. \[\text{mass of } \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} = 0.0081345 \times 90.03 = 0.73205 \text{ g} \]

Step 4: Calculate Mass Percent of Oxalic Acid

The mass percent of oxalic acid can be found using the formula: \[\text{mass percent} = \left( \frac{\text{mass of } \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}}{\text{total mass of mixture}} \right) \times 100 \]Substitute the known values:\[\text{mass percent} = \left( \frac{0.73205}{4.554} \right) \times 100 = 16.07\%\]

Key Concepts

Neutralization reaction

In chemistry, a neutralization reaction occurs when an acid and a base react to form water and a salt. In this particular scenario, we are dealing with oxalic acid \( \text{H}_2\text{C}_2\text{O}_4 \) being neutralized by sodium hydroxide \( \text{NaOH} \). The equation representing this reaction is:\[ \text{H}_2\text{C}_2\text{O}_4(\text{aq}) + 2\text{NaOH}(\text{aq}) \longrightarrow \text{Na}_2\text{C}_2\text{O}_4(\text{aq}) + 2\text{H}_2\text{O}(\ell) \]Here, oxalic acid reacts with two moles of sodium hydroxide. This key ratio of 1:2 is crucial because it tells us that it takes two moles of \( \text{NaOH} \) to completely neutralize one mole of \( \text{H}_2\text{C}_2\text{O}_4 \). Understanding this stoichiometry allows us to figure out how much of each reactant is required and what is produced by the reaction.
By knowing the precise amounts of reactants, it ensures the reaction goes to completion with no excess reactants other than neutralized products.

• Neutralization equations reveal the stoichiometry between reactants.
• 1 mole of oxalic acid is neutralized by 2 moles of sodium hydroxide.
• Products are water and sodium oxalate in this scenario.

Molarity calculations

Calculating molarity is an essential part of understanding solutions in chemistry. Molarity (M) is defined as the number of moles of a solute per liter of solution. The formula is:\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]In our exercise, we first need to determine the moles of sodium hydroxide used in the neutralization reaction. Given that we have a solution of \( 0.550 \text{ M} \text{NaOH} \) and a volume of \( 29.58 \text{ mL} \), it's important to convert this volume from milliliters to liters:\[ \text{Volume in liters} = \frac{29.58}{1000} = 0.02958 \text{ L} \]Then, using the formula for moles:\[ \text{moles of } \text{NaOH} = 0.550 \times 0.02958 = 0.016269 \text{ mol} \]This is crucial for understanding how molarity allows us to translate between the amount of solute in a solution and how it participates in a reaction. By using the balanced equation, we divide by two to find the moles of oxalic acid neutralized since the reaction is 1:2.

• Molarity indicates concentration, calculated as moles per liter.
• Accurate conversions between units are necessary (mL to L).
• Connects to stoichiometric coefficients in reactions.

Mass percent

Mass percent is a way to describe the concentration of a component in a mixture by comparing the mass of the component to the total mass of the mixture, expressed as a percentage. For the exercise, we're asked to find the mass percent of oxalic acid in the mixture.The formula for mass percent is:\[ \text{mass percent} = \left( \frac{\text{mass of component}}{\text{total mass of mixture}} \right) \times 100 \]To find this, we've already calculated the mass of oxalic acid as \( 0.73205 \text{ g} \). The total mass of the mixture given is \( 4.554 \text{ g} \). Plug into the formula:\[ \text{mass percent} = \left( \frac{0.73205}{4.554} \right) \times 100 = 16.07\% \]This calculation indicates how much of the given mixture is composed of oxalic acid, allowing us to determine whether our purification or mixture composition meets certain specifications or expectations. Understanding mass percent lets chemists quantify the purity or concentration of a compound within a mixture.

• Mass percent gives concentration of one part in a mixture.
• Reflects the ratio of a component to the whole in percentage terms.
• Helps assess purity and composition standards.