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An unknown solid acid is either citric acid or tartaric acid. To determine which acid you have, you titrate a sample of the solid with aqueous \(\mathrm{NaOH}\) and from this determine the molar mass of the unknown acid. The appropriate equations are as follows: Citric acid: $$\begin{aligned}\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(\mathrm{aq})+3 \mathrm{NaOH}(\mathrm{aq}) & \rightarrow \\ 3 \mathrm{H}_{2} \mathrm{O}(\ell) &+\mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(\mathrm{aq}) \end{aligned}$$ Tartaric acid: $$\begin{aligned}\mathrm{H}_{2} \mathrm{C}_{4} \mathrm{H}_{4} \mathrm{O}_{6}(\mathrm{aq})+2 \mathrm{NaOH}(\mathrm{aq}) \rightarrow & \\\2 \mathrm{H}_{2} \mathrm{O}(\ell) &+\mathrm{Na}_{2} \mathrm{C}_{4} \mathrm{H}_{4} \mathrm{O}_{6}(\mathrm{aq})\end{aligned}$$ A \(0.956-\mathrm{g}\) sample requires \(29.1 \mathrm{mL}\) of \(0.513 \mathrm{M}\) NaOH to consume the acid completely. What is the unknown acid?

Step by step solution

01

Calculate Moles of NaOH Used

First, determine the moles of NaOH used in the titration. We know that moles are calculated as \( ext{moles} = ext{molarity} \times ext{volume} \). Here, the molarity of \( ext{NaOH} \) is \( 0.513 \text{M} \), and the volume is \( 29.1 \text{mL} = 0.0291 \text{L} \). Thus, the moles of \( ext{NaOH} \) used is \( 0.513 \text{M} \times 0.0291 \text{L} = 0.0149223 \text{mol} \).

02

Determine Moles of Acid Reacted

Use the stoichiometry of the reactions to find the moles of the unknown acid. Depending on whether it's citric or tartaric acid, the stoichiometry is different: - For citric acid: \( ext{moles of acid} = \frac{0.0149223 \text{mol NaOH}}{3} = 0.0049741 \text{mol} \).- For tartaric acid: \( ext{moles of acid} = \frac{0.0149223 \text{mol NaOH}}{2} = 0.00746115 \text{mol} \).

03

Calculate Molar Mass of the Unknown Acid

Calculate the molar mass (g/mol) of the unknown acid by dividing the weight of the sample by the moles calculated.- Assuming it is citric acid: \[ ext{Molar Mass} = \frac{0.956 \text{g}}{0.0049741 \text{mol}} = 192.255 \text{g/mol} \]- Assuming it is tartaric acid: \[ ext{Molar Mass} = \frac{0.956 \text{g}}{0.00746115 \text{mol}} = 128.129 \text{g/mol} \]

04

Compare Molar Mass with Known Values

Citric acid has a molar mass of \( 192.13 \text{g/mol} \) and tartaric acid has a molar mass of \( 150.09 \text{g/mol} \). Compare these with the calculated values above. The calculated molar mass closer to 192.13 g/mol suggests the sample is likely citric acid.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Molar Mass Calculation

Molar mass is a fundamental concept in chemistry that helps us understand the weight of one mole of a particular substance. In this exercise, determining the molar mass of the unknown acid allows us to identify it. To find the molar mass, the basic formula used is:\[ \text{Molar Mass} = \frac{\text{Mass of the Sample (in grams)}}{\text{Moles of the Sample}} \]

• Start by calculating the number of moles involved in the reaction. Here, stoichiometry has helped determine the moles of the acid based on the moles of NaOH used during titration.
• Given a sample mass, you then divide this mass by the number of moles obtained to find the molar mass.
• In this problem, different stoichiometric relationships were used for citric acid and tartaric acid, leading to different molar mass results.

Consistency between the calculated molar mass and the known molar mass of a substance helps confirm the identity of the substance. In this exercise, the calculated molar mass closer to 192 g/mol helped identify the unknown acid as citric acid.

Acid-Base Reaction

An acid-base reaction is a chemical process that generally involves the transfer of hydrogen ions between an acid and a base. During a titration, this type of reaction allows us to determine the concentration or amount of an unknown substance. In this particular exercise, the reaction between NaOH (a base) and the unknown solid acid (either citric or tartaric acid) illustrates how acids and bases interact.

• The citric acid reaction has the equation: \[\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7} + 3 \mathrm{NaOH} \rightarrow 3 \mathrm{H}_{2} \mathrm{O} + \mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7} \]
• The tartaric acid reaction is: \[\mathrm{H}_{2} \mathrm{C}_{4} \mathrm{H}_{4} \mathrm{O}_{6} + 2 \mathrm{NaOH} \rightarrow 2 \mathrm{H}_{2} \mathrm{O} + \mathrm{Na}_{2} \mathrm{C}_{4} \mathrm{H}_{4} \mathrm{O}_{6} \]

In practical terms, these reactions allow us to determine the unknown acid by examining how it reacts with a known base. The number of NaOH moles required to neutralize the acid can be calculated, providing a clear path to the molar mass computation.

Stoichiometry

Stoichiometry is the study of the quantitative relationships within a chemical reaction. By understanding stoichiometry, you can predict how much product can be formed in a reaction and determine the amounts of each reactant needed. In this exercise:

• The stoichiometric coefficients in the equations indicate the ratio of reactants to products, which tells us how many moles of NaOH are needed to neutralize the acid completely.
• For citric acid, the ratio is 1:3, meaning one mole of acid reacts with three moles of NaOH.
• For tartaric acid, the ratio is 1:2, showing one mole of acid reacts with two moles of NaOH.

By understanding these ratios, the problem solver can straightforwardly find how many moles of the acid reacted with a given volume and molarity of NaOH. This forms the basis for determining the further steps in identifying the unknown acid. This type of calculation exemplifies how stoichiometry connects with real-world chemistry tasks, providing crucial insights into chemical compositions and reactions.