Problem 112 - Chemistry The Molecular Science

Question

You are given an acid and told only that it could be citric acid (molar mass \(=192.1 \mathrm{~g} / \mathrm{mol}\) ) or tartaric acid (molar mass \(=150.1 \mathrm{~g} / \mathrm{mol}\) ). To determine which acid you have, you react it with \(\mathrm{NaOH}\). The appropriate reactions are Citric acid: \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7}(\mathrm{aq})+3 \mathrm{NaOH}(\mathrm{aq}) \longrightarrow\) $$\mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(\mathrm{aq})+3 \mathrm{H}_{2} \mathrm{O}(\ell)$$ Tartaric acid: \(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{6}(\mathrm{aq})+2 \mathrm{NaOH}(\mathrm{aq}) \longrightarrow\) $$\mathrm{Na}_{2} \mathrm{C}_{4} \mathrm{H}_{4} \mathrm{O}_{6}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\ell)$$ You find that a \(0.956-\mathrm{g}\) sample requires \(29.1 \mathrm{~mL}\) of \(0.513-\mathrm{M} \mathrm{NaOH}\) to reach the equivalence point. Determine which is the unknown acid.

Step-by-Step Solution

Answer

The unknown acid is citric acid.

Step 1: Calculate the moles of NaOH used

First, calculate the number of moles of NaOH used in the titration. Use the formula: \( \text{moles of } \text{NaOH} = M \times V \), where \( M \) is the molarity and \( V \) is the volume in liters.\[ \text{moles of } \text{NaOH} = 0.513\ \text{mol/L} \times 0.0291\ \text{L} = 0.01493\ \text{mol} \]

Step 2: Relate moles of NaOH to moles of acid

Determine how many moles of the acid reacted based on the balanced reaction equations. For citric acid, 3 moles of NaOH react with 1 mole of citric acid; for tartaric acid, 2 moles of NaOH react with 1 mole of tartaric acid.

Step 3: Calculate the moles of citric acid

Use the moles of NaOH to find the moles of citric acid. Divide the moles of NaOH by 3 (as per its reaction): \[ \text{moles of citric acid} = \frac{0.01493\ \text{mol NaOH}}{3} = 0.004977\ \text{mol citric acid} \]

Step 4: Calculate the moles of tartaric acid

For tartaric acid, divide the moles of NaOH by 2 (as per its reaction): \[ \text{moles of tartaric acid} = \frac{0.01493\ \text{mol NaOH}}{2} = 0.007465\ \text{mol tartaric acid} \]

Step 5: Calculate the masses of possible acids and compare

Calculate the mass of each possible acid by using the respective molar masses: - For citric acid, \[ \text{mass} = 0.004977\ \text{mol} \times 192.1\ \text{g/mol} = 0.955\ \text{g} \]- For tartaric acid, \[ \text{mass} = 0.007465\ \text{mol} \times 150.1\ \text{g/mol} = 1.120\ \text{g} \]Compare the calculated masses with the given mass of the sample, 0.956 g.

Step 6: Determine the identity of the acid

The calculated mass of citric acid (0.955 g) closely matches the given sample mass of 0.956 g, whereas tartaric acid gives a much higher mass (1.120 g). Therefore, the unknown acid is citric acid.

Key Concepts

Citric Acid

Citric acid is a weak organic acid commonly found in citrus fruits such as lemons and oranges. It has the chemical formula \(C_6H_8O_7\). In the context of an acid-base titration, citric acid is significant due to its ability to donate three protons (\(H^+\) ions) to a base. When it reacts with sodium hydroxide (\(NaOH\)), the reaction is:

• \( ext{C}_6 ext{H}_8 ext{O}_7(aq) + 3 ext{NaOH}(aq) \rightarrow ext{Na}_3 ext{C}_6 ext{H}_5 ext{O}_7(aq) + 3 ext{H}_2 ext{O}(l) \)

This stoichiometry allows us to write that 3 moles of \(NaOH\) are required to neutralize 1 mole of citric acid.
In titration, the point where all acid has been exactly neutralized by the base is called the equivalence point. This characteristic feature allows us to use citric acid effectively to determine the concentration of a base or to identify citric acid if its identity is unknown.

Tartaric Acid

Tartaric acid, with the chemical formula \(C_4H_6O_6\), is another weak organic acid that is often found in grapes and bananas. It is a diprotic acid, meaning it can donate two protons (\(H^+\) ions). When it reacts with sodium hydroxide, the chemical reaction is:

• \( ext{C}_4 ext{H}_6 ext{O}_6(aq) + 2 ext{NaOH}(aq) \rightarrow ext{Na}_2 ext{C}_4 ext{H}_4 ext{O}_6(aq) + 2 ext{H}_2 ext{O}(l) \)

This reaction indicates that 2 moles of \(NaOH\) are necessary to neutralize 1 mole of tartaric acid.
Both citric and tartaric acids are useful in chemistry for titrations due to their predictable and distinct stoichiometric ratios. They are also used in various food and industrial applications for their acidulating properties.

Molar Mass Calculation

Molar mass, often referred to as molecular weight, is a measure of the amount of mass contained in one mole of a substance. It is measured in grams per mole (\( ext{g/mol}\)). For organic acids like citric acid and tartaric acid, molar masses are critical in titration calculations.
In a titration problem like this, molar mass of citric acid is \(192.1 ext{ g/mol}\), and for tartaric acid it is \(150.1 ext{ g/mol}\). These values are essential because they allow us to relate moles of the acid to its actual mass.
By calculating the mass of the acid from the moles determined during the titration, we can compare it to the given mass to confirm which acid is present. Accurate molar mass calculations ensure precise results in such experiments.

Equivalence Point

The equivalence point in an acid-base titration is a crucial concept as it signifies the moment when the number of moles of acid equals the number of moles of base added. At this point, the solution is neutralized.
For citric acid, reaching the equivalence point would mean having added enough \(NaOH\) to react with all three protons it can donate. This is calculated by using known amounts of the reactants.
It's important to note that the equivalence point might not always align with the endpoint, which is a measurable color change due to an indicator. Proper interpretation of the equivalence point allows for accurate determination of the unknown substance in a titration experiment.

Stoichiometry

Stoichiometry is the area of chemistry that involves calculating the relative quantities of reactants and products in chemical reactions. It is based on the conservation of mass principles and the concept of moles.
In the context of our acid-base titration, stoichiometry helps us understand how many moles of \(NaOH\) are needed to completely react with each mole of the acid. For citric acid, the stoichiometric ratio is 3:1, meaning it takes 3 moles of \(NaOH\) to neutralize 1 mole of citric acid.

• Citric Acid ratio: 3 \(NaOH\): 1 \(C_6H_8O_7\)
• Tartaric Acid ratio: 2 \(NaOH\): 1 \(C_4H_6O_6\)

Understanding these ratios is key to determining the correct mole calculations, which help in identifying the unknown acid based on the volume and concentration of \(NaOH\) used during the titration.