calculating weight per volume percent of ethanol in whiskey using back titration
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GPT-4o mini
To calculate the weight per volume percent of ethanol in whiskey through back titration, you would follow a procedure that involves several steps. Back titration is often used when the substance you want to measure doesn’t react quickly enough or is difficult to react directly. In the case of ethanol in whiskey, a common method involves the use of an oxidizing agent like potassium dichromate (\(K_2Cr_2O_7\)).
### Materials Needed:
- Whiskey sample
- Potassium dichromate solution (known concentration)
- Sulfuric acid (dilute)
- Standard solution of sodium thiosulfate (or any suitable reducing agent)
- Burette
- Pipette
- Conical flask
- Weighing balance
- Distillation apparatus (optional, for purity)
### General Procedure:
1. **Prepare the Sample:**
- If necessary, distill the whiskey sample to concentrate the ethanol and remove other components that may interfere.
2. **Oxidation Reaction:**
- Set up a reaction where a known volume of the whiskey sample is mixed with a known excess amount of potassium dichromate in acidic medium (sulfuric acid). The potassium dichromate will oxidize the ethanol in the whiskey.
3. **Reaction:**
- The main reaction can be simplified as follows:
\[
C_2H_5OH + K_2Cr_2O_7 + H_2SO_4 \rightarrow 2Cr^{3+} + 2CO_2 + 3H_2O + K_2SO_4
\]
4. **Back Titration:**
- After the oxidation reaction is complete, you would titrate the remaining unreacted potassium dichromate with a standard sodium thiosulfate solution. The reaction between thiosulfate and dichromate can be represented as:
\[
Cr_2O_7^{2-} + 6 e^- + 14 H^+ \rightarrow 2 Cr^{3+} + 7 H_2O
\]
5. **Calculate the Amount of Dichromate Reacted:**
- From the titration data, calculate the amount of potassium dichromate that reacted with the ethanol. This can be done using the volume of titrant used against the known concentration of the solutions.
6. **Calculate Moles of Ethanol:**
- Based on the stoichiometry of the reaction (1 mole of ethanol reacts with 1 mole of potassium dichromate), calculate the moles of ethanol that were present in the original whiskey sample.
7. **Determine Weight of Ethanol:**
- Use the molar mass of ethanol (\(C_2H_5OH\); approximately 46.07 g/mol) to convert moles of ethanol to grams.
8. **Calculate Weight/Volume Percent:**
- Finally, to find the weight per volume percent of ethanol in the whiskey, use the formula:
\[
\text{Weight/Volume Percent} = \left(\frac{\text{grams of ethanol}}{\text{volume of whiskey sample in mL}}\right) \times 100
\]
### Example Calculation:
1. If you started with 50 mL of whiskey and found that 0.025 M \(K_2Cr_2O_7\) reacted with 30 mL of sodium thiosulfate, which was 0.1 M, during back titration.
2. Calculate moles of thiosulfate used:
\[
\text{Moles of } Na_2S_2O_3 = \text{Volume (L)} \times \text{Concentration (mol/L)} = 0.030 \times 0.1 = 0.003
\]
3. Knowing the stoichiometry, if 6 moles of thiosulfate react with 1 mole of \(Cr_2O_7^{2-}\), the moles of \(Cr_2O_7^{2-}\) would be:
\[
\text{Moles of } Cr_2O_7^{2-} = \frac{0.003}{6} \approx 0.0005
\]
4. Calculate the moles of ethanol:
\[
\text{Moles of ethanol} = \text{Moles of } Cr_2O_7^{2-} = 0.0005
\]
5. Convert to grams:
\[
\text{Weight of ethanol} = 0.0005 \times 46.07 \approx 0.02304 \text{ grams}
\]
6. Finally, calculate weight/volume percent:
\[
\text{Weight/Volume Percent} = \left( \frac{0.02304 \text{ g}}{50 \text{ mL}} \right) \times 100 \approx 0.04608\%
\]
This example demonstrates how back titration can be effectively used to measure the ethanol concentration in whiskey, and you would adapt the amounts and concentrations based on your actual laboratory settings.
### Materials Needed:
- Whiskey sample
- Potassium dichromate solution (known concentration)
- Sulfuric acid (dilute)
- Standard solution of sodium thiosulfate (or any suitable reducing agent)
- Burette
- Pipette
- Conical flask
- Weighing balance
- Distillation apparatus (optional, for purity)
### General Procedure:
1. **Prepare the Sample:**
- If necessary, distill the whiskey sample to concentrate the ethanol and remove other components that may interfere.
2. **Oxidation Reaction:**
- Set up a reaction where a known volume of the whiskey sample is mixed with a known excess amount of potassium dichromate in acidic medium (sulfuric acid). The potassium dichromate will oxidize the ethanol in the whiskey.
3. **Reaction:**
- The main reaction can be simplified as follows:
\[
C_2H_5OH + K_2Cr_2O_7 + H_2SO_4 \rightarrow 2Cr^{3+} + 2CO_2 + 3H_2O + K_2SO_4
\]
4. **Back Titration:**
- After the oxidation reaction is complete, you would titrate the remaining unreacted potassium dichromate with a standard sodium thiosulfate solution. The reaction between thiosulfate and dichromate can be represented as:
\[
Cr_2O_7^{2-} + 6 e^- + 14 H^+ \rightarrow 2 Cr^{3+} + 7 H_2O
\]
5. **Calculate the Amount of Dichromate Reacted:**
- From the titration data, calculate the amount of potassium dichromate that reacted with the ethanol. This can be done using the volume of titrant used against the known concentration of the solutions.
6. **Calculate Moles of Ethanol:**
- Based on the stoichiometry of the reaction (1 mole of ethanol reacts with 1 mole of potassium dichromate), calculate the moles of ethanol that were present in the original whiskey sample.
7. **Determine Weight of Ethanol:**
- Use the molar mass of ethanol (\(C_2H_5OH\); approximately 46.07 g/mol) to convert moles of ethanol to grams.
8. **Calculate Weight/Volume Percent:**
- Finally, to find the weight per volume percent of ethanol in the whiskey, use the formula:
\[
\text{Weight/Volume Percent} = \left(\frac{\text{grams of ethanol}}{\text{volume of whiskey sample in mL}}\right) \times 100
\]
### Example Calculation:
1. If you started with 50 mL of whiskey and found that 0.025 M \(K_2Cr_2O_7\) reacted with 30 mL of sodium thiosulfate, which was 0.1 M, during back titration.
2. Calculate moles of thiosulfate used:
\[
\text{Moles of } Na_2S_2O_3 = \text{Volume (L)} \times \text{Concentration (mol/L)} = 0.030 \times 0.1 = 0.003
\]
3. Knowing the stoichiometry, if 6 moles of thiosulfate react with 1 mole of \(Cr_2O_7^{2-}\), the moles of \(Cr_2O_7^{2-}\) would be:
\[
\text{Moles of } Cr_2O_7^{2-} = \frac{0.003}{6} \approx 0.0005
\]
4. Calculate the moles of ethanol:
\[
\text{Moles of ethanol} = \text{Moles of } Cr_2O_7^{2-} = 0.0005
\]
5. Convert to grams:
\[
\text{Weight of ethanol} = 0.0005 \times 46.07 \approx 0.02304 \text{ grams}
\]
6. Finally, calculate weight/volume percent:
\[
\text{Weight/Volume Percent} = \left( \frac{0.02304 \text{ g}}{50 \text{ mL}} \right) \times 100 \approx 0.04608\%
\]
This example demonstrates how back titration can be effectively used to measure the ethanol concentration in whiskey, and you would adapt the amounts and concentrations based on your actual laboratory settings.