Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
To determine the empirical formula of sorbic acid, follow these steps:
1. Determine the moles of Carbon in CO₂:
Given mass of CO₂: \(2.053 \, \text{g}\)
Molar mass of CO₂ \( \left( \text{C} + 2 \text{O} \right) \):
\( 12.01 \, \text{g/mol (C)} + 2 \times 16.00 \, \text{g/mol (O)} = 44.01 \, \text{g/mol} \)
Moles of Carbon in CO₂:
[tex]\[ \text{Moles of C} = \frac{2.053 \, \text{g}}{44.01 \, \text{g/mol}} \approx 0.04665 \, \text{mol} \][/tex]
2. Determine the moles of Hydrogen in H₂O:
Given mass of H₂O: \(0.5601 \, \text{g}\)
Molar mass of H₂O \( \left( 2 \text{H} + \text{O} \right) \):
\( 2 \times 1.008 \, \text{g/mol (H)} + 16.00 \, \text{g/mol (O)} = 18.016 \, \text{g/mol} \)
Moles of Hydrogen in H₂O:
[tex]\[ \text{Moles of H} = \frac{0.5601 \, \text{g}}{18.016 \, \text{g/mol}} \times 2 \approx 0.06211 \, \text{mol} \][/tex]
3. Determine the moles of Oxygen:
First, calculate the mass of C and H in the sample:
Mass of Carbon:
[tex]\[ \text{Mass of C} = 0.04665 \, \text{mol} \times 12.01 \, \text{g/mol} \approx 0.560 \, \text{g} \][/tex]
Mass of Hydrogen:
[tex]\[ \text{Mass of H} = 0.06211 \, \text{mol} \times 1.008 \, \text{g/mol} \approx 0.063 \, \text{g} \][/tex]
Total mass of C and H:
[tex]\[ \text{Mass of C + Mass of H} = 0.560 \, \text{g} + 0.063 \, \text{g} = 0.623 \, \text{g} \][/tex]
Given mass of sample: \(0.8715 \, \text{g}\)
Mass of Oxygen in the sample:
[tex]\[ \text{Mass of O} = 0.8715 \, \text{g} - 0.623 \, \text{g} = 0.2485 \, \text{g} \][/tex]
Moles of Oxygen:
[tex]\[ \text{Moles of O} = \frac{0.2485 \, \text{g}}{16.00 \, \text{g/mol}} \approx 0.01553 \, \text{mol} \][/tex]
4. Determine the molar ratio:
Compare the smallest moles to get the empirical formula:
- Moles of C: \(0.04665 \approx 3.0026\)
- Moles of H: \(0.06211 \approx 4.0022\)
- Moles of O: \(0.01553 = 1\)
(Ratios are calculated based on smallest moles of O.)
Therefore, the ratio is:
[tex]\[ \text{C} : \text{H} : \text{O} = 3.0026 : 4.0022 : 1 \][/tex]
5. Empirical formula:
Round to the nearest whole number:
[tex]\[ \text{C} : \text{H} : \text{O} = 3 : 4 : 1 \][/tex]
Hence, the empirical formula of sorbic acid is [tex]\(\text{C}_3\text{H}_4\text{O}\)[/tex], which matches choice (b).
1. Determine the moles of Carbon in CO₂:
Given mass of CO₂: \(2.053 \, \text{g}\)
Molar mass of CO₂ \( \left( \text{C} + 2 \text{O} \right) \):
\( 12.01 \, \text{g/mol (C)} + 2 \times 16.00 \, \text{g/mol (O)} = 44.01 \, \text{g/mol} \)
Moles of Carbon in CO₂:
[tex]\[ \text{Moles of C} = \frac{2.053 \, \text{g}}{44.01 \, \text{g/mol}} \approx 0.04665 \, \text{mol} \][/tex]
2. Determine the moles of Hydrogen in H₂O:
Given mass of H₂O: \(0.5601 \, \text{g}\)
Molar mass of H₂O \( \left( 2 \text{H} + \text{O} \right) \):
\( 2 \times 1.008 \, \text{g/mol (H)} + 16.00 \, \text{g/mol (O)} = 18.016 \, \text{g/mol} \)
Moles of Hydrogen in H₂O:
[tex]\[ \text{Moles of H} = \frac{0.5601 \, \text{g}}{18.016 \, \text{g/mol}} \times 2 \approx 0.06211 \, \text{mol} \][/tex]
3. Determine the moles of Oxygen:
First, calculate the mass of C and H in the sample:
Mass of Carbon:
[tex]\[ \text{Mass of C} = 0.04665 \, \text{mol} \times 12.01 \, \text{g/mol} \approx 0.560 \, \text{g} \][/tex]
Mass of Hydrogen:
[tex]\[ \text{Mass of H} = 0.06211 \, \text{mol} \times 1.008 \, \text{g/mol} \approx 0.063 \, \text{g} \][/tex]
Total mass of C and H:
[tex]\[ \text{Mass of C + Mass of H} = 0.560 \, \text{g} + 0.063 \, \text{g} = 0.623 \, \text{g} \][/tex]
Given mass of sample: \(0.8715 \, \text{g}\)
Mass of Oxygen in the sample:
[tex]\[ \text{Mass of O} = 0.8715 \, \text{g} - 0.623 \, \text{g} = 0.2485 \, \text{g} \][/tex]
Moles of Oxygen:
[tex]\[ \text{Moles of O} = \frac{0.2485 \, \text{g}}{16.00 \, \text{g/mol}} \approx 0.01553 \, \text{mol} \][/tex]
4. Determine the molar ratio:
Compare the smallest moles to get the empirical formula:
- Moles of C: \(0.04665 \approx 3.0026\)
- Moles of H: \(0.06211 \approx 4.0022\)
- Moles of O: \(0.01553 = 1\)
(Ratios are calculated based on smallest moles of O.)
Therefore, the ratio is:
[tex]\[ \text{C} : \text{H} : \text{O} = 3.0026 : 4.0022 : 1 \][/tex]
5. Empirical formula:
Round to the nearest whole number:
[tex]\[ \text{C} : \text{H} : \text{O} = 3 : 4 : 1 \][/tex]
Hence, the empirical formula of sorbic acid is [tex]\(\text{C}_3\text{H}_4\text{O}\)[/tex], which matches choice (b).
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
