It took 116 hours to produce 603 g of metal X by performing electrolysis on molten XC13 with a current of 2.00 A. Calculate the molar mass of X.
It took 116 hours to produce 603 g of metal X by performing electrolysis on molten XC13 with a current of 2.00 A. Calculate the molar mass of X.
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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![**Electrolysis Calculation to Determine Molar Mass**
**Problem Statement:**
It took 116 hours to produce 603 g of metal X by performing electrolysis on molten XCl₃ with a current of 2.00 A. Calculate the molar mass of X.
**Solution Approach:**
To determine the molar mass of metal X, we will go through the following steps:
1. **Determine the total charge passed:**
- Use the formula \( Q = I \times t \)
- Where \( Q \) is the charge in Coulombs (C), \( I \) is the current in Amperes (A), and \( t \) is the time in seconds (s).
2. **Convert the time:**
- Time given in hours needs to be converted to seconds:
\[ t = 116 \text{ hours} \times 3600 \text{ seconds/hour} \]
3. **Calculate the total charge (Q):**
- Using the current (I = 2.00 A):
\[ Q = 2.00 \text{ A} \times 116 \text{ hours} \times 3600 \text{ s/hour} \]
4. **Use Faraday's Law:**
- Faraday's law of electrolysis relates the amount of substance to the charge passed through the electrolyte:
\[ Q = n \times z \times F \]
- Where \( n \) is the number of moles of substance, \( z \) is the number of moles of electrons, and \( F \) is Faraday’s constant (\( 96485 \text{ C/mol} \)).
5. **Determine moles of X:**
- Knowing \( z = 3 \) (since the compound is XCl₃):
\[ n = \frac{Q}{z \times F} \]
6. **Calculate the molar mass:**
- Using the mass produced (603 g), calculate the moles of X:
\[ \text{Molar Mass (M)} = \frac{\text{mass}}{n} \]
By following these steps, students can calculate the molar mass of the metal X produced through the electrolysis process.
**Note:**
This method highlights the principles of electrolysis and stoichiometric calculations in physical chemistry.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F43ef5448-495e-49e8-9cec-405cabc5c22f%2F1b175c72-6be4-49f9-a1f0-0fa5239bbe7a%2Fvv888tf.jpeg&w=3840&q=75)
Transcribed Image Text:**Electrolysis Calculation to Determine Molar Mass**
**Problem Statement:**
It took 116 hours to produce 603 g of metal X by performing electrolysis on molten XCl₃ with a current of 2.00 A. Calculate the molar mass of X.
**Solution Approach:**
To determine the molar mass of metal X, we will go through the following steps:
1. **Determine the total charge passed:**
- Use the formula \( Q = I \times t \)
- Where \( Q \) is the charge in Coulombs (C), \( I \) is the current in Amperes (A), and \( t \) is the time in seconds (s).
2. **Convert the time:**
- Time given in hours needs to be converted to seconds:
\[ t = 116 \text{ hours} \times 3600 \text{ seconds/hour} \]
3. **Calculate the total charge (Q):**
- Using the current (I = 2.00 A):
\[ Q = 2.00 \text{ A} \times 116 \text{ hours} \times 3600 \text{ s/hour} \]
4. **Use Faraday's Law:**
- Faraday's law of electrolysis relates the amount of substance to the charge passed through the electrolyte:
\[ Q = n \times z \times F \]
- Where \( n \) is the number of moles of substance, \( z \) is the number of moles of electrons, and \( F \) is Faraday’s constant (\( 96485 \text{ C/mol} \)).
5. **Determine moles of X:**
- Knowing \( z = 3 \) (since the compound is XCl₃):
\[ n = \frac{Q}{z \times F} \]
6. **Calculate the molar mass:**
- Using the mass produced (603 g), calculate the moles of X:
\[ \text{Molar Mass (M)} = \frac{\text{mass}}{n} \]
By following these steps, students can calculate the molar mass of the metal X produced through the electrolysis process.
**Note:**
This method highlights the principles of electrolysis and stoichiometric calculations in physical chemistry.
Transcribed Image Text:# Standard Reduction Potentials
The table below provides a comprehensive list of standard reduction potentials for various redox couples. These potentials are measured in volts (V) and provide insight into the tendency of a species to gain electrons (reduce) compared to the standard hydrogen electrode (SHE), which is assigned a potential of 0.00 V.
## Standard Reduction Potentials Table
### Left Column
| Couple | \(E^0\) (Volts) |
|-----------------------|-----------------|
| F2 ↔ HF (H+) | +3.03 |
| F2 ↔ F- | +2.87 |
| S2O8^2- ↔ SO4^2- | +2.05 |
| BiO3^- ↔ Bi^3+ | +2.0 |
| H2O2 ↔ H2O (H+) | +1.78 |
| PbO2 ↔ PbSO4 (H+, SO4^2-) | +1.685 |
| Ce^4+ ↔ Ce^3+ | +1.61 |
| MnO4^- ↔ Mn2+ (H+) | +1.491 |
| ClO3^- ↔ Cl^- | +1.47 |
| PbO2 ↔ Pb2+ (H+) | +1.46 |
| Au^3+ ↔ Au | +1.42 |
| Cl2 ↔ Cl^- | +1.358 |
| Cr2O7^2- ↔ Cr^3+ (H+) | +1.33 |
| MnO2 ↔ Mn2+ (H+) | +1.28 |
| O2 ↔ H2O2 (H2O) | +1.229 |
| Br2 ↔ Br^- | +1.065 |
| NO3^- ↔ NO (H+) | +0.96 |
| Hg2^2+ ↔ Hg2^2+ | +0.910 |
| H2O2 ↔ OH^- | +0.87 |
| O2 ↔ H2O (pH = 7)
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