In the electrolysis of water, how long will it take to produce 1.000 × 102 L of H2 at STP (273 K and 1.00 bar) using an electrolytic cell through which a current of 51.50 mA flows?
In the electrolysis of water, how long will it take to produce 1.000 × 102 L of H2 at STP (273 K and 1.00 bar) using an electrolytic cell through which a current of 51.50 mA flows?
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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![**Title: Electrolysis of Water**
**Question:**
In the electrolysis of water, how long will it take to produce 1.000 × 10² L of H₂ at STP (273 K and 1.00 bar) using an electrolytic cell through which a current of 51.50 mA flows?
**Solution:**
To solve this problem, you need to follow these steps:
1. **Convert the volume of H₂ gas to moles of H₂:**
At STP (Standard Temperature and Pressure), 1 mole of gas occupies 22.414 liters. Hence:
\[
\text{Moles of } H_2 = \frac{\text{Volume of } H_2}{22.414 \text{ L/mol}} = \frac{1.000 \times 10^2 \text{ L}}{22.414 \text{ L/mol}}
\]
2. **Calculate the moles of electrons required:**
The reaction for the electrolysis of water is:
\[
2H_2O(l) \rightarrow 2H_2(g) + O_2(g)
\]
For every mole of \( H_2 \) produced, 2 moles of electrons are required. Hence, the moles of electrons required are:
\[
\text{Moles of electrons} = \text{Moles of } H_2 \times 2
\]
3. **Convert the moles of electrons to charge (Coulombs):**
Using Faraday's constant (1 mole of electrons = 96,485 C):
\[
\text{Charge (C)} = \text{Moles of electrons} \times 96,485 \text{ C/mol}
\]
4. **Calculate the time required:**
The time required can be found using the formula:
\[
\text{Time (s)} = \frac{\text{Charge (C)}}{\text{Current (A)}}
\]
Convert the current from mA to A:
\[
51.50 \text{ mA} = 0.05150 \text{ A}
\]
Combine all these steps to calculate the total time required for the electrolysis process.
By following the above steps carefully, you will be able to](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7e487533-50a5-4edd-80c5-edc489931218%2Fabe9a2a0-32bb-4c9a-9146-53d044a926b1%2Fb1fjx1i.png&w=3840&q=75)
Transcribed Image Text:**Title: Electrolysis of Water**
**Question:**
In the electrolysis of water, how long will it take to produce 1.000 × 10² L of H₂ at STP (273 K and 1.00 bar) using an electrolytic cell through which a current of 51.50 mA flows?
**Solution:**
To solve this problem, you need to follow these steps:
1. **Convert the volume of H₂ gas to moles of H₂:**
At STP (Standard Temperature and Pressure), 1 mole of gas occupies 22.414 liters. Hence:
\[
\text{Moles of } H_2 = \frac{\text{Volume of } H_2}{22.414 \text{ L/mol}} = \frac{1.000 \times 10^2 \text{ L}}{22.414 \text{ L/mol}}
\]
2. **Calculate the moles of electrons required:**
The reaction for the electrolysis of water is:
\[
2H_2O(l) \rightarrow 2H_2(g) + O_2(g)
\]
For every mole of \( H_2 \) produced, 2 moles of electrons are required. Hence, the moles of electrons required are:
\[
\text{Moles of electrons} = \text{Moles of } H_2 \times 2
\]
3. **Convert the moles of electrons to charge (Coulombs):**
Using Faraday's constant (1 mole of electrons = 96,485 C):
\[
\text{Charge (C)} = \text{Moles of electrons} \times 96,485 \text{ C/mol}
\]
4. **Calculate the time required:**
The time required can be found using the formula:
\[
\text{Time (s)} = \frac{\text{Charge (C)}}{\text{Current (A)}}
\]
Convert the current from mA to A:
\[
51.50 \text{ mA} = 0.05150 \text{ A}
\]
Combine all these steps to calculate the total time required for the electrolysis process.
By following the above steps carefully, you will be able to
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