Chapter 25: Problem 8
Current passes through a solution of sodium chloride. In 1.00 s, \(2.68 \times 10^{16}\) Na\({^+}\) ions arrive at the negative electrode and \(3.92 \times 10^{16}\) Cl\({^-}\) ions arrive at the positive electrode. (a) What is the current passing between the electrodes? (b) What is the direction of the current?
Short Answer
Step by step solution
Understanding the Problem
Calculate Charge for Na+ Ions
Calculate Charge for Cl- Ions
Sum Total Charge Transferred
Calculate Current
Determine Direction of Current
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Electrical Current Calculation
To determine the current, we first need to calculate the total charge being transferred by the sodium (Na\(^+\)) and chloride (Cl\(^-\)) ions. We can do this by multiplying the number of ions by the charge of a single ion. The charge of one ion, equivalent to the elementary charge, is approximately 1.602 x 10\(^{-19}\) coulombs. By knowing how many ions reach each electrode, you can multiply this amount by the charge per ion to find the total charge.
Finally, current is calculated by dividing this total charge by time. In this case, the time is 1 second. Hence, using the formula:where \(Q\) is the total charge and \(t\) is the time duration. Plug in the values to get the current flowing between the electrodes.
Ion Charge
For sodium (Na\(^+\)) and chloride (Cl\(^-\)) ions, the individual charge corresponds to approximately 1.602 x 10\(^{-19}\) coulombs. This charge is similar for most singly charged ions, which is dictated by the fundamental properties of electrons and protons.
- Positive Ions (Cations): They move towards the negative electrode (cathode) during electrolysis.
- Negative Ions (Anions): They move towards the positive electrode (anode) during the process.
Electrode Reaction
During electrolysis of a sodium chloride solution:
- At the cathode (negative electrode), sodium ions (Na\(^+\)) gain electrons (reduction reaction) to form neutral sodium atoms.
- At the anode (positive electrode), chloride ions (Cl\(^-\)) lose electrons (oxidation reaction), forming chlorine gas.
Current Direction
Specifically, in the context of electrolysis:
- Sodium ions (Na\(^+\)) migrate towards the cathode. Their movement creates a positive current directed from the anode to the cathode.
- The flow of negative chloride ions (Cl\(^-\)) supplements this by moving toward the anode, further emphasizing the current direction.