Question

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

(a) Current is approximately 0.010 C/s or 10 mA. (b) The direction is from positive to negative electrode.

Step-by-step solution

Understanding the Problem

We need to find the current passing between electrodes when sodium chloride ions move during electrolysis. We'll find the total charge transferred and use it to calculate the current.

Calculate Charge for Na+ Ions

The charge of one Na"+" ion is equal to the elementary charge, approximately 1.602 x 10^{-19} coulombs. To find the total charge of Na"+" ions, we multiply the number of ions by the charge per ion: \( 2.68 \times 10^{16} \times 1.602 \times 10^{-19} \).

Calculate Charge for Cl- Ions

Similarly, the charge of one Cl"-" ion is also approximately 1.602 x 10^{-19} coulombs. For Cl"-" ions, we calculate the total charge using the same method: \( 3.92 \times 10^{16} \times 1.602 \times 10^{-19} \).

Sum Total Charge Transferred

Add the charges from both Na"+" and Cl"-" ions to find the total charge transferred in 1 second. Use \( \text{Total Charge} = \text{Charge from Na}^+ + \text{Charge from Cl}^- \).

Calculate Current

Current is defined as the total charge transferred per unit time. Since we know the total charge in coulombs and the time is 1 second, use the formula \( I = \frac{Q}{t} = \frac{\text{Total Charge}}{1} \).

Determine Direction of Current

By convention, current direction is defined as the flow of positive charge. Since Na"+" ions move towards the negative electrode, the current direction is from the positive to the negative electrode.

Key concepts

Electrical Current Calculation

One fundamental aspect of electrolysis is understanding how to calculate the electrical current flowing between the electrodes. Electrical current is essentially the flow of electric charge. In this exercise, we are looking to find the current in a cell where sodium chloride solution is electrolyzed.

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:

• \( I = \frac{Q}{t} \)

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

Ion charge is a crucial component in understanding electrolysis and current calculation processes. Each ion, whether positive or negative, carries a specific charge magnitude linked directly to the elementary 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.

By understanding the charge value and multiplying it with the number of ions, you determine the total charge moved by those ions in the electrolysis process.

Electrode Reaction

Electrode reactions are key parts of the electrolysis process that take place at each electrode, driving the movement of ions.

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.

These reactions occur due to the pull of the voltage applied across the electrodes, encouraging the ions to move towards the oppositely charged electrode. Understanding these reactions is important to predict the products formed during electrolysis and to balance the charge flow in the system.

Current Direction

The direction of the current in electrolysis may initially seem confusing, but it follows a simple convention: current is defined as the flow of positive charge. Thus, regardless of the electron movement, the direction of conventional current is from positive to negative within the external circuit.

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.

Understanding the direction of current is essential for accurately describing the entire electrolysis process and predicting the effects of electrode activity.