You might need:
Calculator
Problem
An electrolyte solution has an average current density of
\[1\] ampere per square decimeter

\[\left( \dfrac{\text{A}}{\text{dm}^2}\right)\].
What is the current density of the solution in

\[\dfrac{\text{A}}{\text{m}^2}\]?

\[\dfrac{\text{A}}{\text{m}^2}\]

To convert the current density from \(\dfrac{\text{A}}{\text{dm}^2}\) to \(\dfrac{\text{A}}{\text{m}^2}\), we need to understand the relationship between square decimeters (\(\text{dm}^2\)) and square meters (\(\text{m}^2\)).

1. A decimeter (\(\text{dm}\)) is \(0.1\) meters (\(\text{m}\)).
2. Therefore, a square decimeter (\(\text{dm}^2\)) is:
   \[
   (0.1 \, \text{m})^2 = 0.01 \, \text{m}^2
   \]

This means that:
\[
1 \, \text{dm}^2 = 0.01 \, \text{m}^2
\]

To convert the current density from \(\dfrac{\text{A}}{\text{dm}^2}\) to \(\dfrac{\text{A}}{\text{m}^2}\), we use the following conversion factor:
\[
1 \, \dfrac{\text{A}}{\text{dm}^2} = \dfrac{\text{A}}{0.01 \, \text{m}^2} = 100 \, \dfrac{\text{A}}{\text{m}^2}
\]

Therefore, the current density of the solution in \(\dfrac{\text{A}}{\text{m}^2}\) is:
\[
100 \, \dfrac{\text{A}}{\text{m}^2}
\]

Would you like further details or have any questions?

Here are some related questions for further exploration:

1. What is the definition of current density and how is it measured?
2. How do you convert other units of area, such as square centimeters to square meters?
3. What is the significance of current density in an electrolyte solution?
4. How does current density affect the conductivity of an electrolyte?
5. Can you convert \(\dfrac{\text{A}}{\text{cm}^2}\) to \(\dfrac{\text{A}}{\text{m}^2}\)?
6. How does the surface area of electrodes impact the current density in electrochemical cells?
7. What are some practical applications of measuring current density in electrochemistry?
8. How does temperature influence the current density in an electrolyte solution?

**Tip:** Always double-check unit conversions by confirming the relationship between units, especially when dealing with squared or cubed measurements.

Learn how to convert current density from ampere per square decimeter to ampere per square meter with a detailed explanation. This problem involves unit conversion and area measurement, essential for physics and chemistry students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation