/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 50 In an ionic solution, a current ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 25: Problem 50

In an ionic solution, a current consists of Ca\(^2+\) ions (of charge \(+2e\)) and Cl\(^-\) ions (of charge \(-e\)) traveling in opposite directions. If \(5.11 \times 1018\) Cl\(^-\) ions go from \(A\) to \(B\) every 0.50 min, while 3.24 \(\times\) 10\(^{18}\) Ca\(^2+\) ions move from \(B\) to \(A\), what is the current (in mA) through this solution, and in which direction (from \(A\) to \(B\) or from \(B\) to \(A\)) is it going?

Short Answer

Expert verified
The current is approximately 0.752 mA, directed from A to B.

Step by step solution

01

Calculate Charge of Cl- ions

The charge on one Cl\(^-\) ion is \(-e\), where \(e\) is the elementary charge \(1.6 \times 10^{-19} \text{ C}\). The total charge from Cl\(^-\) ions is \(-5.11 \times 10^{18} \times 1.6 \times 10^{-19} \text{ C}\).
02

Calculate Charge of Ca2+ ions

The charge on one Ca\(^{2+}\) ion is \(+2e\). Therefore, the total charge from Ca\(^{2+}\) ions is \(3.24 \times 10^{18} \times 2 \times 1.6 \times 10^{-19} \text{ C}\).
03

Calculate Total Charge Exchange

Since Cl\(^-\) ions and Ca\(^{2+}\) ions move in opposite directions, their charges will add up when calculating the current: \(Q_{\text{total}} = -5.11 \times 10^{18} \times 1.6 \times 10^{-19} + 3.24 \times 10^{18} \times 2 \times 1.6 \times 10^{-19}\).
04

Convert Time Units

Convert 0.50 minutes to seconds: \(0.50 \times 60 = 30 \text{ seconds}\).
05

Calculate Current

The current \(I\) is found by dividing the total charge by the time in seconds: \(I = \frac{Q_{\text{total}}}{30} \text{ A}\).
06

Determine Current Direction

Since the overall charge is positive, the current direction is from \(A\) to \(B\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Ionic Charge Calculation
In the context of ionic solutions, understanding the calculation of ionic charges is crucial. Let's break it down:
  • Individual Charge: Each ion in a solution has a specific charge based on the type of ion. In our example, the Cl\(^-\) ion possesses a charge of \(-e\), where \(e\) represents the elementary charge, or \(1.6 \times 10^{-19} \text{ C}\). The Ca\(^{2+}\) ion holds a charge of \(+2e\).
  • Total Charge for Multiple Ions: To determine the total charge contributed by an entire set of ions, multiply the number of these ions by the charge of a single ion. For instance, 5.11 \(\times 10^{18}\) Cl\(^-\) ions collectively have a charge of \(-5.11 \times 10^{18} \times 1.6 \times 10^{-19} \text{ C}\).
  • Combining Charges: When calculating total charge exchange, consider the direction of ion movement. Opposite charges and directions result in the summation of charges, reflecting the total charge flow in the solution.
Understanding these basics allows you to calculate how much charge ions contribute to a current, an essential step in evaluating the current through a solution.
Current Direction
The direction of current in an ionic solution is determined by calculating the net charge movement resulting from all participating ions. It's typically seen that:
  • The charge carriers (ions) lose or gain electrons, leading to a movement which constitutes the electric current.
  • In solutions with ions moving in opposite directions, the overall current direction is aligned with the net positive charge movement.
  • For the given problem:
    • Cl\(^-\) ions move from \(A\) to \(B\), carrying negative charge;
    • Ca\(^{2+}\) ions move from \(B\) to \(A\), carrying positive charge.
  • After computing the resultant charges, if the total charge is positive, as in our example, the current flows from \(A\) to \(B\).
Recognizing current direction is critical as it influences how circuits and systems are designed and analyzed.
Time Conversion in Physics
Time conversion is a key skill in physics, especially when dealing with rates of change like current, which is defined as charge per unit time. Here's a breakdown:
  • Units and Relevance: Time in physics is often measured in seconds because it is part of the International System of Units (SI). Most formulas, particularly those involving electrical current, utilize seconds.
  • Converting Units: When time is given in units like minutes or hours, it needs conversion to seconds to align with SI units. The conversion rate from minutes to seconds, for instance, is \(1 \text{ minute} = 60 \text{ seconds}\).
  • Application: In our case, 0.50 minutes must be converted to 30 seconds. This step is vital to correctly calculate the current (in Amperes), using the formula \(I = \frac{Q_{\text{total}}}{t}\), where \(t\) is in seconds.
By mastering time conversions, you'll ensure accurate calculations in physics, leading to precise results and analyses.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A lightning bolt strikes one end of a steel lightning rod, producing a 15,000-A current burst that lasts for 65 \(\mu\)s. The rod is 2.0 m long and 1.8 cm in diameter, and its other end is connected to the ground by 35 m of 8.0-mm-diameter copper wire. (a) Find the potential difference between the top of the steel rod and the lower end of the copper wire during the current burst. (b) Find the total energy deposited in the rod and wire by the current burst.

A 5.00-A current runs through a 12-gauge copper wire (diameter 2.05 mm) and through a light bulb. Copper has \(8.5 \times 10^{28}\) free electrons per cubic meter. (a) How many electrons pass through the light bulb each second? (b) What is the current density in the wire? (c) At what speed does a typical electron pass by any given point in the wire? (d) If you were to use wire of twice the diameter, which of the above answers would change? Would they increase or decrease?

Electric eels generate electric pulses along their skin that can be used to stun an enemy when they come into contact with it. Tests have shown that these pulses can be up to 500 V and produce currents of 80 mA (or even larger). A typical pulse lasts for 10 ms. What power and how much energy are delivered to the unfortunate enemy with a single pulse, assuming a steady current?

An 18-gauge copper wire (diameter 1.02 mm) carries a current with a current density of \(3.20 \times 10{^6} A/m{^2}\). The density of free electrons for copper is \(8.5 \times 10^{28}\) electrons per cubic meter. Calculate (a) the current in the wire and (b) the drift velocity of electrons in the wire.

A hollow aluminum cylinder is 2.50 m long and has an inner radius of \(2.75 \mathrm{~cm}\) and an outer radius of \(4.60 \mathrm{~cm} .\) Treat each surface (inner, outer, and the two end faces) as an equipotential surface. At room temperature, what will an ohmmeter read if it is connected between (a) the opposite faces and (b) the inner and outer surfaces?
See all solutions

Recommended explanations on Physics Textbooks

Thermodynamics

Read Explanation

Particle Model of Matter

Read Explanation

Waves Physics

Read Explanation

Torque and Rotational Motion

Read Explanation

Scientific Method Physics

Read Explanation

Engineering Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.