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II-15: Electrolysis, nuclear decay and data analysis

IntoChemistry | General Chemistry II Math Readiness

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Module II-15 · Recommended before: Before electrolysis, nuclear chemistry and lab reports

Electrolysis, nuclear decay and data analysis

Quantitative electricity relates current to charge and electron moles. Nuclear decay uses exponential half-life; both rely on careful unit tracking.

Learn the method

Q = It; mol electrons = Q/F; remaining = initial×(1/2)^(t/t₁/₂)

  1. For electrolysis compute charge Q = I×t in coulombs.
  2. Divide by Faraday’s constant to find electron moles.
  3. Use stoichiometric electron-to-product ratios.
  4. For nuclear decay use fractions of one-half for each half-life.
  5. Report units and measurement uncertainty clearly.

Common mistake: For electrolysis, convert minutes to seconds before multiplying by amperes.

Worked example

Problem: A sample has 80.0 mg of a radioisotope with half-life 5 days. How much remains after 15 days?

Step-by-step solution: Three half-lives: 80.0 × (1/2)³ = 10.0 mg.

Check the units and whether the answer is reasonable before continuing.

More applications of this mathematics

Try each extension before expanding its solution.

Faraday mass calculation

For Cu²⁺+2e⁻→Cu, 1.00 A for 1930 s supplies 1930 C ≈0.0200 mol electrons, enough for 0.0100 mol Cu or about 0.636 g copper.

Decay law and laboratory statistics

Three half-lives leave (1/2)³ = 12.5% of the original amount. In lab data analysis, state whether reported variation is sample standard deviation, standard error, or instrument uncertainty.

Mass defect and binding energy

A nuclear mass defect of 1.00×10⁻³⁰ kg corresponds to E=Δmc²≈8.99×10⁻¹⁴ J using c≈2.998×10⁸ m/s.

Precision in lab reports

For three measurements 1.00, 1.10, 0.90 g, the mean is 1.00 g; sample standard deviation=0.10 g and relative standard deviation=10%.

Independent practice — five questions

Suggested mastery threshold: four out of five. Incorrect answers display a worked explanation after submission.

Choose one response for each question, then select “Check my answers.” No timer. Hints are optional. You can retry freely. Questions are formative, not proctored.

Question 1. A radioisotope begins with 120 mg. How much remains after 3 half-lives?
Hint for question 1

Each half-life halves the previous amount.

Question 2. An electrolysis current of 3 A runs for 180 s. How much charge passes?
Hint for question 2

1 ampere is 1 coulomb per second.

Question 3. A radioisotope begins with 160 mg. How much remains after 4 half-lives?
Hint for question 3

Each half-life halves the previous amount.

Question 4. An electrolysis current of 4 A runs for 240 s. How much charge passes?
Hint for question 4

1 ampere is 1 coulomb per second.

Question 5. A radioisotope begins with 200 mg. How much remains after 2 half-lives?
Hint for question 5

Each half-life halves the previous amount.

Supporting reference

OpenStax Chemistry 2e / NIST — reference for this subject. This lesson’s wording, examples and questions are original. Electrolysis reference: https://openstax.org/books/chemistry-2e/pages/17-introduction

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Applied practice: Electrolysis mass and nuclear half-life

These additional, ungraded problems cover skills beyond the scored five-question check above. Try each before expanding its solution. Your existing score and progress records are unchanged.

  1. Challenge 1. An aqueous Cu²⁺ solution is electrolyzed at 2.00 A for 30.0 min, producing copper. Find the deposited mass (F = 96,485 C/mol e⁻; Cu = 63.55 g/mol).

    Show worked solution for challenge 1

    Q = It = (2.00 A)(1,800 s) = 3,600 C. Cu²⁺ + 2e⁻ → Cu; m = (3,600 C)(63.55 g/mol) / (2 × 96,485 C/mol) = 1.19 g Cu.

  2. Challenge 2. An isotope has a half-life of 8.0 days. A 64 mg sample is measured after 24 days. How much remains?

    Show worked solution for challenge 2

    24/8.0 = 3 half-lives; remaining = 64 mg × (1/2)³ = 8.0 mg.

IntoChemistry original instructional content, 2026. Formative feedback is not an official course grade. Sources are linked for independent reading. Accessibility testing with your institution and assistive technology is still recommended.