LUMS Math Circles - math meet molecules and probability on chance

Exploring Chemistry through Numbers: Math Meets Molecules

On February 14, 2025, the LUMS Math Circle hosted a session titled "Math Meets Molecules," combining mathematics and chemistry. Dr. Adnan Khan started the session by introducing mathematical concepts through a fair share example. Dr. Muhammad Saeed then discussed key chemistry concepts, including the mole, molar mass, and Avogadro’s number.

Key Highlights:

Mathematical Foundations: Dr. Adnan introduced numbers, exponents, and fractions using real-life examples. Mrs. Hobson's money-sharing problem was used to illustrate mathematical expressions.
Counting in Chemistry: Dr. Muhammad Saeed explained terms like couple, dozen, gross, and ream, leading to the concept of the mole.
Mole Concept: Avogadro’s number (6.02 × 10^23) was introduced, with real-world comparisons to illustrate its vastness. To help students grasp the enormity of this number, they were asked to imagine distributing 6.02 × 10^23 grains of rice among the global population. Each person would receive millions of kilograms of rice—an amount beyond human consumption in a lifetime. This comparison helped students visualize why such large numbers are needed in chemistry to describe microscopic entities.
Mole-to-Mass and Mole-to-Particle Conversions: The concept of molar mass was explained as the mass of one mole of a substance, measured in grams per mole. Students calculated molar masses using the periodic table, with water (H₂O) as an example (18 g/mol). They then practiced conversions using the formula:
- Mass-to-Mole Conversion: Mass (g) = molar mass (g/mol) × moles. Students calculated how many moles are present in a given mass of water.
- Mole-to-Particle Conversion: Number of particles = 6.02 × 10^23 × moles. This calculation allowed students to determine the number of water molecules in a specific mass, reinforcing how mathematical tools enable chemists to quantify microscopic particles.
Stoichiometry: The session covered balanced chemical equations, using the reaction between NaHCO₃ and CH₃COOH as an example.
Molarity and the Ideal Gas Law: Students explored molarity and the ideal gas law (PV = nRT) to understand the mathematical basis of chemical behavior.

The session concluded with a live experiment where students learned to produce CO₂ using vinegar and baking soda. Well, the interesting part is that these two reactants are easily available in any household.

The interactive approach, complemented by worksheets and thought-provoking examples, kept the participants engaged and excited about the deep connections between mathematics and chemistry.

Here are some highlights from the event:

Probability on Chance

As part of the newly launched series Math Circles for Epsilons, powered by LUMS Math Circle, a session titled Probability on Chance was held, introducing younger students (Grades 4–7) to the foundational principles of probability through engaging activities.

The session started with real-life problems to ensure the students understood basic probability.
Basic Probability Formula: (number of outcomes that are wanted) ÷ (total number of possible outcomes).
An example used was the "URN of Fate," which contained 2 golden keys, 3 silver keys, and 4 bronze keys. The children were asked to calculate the probability of picking each type of key.
Probability with replacement: When the picked candy is put back in the bag before picking again, the number of candies in the bag stays the same every time, and the chance of picking a certain colour does not change.
Probability without replacement: After picking a candy, you do not put it back in the bag. The number of candies gets smaller after each pick, and the chance of picking a certain colour changes because one candy is missing.
Complement Rule: Since the probability of the sum of all outcomes = 1, P (Something Happening) = 1 – (Something NOT happening).

Conclusion

Both sessions successfully engaged participants by combining mathematical concepts with real-world applications. "Math Meets Molecules" showcased the role of mathematics in chemistry, while "Probability on Chance" provided younger students with a strong introduction to probability through interactive learning. The LUMS Math Circle continues to be a thriving platform for students to explore the beauty and utility of mathematics in various disciplines.

We look forward to future sessions that will continue to inspire a love for mathematical exploration!

Both sessions were a resounding success, brimming with curiosity, discovery, and fun.

A heartfelt thank you to our dedicated instructors, Dr. Muhammad Saeed, Dr. Adnan Khan, Ms. Zainab Imran, and Ms. Amtul HadiBint E Khalid, for their inspiring sessions. We are also deeply grateful to Ms. Noreen Sohail and Mr. Qamar Hussain for their invaluable organizational support.

Finally, thanks to Mr. Muhammad Javaid Qayoom for compiling this wonderful recap.

Here are some highlights from the event: