Lizzie Tutoring

Wednesday, March 4, 2026

New ACT Preparation Courses - May 2026

Is your student ready for the NEW "Enhanced" ACT?
The ACT has undergone its biggest change in 35 years. Starting in 2025/2026, the test is shorter, the science section is optional, and the math questions have fewer answer choices. Is your student prepared for the new format?

Join my 2.5-hour Fast-Track Workshop to master the 2026 version of the ACT. We cover the core composite essentials while giving students the clarity they need on the new optional segments.

We will cover:
- The Big 3 Core: High-impact strategies for English, Math, and Reading (the sections that now determine the Composite score).
- The "Science" Decision: Should you take the optional Science section? We’ll help you decide based on your college goals (more details here).
- New Pacing Rules: With 22% more time per question, "speed-reading" is out and "precision-scoring" is in.
- Math Odds: How the move to 4 answer choices changes your guessing strategy.

I am offering the test preparation course at two different times (each track will cover the same material). See below.

Track 1 will meet in person in Eden Prairie. Track 2 will meet over Zoom. If neither of the dates listed below works for you and you are still interested in the class, please contact me through the contact form, and we can try to work something out.

Track 1 will meet for one 2.5-hour session. We will cover all three required sections of the ACT, as well as the two optional sections (Science and Writing).
It will meet on a Thursday from 10 am to 12:30 pm.
Date: May 21, 2026
Location: Eden Prairie

Track 2 will meet for one 2.5-hour session. We will cover all three required sections of the ACT, as well as the two optional sections (Science and Writing).
It will meet on a Thursday afternoon from 2 pm to 4:30 pm.
Date: May 21, 2026
Location: online through Zoom

Cost: $90.00 per student for the entire course. Includes materials.

Registration deadline: Friday, May 15, 2026

Register here.

Online High School Physics Class 2026-2027

We are thinking of offering a high school Physics class online next school year (2026-2027). If you are interested in registering a student for that class, please contact us through the contact form linked on the right-hand side of your screen.

Ongoing Online Classes

Tchaikovsky’s 1812 Overture - A Musical Journey (self-paced)

Tuesday, March 3, 2026

Chemistry - Le Chatelier's Principle

Le Chatelier's Principle describes how a chemical system at equilibrium reacts when it experiences a change in conditions. Think of it as a balancing act: if you push a system out of balance, it will shift its weight to counteract that push and find a new state of stability.

The formal definition is: If a system at equilibrium is subjected to a change in concentration, temperature, or pressure, the system will shift its equilibrium position to counteract the effect of the disturbance.

The Three Main Stressors

There are three primary ways to stress a system at equilibrium:

Concentration
Add more reactant: The system shifts right (toward products) to use up the extra reactant.
Remove a product: The system shifts right to replace what was lost.
Add more product: The system shifts left (toward reactants) to use up the extra product.
Temperature
To predict temperature shifts, you must treat heat as either a reactant or a product:
Exothermic Reactions (negative Delta H): Heat is a product. Increasing temp shifts the reaction left.
Endothermic Reactions (positive Delta H): Heat is a reactant. Increasing temp shifts the reaction right.
Pressure (Gases Only)
Pressure only affects systems with different numbers of gas molecules on each side:
Increase Pressure: The system shifts toward the side with fewer moles of gas to reduce the crowding.
Decrease Pressure: The system shifts toward the side with more moles of gas.

Practice Problems

Use the following reversible reaction for the questions below:

N2(g) + 3H2(g) <=> 2NH3(g) + heat

Concentration Change
If you inject more N2 gas into the container, which way will the equilibrium shift?
A) Toward the products (Right)
B) Toward the reactants (Left)
C) No change
Temperature Change
If the reaction vessel is placed in an ice bath (decreasing the temperature), which way will the equilibrium shift?
A) Left, favoring N2 and H2
B) Right, favoring NH3
Pressure Change
If the volume of the container is decreased (increasing the pressure), how will the system respond?
A) Shift left (4 moles of gas to 2 moles of gas)
B) Shift right (4 moles of gas to 2 moles of gas)
C) No shift because both sides are gases.
The Catalyst Question
If a catalyst is added to this reaction at equilibrium, what happens to the equilibrium position?
A) Shifts Right
B) Shifts Left
C) No change in position, but it reaches equilibrium faster.

Answer Key

A (Right): The system tries to consume the added N2.
B (Right): Since it is exothermic, removing heat pulls the reaction toward the heat-producing side.
B (Right): The left side has 4 moles (1+3), and the right side has 2 moles. Higher pressure favors the side with fewer moles.
C (No change): Catalysts speed up both the forward and reverse reactions equally!

Sunday, February 22, 2026

Chemistry - Reaction Rates

What are Reaction Rates?

A reaction rate is simply a measure of how fast a chemical reaction occurs. It describes how quickly the reactants are used up or how quickly the products are formed over a specific period of time. You can think of it like the speed of a car, but instead of measuring miles per hour, chemists measure change in concentration per second or minute.

Determining Rate Laws from Experimental Data

To find the rate law, we look at how the initial rate of a reaction changes when we change the concentration of one reactant at a time.

Rate Law Format: Rate = k[A]^x[B]^y

k = Rate constant

x = Order of reactant A

y = Order of reactant B

Practice Problem 1: Determining Reaction Orders

Consider the following reaction: 2 NO(g) + Cl2(g) -> 2 NOCl(g)

The following data was collected at a constant temperature:

Trial 1: [NO] = 0.10 M, [Cl2] = 0.10 M, Initial Rate = 0.18 M/s

Trial 2: [NO] = 0.10 M, [Cl2] = 0.20 M, Initial Rate = 0.36 M/s

Trial 3: [NO] = 0.20 M, [Cl2] = 0.10 M, Initial Rate = 0.72 M/s

Questions:

What is the reaction order for Cl2 (the value of y)?
What is the reaction order for NO (the value of x)?
What is the overall rate law for the reaction?
Calculate the value of the rate constant (k).

Practice Problem 2: The Zero Order Case

Consider the reaction: A + B -> Products

Trial 1: [A] = 1.0 M, [B] = 1.0 M, Initial Rate = 0.05 M/s

Trial 2: [A] = 2.0 M, [B] = 1.0 M, Initial Rate = 0.05 M/s

Trial 3: [A] = 1.0 M, [B] = 2.0 M, Initial Rate = 0.10 M/s

Questions:

What is the reaction order for A (the value of x)?
What is the reaction order for B (the value of y)?
Write the rate law for this reaction.

Answer Key

Problem 1 Answers:

Order for Cl2 (y): Compare Trials 1 and 2. [NO] stays the same, but [Cl2] doubles. The rate also doubles (0.18 to 0.36). This means y = 1.
Order for NO (x): Compare Trials 1 and 3. [Cl2] stays the same, but [NO] doubles. The rate quadruples (0.18 to 0.72). Since 2 squared is 4, x = 2.
Rate Law: Rate = k[NO]^2[Cl2]^1
Rate Constant (k): Use Trial 1 data. 0.18 = k[0.10]^2[0.10]. Solving for k gives 180 M^-2s^-1.

Problem 2 Answers:

Order for A (x): Compare Trials 1 and 2. [A] doubles, but the rate stays exactly the same. This means x = 0.
Order for B (y): Compare Trials 1 and 3. [B] doubles and the rate doubles. This means y = 1.
Rate Law: Rate = k[B] (Reactant A is not included because its order is 0).

Chemistry - Kinetics

Chemical kinetics is the area of chemistry that deals with the speeds, or rates, of chemical reactions. While thermodynamics tells us if a reaction can happen, kinetics tells us how fast it will happen and the specific steps the molecules take to get there.

The Collision Theory
The foundation of kinetics is the collision theory. For a reaction to occur, reactant particles must collide with one another. However, not every collision results in a reaction. To be successful, a collision must meet two criteria:

Collision Orientation: The molecules must hit each other in the correct position so that the right atoms can bond.

Activation Energy: The particles must collide with enough kinetic energy to break existing chemical bonds.

The activation energy is the minimum amount of energy required to start a chemical reaction. You can think of it like a hill that molecules must climb over before they can roll down the other side into the product state.

Factors Affecting Reaction Rates
Several factors can change how frequently or how forcefully particles collide, which in turn changes the reaction rate:

Concentration: Increasing the concentration of reactants means there are more particles in the same amount of space. This leads to more frequent collisions. In gases, increasing the pressure has the same effect.

Temperature: Increasing the temperature makes particles move faster. This increases the frequency of collisions and, more importantly, ensures that a higher percentage of those collisions have enough energy to surpass the activation energy.

Surface Area: For reactions involving solids, breaking the solid into smaller pieces increases the surface area. This exposes more particles to the other reactants, leading to more frequent collisions.

Catalysts: A catalyst is a substance that speeds up a reaction without being consumed. It works by providing an alternative pathway for the reaction that has a lower activation energy. Because the "hill" is lower, more particles have enough energy to cross it.

Reaction Mechanisms and the Rate-Determining Step
Most chemical reactions do not happen in one single step. Instead, they occur through a series of simpler steps called a reaction mechanism. Each individual step is called an elementary step.

Even if most steps in a mechanism are fast, the overall speed of the reaction is limited by the slowest step. This is known as the rate-determining step. It is like a funnel; no matter how wide the top is, the water can only flow as fast as the narrow neck allows.

Rate Laws
Chemists express the relationship between the rate of a reaction and the concentration of reactants using a mathematical equation called a rate law. A typical rate law looks like this: Rate = k[A]^x [B]^y.

In this equation, k is the rate constant, which is specific to each reaction at a certain temperature. The brackets [A] and [B] represent the molar concentrations of the reactants. The exponents (x and y) are called the reaction orders and must be determined by experiments, not just by looking at the balanced equation.

Chemistry - Entropy and Gibbs Free Energy

To understand why some chemical reactions happen spontaneously (like a nail rusting) while others don't (like a pile of rust turning back into a nail), we look at two main factors: Entropy and Gibbs Free Energy.

Entropy (S): The Measure of Disorder

Entropy is often described as a measure of randomness or disorder in a system. In chemistry, it is more accurately described as the number of ways energy can be distributed among particles.

Low Entropy: Particles are organized, confined, or in a fixed position, like a solid crystal.

High Entropy: Particles are spread out, moving rapidly, or disorganized, like a gas.

The Second Law of Thermodynamics states that the total entropy of the universe is always increasing. This means nature naturally tends toward a state of higher disorder.

Factors that Increase Entropy:

Phase Changes: Moving from solid to liquid to gas.

Temperature: Increasing temperature makes particles move faster and more randomly.

Dissolving: Breaking a solid solute into ions in a solution.

Number of Moles: If a reaction produces more moles of gas than it started with, entropy increases.

Gibbs Free Energy (G): The Deciding Factor

While entropy tells us about disorder, it doesn't tell us the whole story. We also have to consider Enthalpy (H), which is the heat energy of the system.

Nature generally prefers low energy (exothermic reactions) and high disorder (increased entropy). Gibbs Free Energy combines these two ideas into one value to determine if a reaction is spontaneous, meaning it can occur without a continuous input of energy.

The Gibbs Equation:

Change in Gibbs Free Energy = (Change in Enthalpy) - (Temperature in Kelvin * Change in Entropy)

Change in G: Change in Free Energy (kJ/mol)

Change in H: Change in Enthalpy (Heat)

T: Temperature (in Kelvin)

Change in S: Change in Entropy

Is the Reaction Spontaneous?

The sign of the change in Gibbs Free Energy tells you if the reaction will "go" under specific conditions:

If the change in G is negative (less than 0): Energy is released and available to do work. The reaction is spontaneous.

If the change in G is positive (greater than 0): Energy must be added for the reaction to occur. The reaction is non-spontaneous.

If the change in G equals 0: The system has reached a state of balance called equilibrium.

The Tug-of-War:

Sometimes enthalpy and entropy disagree. For example, melting ice is endothermic (it absorbs heat, which nature usually resists), but it results in higher entropy because liquid water is more disordered than ice. At room temperature, the entropy gain is large enough to make the change in Gibbs Free Energy negative, so ice melts spontaneously.

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