👩🏽‍🔬Honors Chemistry Unit 7 Review

Molarity and percent composition are two ways to describe how much of something is present in a mixture. Molarity tells you the concentration of a solute in a solution, while percent composition tells you how much of each element (by mass) makes up a compound. Both are essential for preparing solutions and analyzing chemical formulas.

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Methods of Expressing Concentration

Molarity (M)

Molarity is the most common way to express solution concentration in chemistry. It tells you how many moles of solute are dissolved per liter of solution.

Formula: $M = \frac{n}{V}$

$M$ = molarity (mol/L)

$n$ = moles of solute

$V$ = volume of the solution (in liters)

Application: Use molarity when you need to know how much solute is dissolved in a given volume of solution. This comes up constantly in stoichiometry and lab work.

One thing to watch: the volume in the molarity formula is the volume of the entire solution, not just the solvent. If you dissolve salt in water and the final solution volume is 1.0 L, that's the value you use for $V$ .

✨ Tips for Success, physical chemistry - Temperature dependence of molarity and molality - Chemistry Stack Exchange

Molality (m)

Molality measures concentration differently: it's the number of moles of solute per kilogram of solvent (not solution).

Formula: $m = \frac{n_{\text{solute}}}{m_{\text{solvent}}}$

$m$ = molality (mol/kg)

$n_{\text{solute}}$ = moles of solute

$m_{\text{solvent}}$ = mass of the solvent (in kilograms)

Application: Molality is used for calculating colligative properties like boiling point elevation and freezing point depression, because it doesn't change with temperature.

Why does molality exist when we already have molarity? Volume changes with temperature (liquids expand when heated), so molarity technically shifts as temperature changes. Mass doesn't change with temperature, so molality stays constant. That's why it's preferred for colligative property calculations.

Quick example: If you dissolve 2 moles of salt into exactly 1 kilogram of water, you've made a 2 molal (2 m) solution.

Percent Composition

Percent composition describes the percentage by mass (or volume) of each component in a compound or mixture.

By Mass

Definition: The mass of a specific element divided by the total molar mass of the compound, multiplied by 100.

Formula: $\text{Percent composition} = \frac{\text{Mass of element}}{\text{Molar mass of compound}} \times 100\%$

Application: Helps you figure out what fraction of a compound's mass comes from each element. This is useful for identifying unknown compounds and verifying chemical formulas.

By Volume

Definition: The volume of a specific component divided by the total volume of the mixture, multiplied by 100.

Formula: $\text{Percent composition} = \frac{\text{Volume of component}}{\text{Total volume of mixture}} \times 100\%$

Application: Used when dealing with liquid or gas mixtures where volume is easier to measure than mass.

For percent by mass, think of a chocolate bar labeled "70% Cocoa." Out of every 100 grams of that bar, 70 grams come from cocoa. For percent by volume, think of a bottle labeled "5% Alcohol." In every 100 mL of that drink, 5 mL is alcohol.

✨ Tips for Success, homework - Getting the molality of a solution given molarity and density - Chemistry Stack Exchange

Practice Problems

Problem 1: Preparing a Solution

To make a 1 M sugar water solution, how many moles of sugar do you need for half a liter?

Write down what you know: $M = 1 \text{ mol/L}$ , $V = 0.5 \text{ L}$
Rearrange the molarity formula to solve for moles: $n = M \times V$
Plug in: $n = 1 \text{ mol/L} \times 0.5 \text{ L} = 0.5 \text{ mol}$

Answer: You need 0.5 moles of sugar.

Problem 2: Percent Composition by Mass

A lotion contains 60 g of glycerin in a 150 g mixture. What's the percent composition by mass of glycerin?

Identify your values: mass of glycerin = 60 g, total mass of mixture = 150 g
Apply the formula: $\text{Percent composition} = \frac{60 \text{ g}}{150 \text{ g}} \times 100\%$
Simplify: $\frac{60}{150} = 0.4$
Convert: $0.4 \times 100\% = 40\%$

Answer: The glycerin makes up 40% of the lotion by mass.

Tips for Success

Track your units carefully. Units will guide you to the right answer and help you catch mistakes. If your units don't cancel properly, something's off.
Don't confuse molarity and molality. Molarity uses liters of solution; molality uses kilograms of solvent. Mixing these up is one of the most common errors on exams.
Molality is temperature-independent. Since it's based on mass rather than volume, temperature changes don't affect it. Molarity can shift slightly with temperature because volume changes.
Label everything when solving problems. Write down what each number represents before plugging into a formula. It keeps you from getting lost in the math.
Watch the percent composition formula direction. The element or component mass goes in the numerator, and the total goes in the denominator. Flipping them gives you a nonsensical answer.

👩🏽‍🔬Honors Chemistry Unit 7 Review