CHEM 1127Q - Chapters 0-1

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• Base SI units and prefixes foundations; prefixes are like tiny "power-ups" or "mini-words" that attach to units to make them bigger or smaller, so we don't have to write huge or tiny numbers with lots of zeros.

• Derived units commonly used: These are units we make by mixing the basic units.

  • Volume: How much space something takes up, like the amount of water in a bottle. We measure it in $m^3$ (cubic meters) or L (liters); 1 L is roughly about the same as $1.0\times 10^{-3}\ \mathrm{m^3}$. (A liter is often like a big soda bottle).

  • Density: How much "stuff" is packed into a certain amount of space. If something is very dense, it feels heavy for its size. The formula is $d = \dfrac{m}{v}$. We measure it in $kg/m^3$ or (g/mL).

  • Concentration: How much of one thing is mixed into another, especially when it's dissolved in a liquid. Like how much sugar is in your juice. We use molarity $\mathrm{mol/L}$.

  • Pressure: How much a push spreads out over an area. Like when you push your hand against a wall. We use $\text{Pa}$.

  • Energy: The ability to do work or make things happen. It's what makes lights turn on or cars move. We use $\text{J}$ (joules).

  • Power: How fast you use energy or how quickly you do work. We use $\text{W}$ (watts).

• Temperature scales: Just different ways to measure how hot or cold something feels.

  • $K = ^\circ C + 273.15$

  • Room temp $\approx 25^\circ C = 298.15\ \text{K}$ (A nice, comfy temperature).

  • Freezing point: $0^\circ C = 273.15\ \text{K}$ (When water turns into ice).

  • Boiling point: $100^\circ C = 373.15\ \text{K}$ (When water turns into steam).

• Zeros: Celsius and Kelvin start counting heat at different places. Absolute zero is 0 K. It's the coldest possible temperature, where everything stops wiggling completely. Nothing can ever get colder than that!

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• SI Derived Units (examples): Units we make by combining the basic ones.

  • Volume: How much space something fills, like the space in a box, $m^3$.

  • Speed: How fast you are moving, like a car going down the road, $m/s$.

  • Acceleration: How quickly your speed changes, like when a car speeds up or slows down, $m/s^2$.

  • Density: How much stuff is squished into a space, $kg/m^3$.

  • Frequency: How often something happens, like how many times a swing goes back and forth in a second, $Hz$.

  • Force: A push or a pull, like when you push a door open, $N$.

• SI Prefixes (selected): These are the "power-ups" for our units, making them bigger or smaller.

  • Tera- (T): $10^{12}$ (Super duper big! A trillion.)

  • Giga- (G): $10^{9}$ (Super big! A billion, like a gigabyte of data).

  • Mega- (M): $10^{6}$ (Very big! A million).

  • Kilo- (k): $10^{3}$ (Big! A thousand, like 1 kilometer = 1,000 meters).

  • Deci- (d): $10^{-1}$ (A bit smaller! One-tenth).

  • Centi- (c): $10^{-2}$ (Smaller! One-hundredth, like 1 centimeter is 1/100 of a meter).

  • Milli- (m): $10^{-3}$ (Even smaller! One-thousandth).

  • Micro- (μ): $10^{-6}$ (Tiny! A millionth).

  • Nano- (n): $10^{-9}$ (Super tiny! A billionth).

  • Pico- (p): $10^{-12}$ (Ultra tiny! A trillionth).

  • Femto- (f): $10^{-15}$ (Even tinier!).

  • Atto- (a): $10^{-18}$ (The absolute tiniest!).

• SI Base Units (summary): These are the basic "LEGO bricks" for all measurements.

  • Length: Meter ($m$) (How long something is).

  • Mass: Kilogram ($kg$) (How much "stuff" is in something).

  • Time: Second ($s$) (How long something takes).

  • Temperature: Kelvin ($K$) (How hot or cold).

  • Amount of substance: Mole ($mol$) (How many tiny particles).

  • Electric current: Ampere ($A$) (How much electricity flows).

  • Luminous intensity: Candela ($cd$) (How bright a light is).

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• Exponents and Scientific Notation:

  • Exponents are a shortcut for multiplying the same number many times: $5^3$ means $5 \times 5 \times 5$.

  • Negative exponents mean you flip the number and make it a fraction: $5^{-3}$ means $\dfrac{1}{5^3}$.

  • Any number raised to the power of 0 is always 1: $a^0 = 1$.

  • Scientific notation is a super cool way to write very, very big or very, very small numbers without writing tons of zeros. You use a number between 1 and 10, multiplied by a "power of 10" (like $10^3$ for 1000). For example, $1.73\times 10^3 = 1730$.

  • The rule for the first number (the coefficient) is that it has to be between 1 and 10 and only have one digit before the decimal point.

  • Example: $150{,}000 = 1.5\times 10^5$.

  • When comparing numbers in scientific notation, first look at the "power of 10" part. If those are the same, then look at the number in front. For example, $2.0\times10^{-2} \; \text{vs}\; 1.4\times10^{-2}$, the first one is bigger because 2.0 is more than 1.4.

• Order of Operations (PEMDAS): This is a special rule to make sure everyone solves math problems in the same way, always doing steps in a particular order.

  • Start with Parentheses, then Exponents, then Multiplication and Division (do whichever comes first from left-to-right), and finally Addition and Subtraction (again, whichever comes first from left-to-right).

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• Algebra (rearranging equations): This is like solving a puzzle to find a mystery number or letter by moving other numbers and letters around.

  • To move numbers or letters (variables) from one side of an equal sign to the other, you do the opposite operation (if it's multiplying, you divide; if it's adding, you subtract). You can also flip the whole equation around!

  • Example: solve for z from $a = (b-c)\left(\frac{1}{z} + 3\right)$.

  • Step 1: Get rid of the $(b-c)$ part by dividing both sides by it: $\frac{a}{(b-c)} = \frac{1}{z} + 3$

  • Step 2: Get rid of the $+3$ by subtracting 3 from both sides: $\frac{a}{(b-c)} - 3 = \frac{1}{z}$

  • Step 3: If you have $\frac{1}{z}$, to find $z$, you just flip both sides upside down: $z = \dfrac{1}{\frac{a}{(b-c)} - 3}$

  • If you want to get rid of a square root, you "square" both sides (multiply both sides by themselves). Make sure to use parentheses if there's more than one thing on a side!

  • FOIL: This is a trick to multiply two small math sentences with two parts each. FOIL stands for First, Outer, Inner, Last. For example: $(8d - e)(8d - e) = 64d^2 - 16de + e^2$.

  • Distributive property: This means that a number or letter outside a parenthesis gets shared by everything inside. So, $a(b+c-d) = ab+ac-ad$. You can also do it backward to group things: $x(y+z) = xy + xz$.

  • Canceling: You can make factors (numbers being multiplied) disappear by multiplying by their opposite, called a reciprocal. For example, to cancel a $\frac{1}{2}$, you multiply by 2.

  • Complex fractions: These are fractions with other fractions inside them. A good trick is "Keep-Change-Flip" (KCF): Keep the top fraction the same, Change the division sign to multiplication, and Flip (turn upside down) the bottom fraction.

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• Logarithms and Antilogs:

  • A logarithm (usually written as "log") tells you what power you need to raise the number 10 to, to get another number. For example, $\log(100) = 2$ because $10^2$ (10 times 10) equals 100.

  • Logs are like a special ruler where numbers get spaced out differently. A jump of 1 on the "log ruler" means the original number got 10 times bigger or smaller.

  • For numbers that aren't easy powers of 10, we can use a calculator. For example, $\log(4.5 \times 10^{-7}) = -6.35$.

  • Antilog: This is the opposite of a log. If you know the log of a number, say $\log(x) = y$, then to find $x$, you just use the formula $x = 10^y$. For example, if $\log(x) = -4.76$, then $x = 10^{-4.76}$ which is about $1.74\times 10^{-5}$.

  • When you go from a log back to a regular number, the number of digits in your answer (the precise part) should match the number of digits after the decimal point in your log value.

  • Example: $\log(x) = 2.53 \rightarrow x = 10^{2.53}$ which is about 339.

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• Natural Log (ln):

  • This is like a regular log, but it uses a special number called $e$ (which is roughly 2.71828) instead of 10 as its base. It's written as $\ln x$.

  • To undo a natural log, you raise the special number $e$ to that power: $x = e^{\ln x}$. So if $\ln x = y$, then $x = e^y$.

  • Example: $\ln(2.00) = 0.693$, so if you do $e^{0.693}$, you'll get about 2.00.

  • Example: If $\ln x = 1.81$, then $x = e^{1.81}$ which is about 6.1.

• Percentages (0.6):

  • Percent means "out of 100." So, if you have 15% of something, it means 15 out of every 100 parts. 1% is the same as $\frac{1}{100}$. The formula is $Percent = \text{part}/\text{whole} \times 100\%$.

  • Examples: 15% of 60 means $0.15 \times 60 = 9$. If 8 is 20% of 40, it's true because 8 divided by 40 is 0.20, which is 20%. If 2 is 25% of a mystery number $x$, then $2 = 0.25x$, so $x = 8$.

  • You can use percentages to figure out parts of a whole or the whole amount. Like if a rock has 25% iron, that means for every 100 grams of rock, there are 25 grams of iron. So in 72 grams of rock, you'd have $0.25 \times 72 = 18$ grams of iron.

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• Graphs and Proportionality (0.7, 0.8):

  • On a graph, the independent variable (the thing you change) goes on the x-axis (the flat one). The dependent variable (the thing you measure) goes on the y-axis (the standing-up one).

  • Interpolation: This is like guessing an answer that's between the points you've already measured on your graph.

  • Extrapolation: This is like guessing an answer outside the points you've measured. It's often less accurate because you're guessing far away.

  • Slope: This tells you how steep a line on a graph is. The formula for slope is $m = \dfrac{y<em>2 - y</em>1}{x<em>2 - x</em>1}$.

  • Line: The rule for a straight line is $y = mx + b$. Here, $m$ is the slope (steepness), and $b$ is where the line crosses the y-axis.

  • Direct relationship: This means that if one thing goes up, the other thing goes up too. Or if one goes down, the other goes down. If one thing is always a certain number of times bigger than the other, we say they are "directly proportional," and the graph is a straight line through (0,0).

  • Inverse relationship: This means that if one thing goes up, the other thing goes down. It's not a straight line on a graph. For example, if you double your speed, it takes half the time to get somewhere.

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• Weighted Average (0.9):

  • A weighted average is like finding a normal average, but some numbers count more than others. You multiply each number by how much it "counts" (its weight), add them all up, and then divide by the total weight. The "weights" don't have to be equal.

  • Example: If you drive 60 mph for 83% of your trip and 70 mph for 17% of your trip, your average speed isn't just (60+70)/2. It's $(0.83 \times 60) + (0.17 \times 70) = 61.7\ \text{mph}$ because you spent more time driving at 60 mph.

• Quadratic Formula (0.10):

  • This is a special, magic formula used to solve equations that have an $x^2$ in them (like $ax^2 + bx + c = 0$). These are called quadratic equations.

  • To solve them, you use this formula: $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. The $\pm$ sign means there can be two different answers for $x$!

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• Quick reference key terms and equations (summary):

  • Slope of a line: $m = \dfrac{y<em>2 - y</em>1}{x<em>2 - x</em>1}$

  • Equation for a straight line: $y = mx + b$

  • The special kind of equation with an $x^2$: $ax^2 + bx + c = 0$

  • The magic formula to solve it: $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

  • Also, remember what log and ln mean, including $\log(x) = y \Rightarrow x = 10^y$ and $\ln x = y \Rightarrow x = e^y$. The order of operations (PEMDAS), how to use percentages ($Percent = \text{part}/\text{whole} \times 100\%$), what exponents (powers) are, and how to use a scientific calculator.

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• Science and Measurement: Classification of Matter 1.1

  • Chemistry = The scientific study of all the "stuff" around us (called matter) and how it changes.

  • Matter: Anything that has weight (mass) and takes up space (volume).

  • Elements: These are the basic "LEGO bricks" or building blocks of everything. You can't break them down into simpler things. There are about 100 different kinds of elements known.

  • Atoms: The smallest piece of an element that still acts like that element. Atoms can stick together with special "chemical bonds" to make compounds.

  • Compound: When two or more different kinds of elements (LEGO bricks) stick together in a certain way, they form a compound. It's like building something new out of LEGOs, like water ($H_2O$) or table salt (NaCl). The new thing has its own special properties.

  • Acids: Substances that make hydrogen ions ($H^+$) in water (like lemon juice or vinegar).

  • Bases: Substances that make hydroxide ions ($OH^-$) in water or grab hydrogen ions (like soap).

  • Ionic compounds (salts): These are compounds made from tiny charged pieces that attract each other, like most salts (e.g., baking soda $NaHCO_3$).

  • Pure substance: This means it's just one kind of stuff, like only gold (an element) or only water (a compound). Mixtures are not pure.

  • Mixture: When you have two or more pure substances all mixed up, but they're not chemically stuck together. You can often separate them very easily, like picking out the different candies in a bag.

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• Mixtures (1.2): heterogeneous vs homogeneous

  • Heterogeneous: A mixture where you can easily see the different parts because they're not evenly spread out. Like a bowl of cereal with milk, or a fruit salad.

  • Homogeneous (solutions): A mixture where everything looks the same all the way through because the parts are perfectly mixed. You can't tell them apart, like sugar dissolved in water (it just looks like clear water).

  • Carbonated water: Think of a soda bottle. Before you open it, the bubbles are dissolved and it's a homogeneous mix. After you open it, the gas escapes, and you can see bubbles, so it becomes heterogeneous.

  • Dissolving: When one substance seems to "disappear" into another, making a homogeneous mixture (a solution). If a substance can dissolve, we say it's "soluble" (like sugar is soluble in water).

  • Reactant: The stuff you start with in a chemical change (the ingredients).

  • Product: The new stuff you get after a chemical change (what you made).

  • Physical vs chemical changes: A physical change just changes how something looks but not what it is (like cutting paper or melting ice). A chemical change turns something into something totally new with different properties (like burning wood, which turns into ash and smoke).

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• Properties of Matter (1.2):

  • Physical properties: These are things you can see, feel, or measure about a substance without changing what it basically is. Like its color, how hard it is, if it melts easily, or if it sinks or floats.

  • Chemical properties: These describe how a substance acts or changes when it reacts with other things, turning into something new. Like if it can burn (flammability) or if it bubbles when you put acid on it.

  • Extensive properties: These depend on how much of the substance you have. For example, a big rock has more mass and more volume than a small rock.

  • Intensive properties: These don't depend on how much of the substance you have. For example, the color of a rock is the same whether it's a tiny pebble or a huge boulder. Density and melting point are also intensive properties.

  • Compounds vs mixtures (summary): Compounds are like LEGO models where the bricks are glued together and make a new thing. Mixtures are just LEGO bricks tossed into a bin – they're still separate bricks, just mixed up.

  • Dissolves vs soluble; Reactant vs product; Physical changes keep composition; chemical changes result in new substances. These are key distinctions in chemistry.

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• Chemical Reactions:

  • In chemical reactions, old connections between atoms (chemical bonds) break, and new connections form. This changes what the substances are made of and how they're put together.

  • Breaking bonds absorbs energy, like pulling apart two strong magnets.

  • Forming bonds releases energy, like when two magnets snap together.

  • Law of conservation of energy: This is a rule that says you can't create energy out of nothing, and you can't make energy disappear. It just changes from one form to another, like a flashlight turning chemical energy into light energy.

• Energy types (short list): These are different forms that energy can take: Heat (makes things warm), Chemical (stored in things like batteries or food), Nuclear (from tiny parts of atoms), Mechanical (moving things, like a ball rolling or stretched rubber band), Electrical (from flowing charges), Sound (what you hear), Electromagnetic radiation (like light).

• Chemical energy: This is energy stored away inside the connections (bonds) between atoms in different substances. When these bonds re-form during reactions, that energy can come out or go in. It's like stored-up potential energy.

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• Energy forms (continued):

  • Electrical energy: The energy carried by tiny moving charges, like the electricity that flows through wires to power your TV.

  • Kinetic energy: The energy of moving things. The faster or heavier something is, the more kinetic energy it has. The formula is $KE = \frac{1}{2}mv^2$.

  • Potential energy: This is stored-up energy, waiting to do something. Like a ball held up high has gravitational potential energy, or a stretched spring has elastic potential energy.

• Example conversions:

  • Flashlight application: Chemical energy (in the battery) $\rightarrow$ Electrical energy (flows through circuit) $\rightarrow$ Light energy (from the bulb) + Heat energy.

  • Recharging phone: Electrical energy (from the wall) $\rightarrow$ Chemical energy (stored in the phone's battery).

• Scientific Method (1.4): This is like a detective's plan that scientists use to ask questions and find answers about the world.

  • Observation: You notice something interesting or collect facts.

  • Question: You ask "why does this happen?"

  • Hypothesis: You make a smart guess or a testable idea about what's happening. It's an explanation you can try to prove or disprove.

  • Experiment: You do a careful test to see if your smart guess is right.

  • Conclusion: You look at what happened in your test and decide if your smart guess was right or wrong.

  • Theory: A big idea that explains a lot of things and has been tested many, many times, always proving true (like the idea that tiny atoms make up everything).

  • Scientific Law: A simple rule that describes something that always happens in nature, with no known exceptions (like gravity always pulling things down). It tells you what happens, not why.

  • Law of conservation of mass: This rule says that you can't create or destroy "stuff" (mass) in a regular chemical change.

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• International System of Units (SI): A global standard for measurement that scientists around the world use.

  • SI base quantities: These are the seven main things we measure that are all different from each other: length, mass, time, electric current, temperature, amount of substance, and luminous intensity.

  • Base units commonly used in chemistry: We mostly use meter (for length), kilogram (for mass), second (for time), kelvin (for temperature), and mole (for amount).

  • Derived units: These are units we get by mixing the basic units together, like what we use for area, volume, speed, and acceleration.

  • Speed: How fast something is moving, measured in $m/s$.

  • Acceleration: How quickly something's speed changes, measured in $m/s^2$.

  • Frequency: How many times something happens in one second, measured in $Hz$ (Hertz).

  • Force: A push or pull that can make things move or stop, measured in $N$ (Newtons) or $kg\cdot m/s^2$.

  • Liter ($L$) is a common unit for the amount of liquid, and it's the same as 1 cubic decimeter ($dm^3$); 1 mL is the same as 1 cm^3.

  • English system reminder: We sometimes still use old units like 12 inches = 1 foot; 5280 feet = 1 mile.

• Common base units in chemistry: Meter, kilogram, second, kelvin, mole. These five are the ones you'll see the most.

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• SI area/volume concepts; derived units include speed and acceleration; Atomic-scale units not shown here but implied (like super tiny measurements for atoms).

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• Significant Digits (1.6): Also called significant figures (SF), these numbers tell us how carefully a measurement was made. More significant digits mean a more precise measurement.

  • Qualitative observations: Descriptions using words, not numbers (like "the sky is blue").

  • Quantitative observations: Measurements using numbers (like "the rock weighs 5 grams").

  • Accuracy: How close your measurement is to the real or correct answer.

  • Precision: How close your different measurements are to each other (how consistent they are).

• Rules for determining significant digits (high-level):

  • Nonzero digits are always significant (e.g., 345 has 3 SF).

  • Leading zeros (zeros at the very beginning) are never significant; they're just placeholders (e.g., 0.0025 has 2 SF because the zeros before the 2 don't count).

  • Zeros between significant digits (captive zeros) are always significant (e.g., 1002 has 4 SF, 1.02 has 3 SF).

  • Trailing zeros in a decimal number (zeros at the end after a decimal point) are significant (e.g., 1.00 has 3 SF, 25.0 has 3 SF).

  • Trailing zeros in a whole number without a decimal point might be tricky; by convention, they usually don't count unless stated (e.g., 400 usually has 1 SF, but 400. has 3 SF).

  • All digits in the first part of a number written in scientific notation are significant (e.g., $1.73 \times 10^3$ has 3 SF).

  • Exact numbers have infinite significant figures (like counting 12 apples, or defined facts like 1 inch = 2.54 cm exactly).

  • When adding or subtracting: Your answer should be rounded to have the same number of decimal places as the number in your problem that had the fewest decimal places.

  • When multiplying or dividing: Your answer should be rounded to have the same number of significant figures as the number in your problem that had the fewest significant figures.

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• More on significant figures and examples (brief):

  • When you want to show that trailing zeros in a whole number are significant (e.g., 4000 g that you measured very precisely), you can add a decimal point (e.g., 4000. g) or use scientific notation ($4.000 \times 10^3$ g).

  • Example rounding for addition: If you add $125.6\ \text{g} + 43.28\ \text{g}$ you get 168.88 g. Since 125.6 has only one decimal place (the least precise), your final answer rounds to one decimal place: $168.9\ \text{g}$.

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• Dimensional Analysis (1.7):

  • This is also called "unit analysis" or the "factor-label method." It's a very helpful trick for solving problems where you need to change units (like changing inches to feet).

  • You use "conversion factors," which are fractions that equal 1 (like $\frac{1\ \text{foot}}{12\ \text{inches}}$). They let you change units without changing the actual value.

  • Steps: Start with the number and unit you know. Then multiply it by conversion factors, making sure the old units cancel out (one on top, one on bottom) until you get the units you want.

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• Examples of Dimensional Analysis:

  • Convert 5445 minutes to hours: $5445\ \text{min} \times \left(\frac{1\ \text{h}}{60\ \text{min}}\right) = 90.75\ \text{h}$. See how 'min' cancels out!

  • Money calculations using rates (e.g., earning $378 at a rate of $9/hour): To find total hours, you multiply your money by a conversion factor that gets rid of dollars: $378\ \text{dollars} \times \left(\frac{1\ \text{h}}{9\ \text{dollars}}\right) = 42\ \text{h}$.

  • Note: The conversion factor usually goes in the middle of your calculation. Always keep track of your units to make sure they cancel correctly.

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• Quick conversion reminders:

  • When asked how many meters are in 5.200 km, you know 1 km = 1000 m, so you multiply: $5.200\ \text{km} \times \left(\frac{1000\ \text{m}}{1\ \text{km}}\right) = 5200\ \text{m}$.

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• Density (1.8):

  • Definition: Density ($d$) tells you how much "stuff" (mass) is packed into a certain amount of space (volume); the formula is $d = \dfrac{m}{v}$.

  • If something has greater density, it feels heavier for the same size (like lead). If it's less dense, it feels lighter for the same size (like cotton).

  • Density is an intensive property, meaning it doesn't change even if you have a tiny piece or a huge amount of the substance. This makes it good for identifying things!

  • We often use density to figure out what an unknown substance is (e.g., real gold is much denser than fake gold).

  • If an object floats in a liquid, it's less dense than the liquid. If it sinks, it's denser.

  • Specific gravity: This is a way to compare a substance's density to the density of water. It's just a number, no units: $SG = \dfrac{d<em>{\text{substance}}}{d</em>{\text{water}}}$ (water's density is usually $1.000\ \text{g/mL}$).

  • Hydrometer readings: A hydrometer is a tool that floats higher in liquids that are more dense, and sinks lower in liquids that are less dense.

  • Graduated cylinder: A common lab tool used to measure the volume of liquids very carefully. You read the liquid level at the bottom of its curved surface (the meniscus).

  • Lab balances: These are tools to measure how much something weighs (its mass). Examples include old-fashioned Triple beam balances and modern electronic balances that often measure to about 0.01 g.

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• Temperature Scales (1.9):

  • Fahrenheit ($^\circ F$): Water freezes at 32°F and boils at 212°F.

  • Celsius ($^\circ C$): Water freezes at 0°C and boils at 100°C. This is what most scientists and countries use.

  • Kelvin ($K$): This is an absolute temperature scale. Water freezes at 273.15 K and boils at 373.15 K. Important: you don't use a degree symbol ($^\circ$) with Kelvin. 0 K is absolute zero, the coldest possible!

• Common conversions (useful):

  • Fahrenheit to Celsius: $C = \dfrac{5}{9}(F - 32)$

  • Celsius to Fahrenheit: $F = \dfrac{9}{5}C + 32$

  • Celsius to Kelvin: $K = C + 273.15$

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• Wrapping Up Chapter 1: Key terms (glossary snapshot)

  • Important concepts covered: accuracy, precision, significant digits, qualitative vs quantitative, pure substance, mixture, compound, element, reactant, product, dissolving/soluble, intensive vs extensive properties, density, solution, homogeneous vs heterogeneous, physical vs chemical changes, scientific method, theory vs law, SI unit, dimensional analysis.

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• Density lab notes (Density – Lab):

  • Density is a fundamental physical property used to characterize substances: $d = \dfrac{m}{v}$.

  • Common density units: $g/cm^3$ or $g/mL$ (for solids/liquids) and $g/L$ (often for gases).

  • Water's density is highest (about $1.000\ g/cm^3$) at 4°C. Density usually changes a little with temperature and pressure.

  • Specific gravity (SG): Compares a substance's density to water's density: $SG = \dfrac{d<em>{\text{substance}}}{d</em>{\text{water}}}$.

  • Hydrometer readings: A hydrometer floats higher in denser liquids.

  • Volume measurement tools: A graduated cylinder is used for precise liquid volume; always read the liquid level at the bottom of the curved meniscus.

  • Lab balances: Tools for measuring mass accurately, like Triple beam balances or electronic top-loading balances (which are usually precise to about 0.01 g or even better).