Dimensional Analysis
Why do we do dimensional analysis?
So we can report the same data using different units.
What is the difference between a physical and chemical property?
Physical properties can be observed without changing a substance’s identity (e.g., melting point, color). Chemical properties describe how a substance reacts to form new substances (e.g., flammability, reactivity with acid).
Give an example of two base units in the metric system.
Meter (length), second (time), gram (mass), ampere (electric current), kelvin (temperature), mole (amount), candela (light intensity).
Write 5,200 in scientific notation
5.2×103
How many significant figures are in the number 0.00450?
3 sig figs (zeros before the 4 are placeholders, but the trailing zero after the 5 counts).
What is the difference between a pure substance and a mixture?
A pure substance has only one type of particle (element or compound). A mixture contains two or more substances physically combined.
What separation method would you use to separate sand from water?
Filtration — sand particles are trapped, water passes through
Convert 3.5 hours into seconds using dimensional analysis.
12,600 s
Identify whether ice melting is a physical or chemical change, and explain why.
Physical change — it changes state (solid → liquid) but is still H₂O.
Convert 4.2 kilometers (km) into meters (m).
4.2 km×1000=4200 m.
Write 0.00084 in scientific notation
8.4×10-4
Round 52.467 g to 3 significant figures.
52.5 g
Classify each as an element, compound, or mixture:
(a) Oxygen gas (O₂)
(b) Salt water
(c) Carbon dioxide (CO₂)
(a) Element, (b) Mixture, (c) Compound
How could you separate salt dissolved in water?
Evaporation (or distillation). Evaporation leaves the salt behind; distillation collects pure water.
A car travels at 65 miles per hour. Use dimensional analysis to find the speed in meters per second. (1 mile = 1.609 km)
29.05 m/s
Classify each as a physical or chemical property:
(a) Density of aluminum = 2.7 g/mL
(b) Iron rusting in moist air
(c) Boiling point of ethanol = 78 °C
(a) Physical property, (b) Chemical property, (c) Physical property
Convert 75,000 milligrams (mg) into grams (g)
75 g
Multiply: (3.0×104)×(2.0×103)
6.0×107
Perform the operation with correct sig figs:
(2.45×3.2)
7.8
Is brass (a combination of copper and zinc) an element, compound, or mixture?
Brass is a homogeneous mixture (solution) because copper and zinc are blended uniformly.
You are given a mixture of iron filings and sulfur powder. How could you separate them?
Use a magnet — iron is magnetic, sulfur is not.
The density of a liquid is 1.2 g/mL. What is this density in kg/L?
1.2 kg/L
A silver spoon turns dark after sitting out in the air. Is this a physical or chemical change? How do you know?
Chemical change — silver reacts with sulfur in the air to form silver sulfide (a new substance with different properties).
Convert 8.5 gigameters (Gm) into megameters (Mm)
8500 Mm
Divide: (9.0×106)/(3.0×102)
3.0×104
Perform the addition with correct sig figs:
135.6+2.37+14.2
152
A cloudy liquid is left to sit, and solid particles settle to the bottom. What type of mixture is this, and how do you know?
It is a heterogeneous mixture (suspension) because the particles are large enough to separate and do not stay evenly mixed.
A laboratory sample contains a mixture of different pigments in ink. Which method should be used to separate and identify the pigments?
Chromatography — separates components based on how they travel through a medium.
The world record for the men’s marathon is about 2 hours and 1 minute. Use dimensional analysis to calculate the runner’s average speed in meters per second if the marathon distance is 26.2 miles. (1 mile = 1.609 km)
5.81 m/s
You mix two clear liquids. A solid forms, heat is released, and bubbles are produced. Which specific pieces of evidence indicate a chemical change, and why is this not just a physical change?
Formation of a precipitate (solid), release of gas (bubbles), and energy change (heat) are all indicators of a chemical change — new substances with new properties formed, not just a state or size change.
6.3 × 10¹² picoseconds (ps) into seconds (s)
6.3 s
The wavelength of red light is about 0.00000065 m. Express this in scientific notation and then convert it into nanometers (nm).
650 nm
A sample has a mass of 4.327 g and a volume of 1.46 mL. Calculate the density with correct sig figs.
2.96 g/mL
A student tests four samples: gold, salt, salt water, and air.
Which are pure substances, and which are mixtures?
Which mixtures are homogeneous vs. heterogeneous?
Pure substances: gold (element), salt (compound).
Mixtures: salt water (homogeneous), air (homogeneous).
None of these are heterogeneous.
Crude oil is a mixture of many hydrocarbons with different boiling points. Which technique is used in industry to separate it into usable parts like gasoline, kerosene, and diesel?
Distillation — separates by differences in boiling points