proportional
Summary
Two quantities are proportional when their ratio is constant, so y = kx: doubling x doubles y, and the graph of y versus x is a straight line through the origin. Most testable: gas-law temperature must be in kelvin, because 0 °C is not absolute zero, so only kelvin temperature is proportional to volume or pressure.
Detail
Meaning: Directly proportional (y ∝ x) means the ratio y/x stays constant, so multiplying x by any factor multiplies y by that same factor. Inversely proportional (y ∝ 1/x) means the product xy is constant, as in Boyle's law; its graph is a hyperbola. If y ∝ x², doubling x quadruples y.
Equation: y = kx, where k is the proportionality constant (units of y per unit of x). Charles's law: V = kT, where V is volume in m³, T is absolute temperature in K, and k is a constant in m³/K at fixed pressure and moles of gas.
On the MCAT: Passages ask how one variable responds to another: pressure with absolute temperature at constant volume, absorbance with concentration (Beer-Lambert law), gas solubility with partial pressure (Henry's law), first-order rate with [A]. Solve with ratios, such as P₁/T₁ = P₂/T₂, rather than finding k.
Common confusion: Linear is not always proportional. A line y = mx + b with b ≠ 0 is linear but not proportional. Volume against Celsius temperature is a line, but volume is proportional to kelvin temperature: 200 K to 400 K doubles it; 20 °C to 40 °C does not.
Sources
- Chemistry: The Central Science
- General Chemistry: Principles and Modern Applications
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.