exponents
Summary
An exponent tells how many times a base is multiplied by itself. In general chemistry it appears in powers of ten, equilibrium expressions (coefficients become exponents) and rate laws (reaction orders). Most testable: exponents add when you multiply and subtract when you divide, so 10⁻⁵ ÷ 10⁻³ = 10⁻².
Detail
Meaning: In aⁿ, the exponent n counts the factors of a. A negative exponent means a reciprocal, and a fractional exponent means a root. Chemistry uses them in scientific notation (Kw = 1 × 10⁻¹⁴), in Keq expressions where each coefficient becomes the exponent on its concentration, and in rate laws, rate = k[A]^m[B]^n, where m and n are reaction orders. For a multistep reaction the orders come from experiment, not from the balanced equation.
Equation: aᵐ × aⁿ = aᵐ⁺ⁿ; aᵐ ÷ aⁿ = aᵐ⁻ⁿ; (aᵐ)ⁿ = aᵐⁿ; a⁻ⁿ = 1/aⁿ; a^(1/2) = √a. Here a is a nonzero base, and m and n are the exponents. Exponents are pure numbers, so they have no SI unit.
On the MCAT: There is no calculator, so you estimate with powers of ten. Typical items: doubling [A] in a second-order reaction quadruples the rate; reversing a reaction gives 1/K; doubling all coefficients squares K; a weak acid gives [H⁺] ≈ √(Ka × C), which halves the exponent.
Common confusion: Students add exponents when they add numbers. 10³ + 10³ = 2 × 10³, not 10⁶. The exponent rules apply to multiplication and division of the same base. Also, 10⁻³ is larger than 10⁻⁵, because a more negative exponent means a smaller number.
Sources
- Chemistry: The Central Science
- Chemistry (Zumdahl)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.