For a reaction with rate law rate = k [A]^2 [B], determine the overall order and how to experimentally determine the exponents

For a reaction with rate law rate = k [A]^2 [B], determine the overall order and how to experimentally determine the exponents

• A. Overall order is 3; determine exponents by varying [A] and [B] independently and observing rate changes.
• B. Overall order is 2; vary [A] and [B] together
• C. Overall order is 3; measure temperature only
• D. Overall order is 1; measure initial concentrations

Answer: (A)

The rate law r = k [A]^2 [B] means the reaction rate scales with A squared and B to the first power, so the overall reaction order is 2 + 1 = 3. To figure out the exponents experimentally, vary one concentration at a time while holding the others constant and observe how the rate responds. If you change [A] and keep [B] fixed, the rate should change as [A]^2, so you infer an exponent of 2 for A. Then vary [B] with [A] held constant; the rate should change linearly with [B], giving an exponent of 1 for B. A reliable way to extract these exponents is to plot log(rate) versus log([A]) and log(rate) versus log([B]); the slopes of the lines give the respective exponents. Varying both reactants together or focusing only on temperature changes won’t reveal the exponents, and merely measuring initial concentrations won’t show how rate scales with each concentration.

The rate law r = k [A]^2 [B] means the reaction rate scales with A squared and B to the first power, so the overall reaction order is 2 + 1 = 3. To figure out the exponents experimentally, vary one concentration at a time while holding the others constant and observe how the rate responds. If you change [A] and keep [B] fixed, the rate should change as [A]^2, so you infer an exponent of 2 for A. Then vary [B] with [A] held constant; the rate should change linearly with [B], giving an exponent of 1 for B. A reliable way to extract these exponents is to plot log(rate) versus log([A]) and log(rate) versus log([B]); the slopes of the lines give the respective exponents. Varying both reactants together or focusing only on temperature changes won’t reveal the exponents, and merely measuring initial concentrations won’t show how rate scales with each concentration.