Question

The disaccharide lactose can be decomposed into its constituent sugars galactose and glucose. This decomposition can be accomplished through acid-based hydrolysis or by the enzyme lactase. Lactose intolerance in humans is due to the lack of lactase production by cells in the small intestine. However, the stomach is an acidic environment; therefore, one might expect lactose hydrolysis to still be an efficient process. The following data were obtained on the rate of lactose decomposition as a function of acid and lactose concentration.

Initial Rate (M^-1 s^-1) [Lactose]o (M) [H+](M)
0.00116 0.01 0.001
0.00232 0.02 0.001
0.00464 0.01 0.004


Required:
Using this information, determine the rate law expression for the acid-based hydrolysis of lactose.

Answer 1

Rate = 116m⁻¹s⁻¹[lactose][H]⁺

Step-by-step explanation:

the formula for rate of reaction is given as

Rate = k[lactose]∧α[H]⁺∧β

we solve for the value of α and β

([lactose]₁/[lactose]₂)∧α

α =
`(ln(0.00116)/(0.00232) )/(ln(0.01)/(0.02) )`

when we divide this equation

α =
`(ln0.5)/(ln0.5)`

α = 1

we find β

R₁/R₂ = 0.01/0.02(0.001/0.001)∧β

0.00116/0.00232 = 0.5(1)∧β

β = 1

Rate = k[lactose]∧α[H]⁺∧β

we have to find the value for k

k = 0.00116/0.01(0.001)

k = 0.00116/0.00001

= 116m⁻¹s⁻¹

Rate = 116m⁻¹s⁻¹[lactose][H]⁺