At 345K, the half-life for the decomposition of a sample of a gaseous compound initially at 55.5 kPa was 340s. When the pressure was 27.8 kPa, the half-life was found to be 170s. The order of the reaction is ______.(Integer answer)

Determining Reaction Order from Half-Life Data

At 345K, the half-life for the decomposition of a gaseous compound initially at 55.5 kPa was 340s. When the pressure was 27.8 kPa, the half-life was found to be 170s.

Given Data:

• Temperature: T = 345K (constant)
• At P₁ = 55.5 kPa: (t_1/2)₁ = 340s
• At P₂ = 27.8 kPa: (t_1/2)₂ = 170s

Step 1: Half-Life Relationship

For a reaction of order n, the half-life relationship is:

(t_1/2)₁ / (t_1/2)₂ = (P₁ / P₂)^1-n

Step 2: Substitute Values

340/170 = (55.5/27.8)^1-n 2 = (2)^1-n

Step 3: Solve for n

Since the bases are equal (both = 2), the exponents must be equal:

1 = 1 - n ∴ n = 0

Step 4: Verification

For a zero-order reaction:

• Half-life is inversely proportional to initial concentration (or pressure)
• t_1/2 ∝ 1/P₀
• This matches our observation: higher pressure → shorter half-life

The order of the reaction is: 0 (Zero Order)

Conclusion:

The reaction is zero-order with respect to the gaseous compound. In zero-order reactions, the rate is independent of the concentration of the reactant, and the half-life is inversely proportional to the initial pressure.