He rate constant for this zero‑order reaction is 0.0130 M ⋅ s − 1 at 300 ∘ C. A ⟶ products How long (in seconds) would it take for the concentration of A to decrease from 0.890 M to 0.280 M?

188 s

Explanation:

We are told the reaction is second order respect to A so we know the expression for the rate law is

rate = - Δ[A]/Δt = k[A]²

where the symbol Δ stands for change, [A] is the concentration of A, and k is the rate constant.

The integrated rate law for this equation from calculus is

1 / [A]t = kt + 1/[A]₀

where  [A]t is the concentration of A at time t, k is the rate constant, and [A]₀ is the initial concentration.

Since we have all the information required to solve this equation lets plug our values

1 / 0.280= 0.0130x t  + 1 / 0.890

( 1 / 0.280 - 1 / 0.890)M⁻¹ = 0.0130 M⁻¹ ·s⁻¹t

t = 188 s

the density of gold = 19.3 g/cm3

the relation between density and mass and volume is

density = mass / volume

given :

mass of gold = 13 g

density = 13g / volume = 19.3

volume = 13 /19.3 = 0.67 cm^3

thus volume of gold nugget = 0.67 cm^3