(i) What is the two dimensional coordination number of a molecule in square close packed layer?
(ii) Derive the integrated rate law for a first order reaction?

Explanation

(i) Square close packing : When the spheres of the second row are placed exactly above those of the first row. This way the spheres are aligned horizontally as well as vertically. The arrangement is AAA type. Coordination number is 4.

(ii) A reaction whose rate depends on the reactant concentration raised to the first power is called a first order reaction.
First order reaction is
`A to` product
Rate law can be expressed as, Rate `=k[A]^(1)`
Where, k is the first order rate constant
`(-d[A])/(dt)=k[A]^(1) rArr (-d[A])/([A])=k.dt " " ...(1)`
Integrate the above equation (1) between the limits of time t = 0 and time equal to t, while the concentration varies from initial concentration `[A_(0)]` to [A] at the later time.
`int_(A_(0))^(A) (-d[A])/([A])=k int_(0)^(t) dt`
`-In[A]_(A_(0))^(A)=k(t)_(0)^(t)`
`-In[A]-(-In[A_(0)])=k(t-0) rArr -In[A]+In[A_(0)]=kt`
`In(([A_(0)])/([A]))=kt " " ...(2)`
This equation (2) is in natural logarithm. To convert it into usual logarithm with base 10, we have to multiply the term by 2.303
`2.303 log(([A_(0)])/([A]))=kt rArr k=(2.303)/(t)log(([A_(0)])/([A]))" "...(3)`