Question

How do i estimate the density of a solution of two compounds, when im given wt% and the specific gravity?

Answer 1

`\rho_s=(\rho_w)/((wt1)/(SpGr1)+(wt2)/(SpGr2))`

The only other data you need is the density of water ρw.

Step-by-step explanation:

We can start by the volume balance

`V_s=V_1+V_2`

We can replace the volumes with V=M/ρ

`(M_s)/(\rho_s)=(M_1)/(\rho_1)+(M_2)/(\rho_2)`

If we divide every term by Ms

`(M_s/M_s)/(\rho_s)=(M_1/M_s)/(\rho_1)+(M_2/M_s)/(\rho_2)`

By definition, wt=Mi/Msol, so we can replace that in the expression

`(1)/(\rho_s)=(wt1)/(\rho_1)+(wt2)/(\rho_2)`

Then we have the expression of the density of the solution

`\rho_s=(1)/((wt1)/(\rho_1)+(wt2)/(\rho_2))`

To replace ρ1 and ρ2, you have to multiply the specific gravity of the components and the density of water.

`\rho_s=(1)/((wt1)/(SpGr1\rho_w)+(wt2)/(SpGr2\rho_w))\\\\\rho_s=(\rho_w)/((wt1)/(SpGr1)+(wt2)/(SpGr2))`