A 5 g igal reguires addinng 8.6 ml diluent to get concentration of 250 mg/ml. The powder volume is __ ml a.9.3 b.10.6 c.11.4 d.12.8

Does the powder form a solution or a colloid? IT makes a big difference. In solutions, the sum of the powder volume and the solvent volume seldom equals the solution volume: the solute finds a way to "fit" inside the solvent particles.

Now if the powder is a colloid, often the volumes do add. In this case, I don't see that any of the answers are correct.
Powder volume + 8.6=total
Powder mass=500mg

concentration= 500mg/(8.6 +PV)=250/1
which has no solution.

5 gm/X=250mg/1ml 5gm=5000mg

5000mg/X=250mg/1 ml where X=final volm
5000/250=X
X=20ml
you added 8.6 ml so difference is
20-8.6=11.4ml powder vol

To solve for the powder volume, we can use the given information:

1. The concentration of the solution is 250 mg/ml.
2. The mass of the powder is 5 g.
3. 8.6 ml of diluent is added.

We can set up the equation for concentration as follows:

(concentration) = (mass of powder) / (volume of solution)
250 mg/ml = 5000 mg / (volume of solution)

To find the volume of the solution, we need to rearrange the equation:
volume of solution = 5000 mg / (250 mg/ml)
volume of solution = 5000/250 ml
volume of solution = 20 ml

Since 8.6 ml of diluent is added to the powder, we can determine the volume of the powder by subtracting the diluent volume from the total volume of the solution:
volume of powder = volume of solution - volume of diluent
volume of powder = 20 ml - 8.6 ml
volume of powder = 11.4 ml

Therefore, the answer is option c) 11.4 ml.