Ammonium sulfate has a chemical formula of `(NH_4)_2 SO_4` and molecular mass of 132.14 g. The molarity of a solution is the ratio of number of moles of solute to the volume of solution in liters.
Here, we have 10.8 g of ammonium sulfate and hence the number of moles of solute are:
number of moles = mass / molecular mass = 10.8 g / 132.14 g/mol = 0.082 moles
Volume of solution = 100 mL = 0.1 L
Thus, molarity of ammonium solution = 0.082 moles / 0.1 l = 0.82 M
Now, this solution is diluted by taking 10 ml of this solution and adding 40 ml water to it. We can use the following relationship
C1V1 = C2V2
where C1 and C2 are the concentrations of solutions before and after dilution and V1 and V2 are the volumes of solutions before and after the dilution.
Thus, 0.82 M x 10 ml = C2 x 50 ml
or, C2 = 0.164 M
Thus, the resulting solution has a concentration of 0.164 M.
Hope this helps.