Four solution are prepared and mixed together:

Start with 100.0ml of 0.100M BaCl2.
Add 50.0ml of 0.100M AgNO3.
Add 50.0ml of 0.100M H2So4.
Add 250.0ml of 0.100M NH4.
Write an equation for any reaction that occurs after each step and calculate the concentration of Ba,CL,NO3,NH4 in the final solution assuming that all reaction go to completion

This is a work horse of a problem. I'll start the first one.

2AgNO3 + BaCl2 ==> 2AgCl + Ba(NO3)2
(Ba^2+) = 0.1 M x (100/450) = ?
(NO3^-) = 0.1 M x (50/450) = ?
etc.

To write the equations for each reaction and calculate the final concentration of Ba, Cl, NO3, and NH4, we first need to identify the possible reactions and products in each step.

Step 1: BaCl2 + AgNO3
The combination of BaCl2 and AgNO3 can potentially produce a white precipitate of AgCl and a solution of Ba(NO3)2.
The balanced equation for this reaction is:
BaCl2 + 2AgNO3 -> 2AgCl + Ba(NO3)2

Step 2: Ba(NO3)2 + H2SO4
The reaction between Ba(NO3)2 and H2SO4 can result in the formation of a white precipitate of BaSO4. The balanced equation is:
Ba(NO3)2 + H2SO4 -> BaSO4 + 2HNO3

Step 3: BaSO4 + 2NH4OH
When BaSO4 reacts with NH4OH, it forms a white precipitate of Ba(OH)2 and ammonium sulfate (NH4)2SO4. The balanced equation is:
BaSO4 + 2NH4OH -> Ba(OH)2 + (NH4)2SO4

Now, let's calculate the concentration of each ion in the final solution, assuming all the reactions go to completion.

Step 1:
In 100.0 mL of 0.100M BaCl2, there are:
0.100 mol/L x 0.100 L = 0.010 mol of Ba2+
0.100 mol/L x 0.100 L = 0.010 mol of Cl-

Step 2:
After mixing 50.0 mL of 0.100M AgNO3, you have:
0.100 mol/L x 0.050 L = 0.005 mol of Ag+
0.100 mol/L x 0.050 L = 0.005 mol of NO3-

Step 3:
After adding 50.0 mL of 0.100M H2SO4, since the reaction goes to completion, there will be no H2SO4 left, and only the products remain.

Step 4:
Lastly, after adding 250.0 mL of 0.100M NH4OH, there are:
0.100 mol/L x 0.250 L = 0.025 mol of NH4+
0.100 mol/L x 0.250 L = 0.025 mol of OH-

Now, let's summarize the final concentrations of each ion in the solution:
- Ba2+: 0.010 mol
- Cl-: 0.010 mol
- Ag+: 0.005 mol
- NO3-: 0.005 mol
- NH4+: 0.025 mol
- OH-: 0.025 mol

Note that since the reaction goes to completion, the final concentrations are equal to the initial moles present in each step.