How many grams of barium nitrate is needed to form a solution with 5.00 mass% Ba (NO3)2 in 400 grams of water.

% by mass = (mass solute/g soln)*100

let x = mass solute
[(x)/(400+x)]*100 = 5
Solve for x.

To determine the quantity of barium nitrate needed, we first need to calculate the mass of barium nitrate required to achieve a 5.00 mass% concentration in the solution.

Step 1: Calculate the mass of the solute (barium nitrate) in the solution.
Mass of solution = Mass of water + Mass of solute
Mass of solute = Mass of solution - Mass of water

Since we have 400 grams of water, the mass of solute is:
Mass of solute = Mass of solution - 400 grams

Step 2: Calculate the concentration of the solute.
Concentration (mass%) = (Mass of solute / Mass of solution) * 100

Substituting the given concentration (5.00 mass%) and rearranging the formula, we get:
Mass of solute = (Concentration * Mass of solution) / 100

Plugging in the values, we have:
Mass of solute = (5.00 * Mass of solution) / 100

Step 3: Calculate the mass of barium nitrate.
Barium nitrate (Ba(NO3)2) has a molar mass of 261.34 g/mol. It consists of one barium atom (Ba) and two nitrate ions (NO3). The molar mass of nitrate ions can be calculated as follows:
Molar mass of nitrate ions (NO3) = Molar mass of nitrogen (N) + 3 * Molar mass of oxygen (O)
Molar mass of nitrate ions (NO3) = 14.01 g/mol + 3 * 16.00 g/mol

Using the calculated molar mass of nitrate ions, we can find the molar mass of barium nitrate:
Molar mass of Ba(NO3)2 = Molar mass of barium (Ba) + 2 * Molar mass of nitrate ions (NO3)

Step 4: Use the molar mass to convert from moles to grams.
Number of moles of Ba(NO3)2 = Mass of solute / Molar mass of Ba(NO3)2

Finally, we can calculate the mass of barium nitrate needed to achieve a 5.00 mass% concentration in the solution.

Note: To complete the calculation, we need the molar mass of barium nitrate.