Homework problem G13

[april_bussey_1C]

To prepare a fertilizer solution, a fl orist dilutes 1.0 L of
0.20 m NH4NO3(aq) by adding 3.0 L of water. The fl orist then
adds 100. mL of the diluted solution to each plant. How many
moles of nitrogen atoms will each plant receive? Solve this
exercise without using a calculator. I have no idea how to go about solving this problem. When it comes to dilutions I get confused on what the problem is asking of me and what steps I should be taking to answer the problem.

[Patience Olsen 1A]

Refer to the answer for viewtopic.php?f=10&t=30583 .

The first step is to find the molarity of the diluted solution.
The person asking the question above solved this by using the dilution formula M1V1 = M2V2. This formula is based on the fact that the number of moles of solute will remain the same when more solvent is added: (mol = mol) so (mol/L * L = mol/L * L).

The original solution is 1.0 L of 0.20 M NH4NO3. The diluted solution is 4.0 L (1.0 L for original solution + 3.0 L water added) of an unknown concentration of NH4NO3.
M1V1 = M2V2
0.20 mol/L * 1.0 L = M2 * 4.0 L
M2 = 0.050 M

Use the concentration of the solution to find the moles of NH4NO3 in each 100. mL sample:
0.050 mol NH4NO3/L * 0.100 L = 0.0050 mol NH4NO3

In each molecule of NH4NO3, there are 2 nitrogen atoms. Multiply by this ratio to find the moles of nitrogen:
0.0050 mol NH4NO3 * 2 mol N/1 mol NH4NO3 = 0.0100 mol N

Each plant receives 0.0100 mol N.