Fundamental G Problem Help

[Stacey Phan 2I]

To prepare a fertilizer solution, a florist dilutes 1.0 L of 0.20 M NH4NO3(aq) by adding 3.0 L of water. The florist 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.

The answer key said 0.01 moles.

I tried to solved it by rearranging mol/L=M to mol=L*M because initial moles = final moles. 1L * 0.2M = 0.2 moles. Since there are two nitrogen atoms in the chemical formula, I multiplied the 0.2 moles * 2 = 0.4 moles. I am confused how to get 0.01 moles?

Please help me I am confused and stressed about the midterm :)

[Bronson Mathos 1H]

In order to solve this problem, I started off by using the equation M initial x V initial=M final x V final, and with this equation you plug in all known values to find that M final is unknown, meaning you must solve for it and you should get 0.05 moles per liter. From here, you use this molarity and 100.ml(in liters) to find the amount of moles of NH4NO3 present, using the equation mol NH4NO3=MV, which yields a result of: (0.05mol*L^-1)(100x10^-3L)=5x10^-3 mol NH4NO3. From here, you simply need to solve for moles of N by converting mol NH4NO3 to mol N: (5x10^-3 mol NH4NO3)x(2molN/1 mol NH4NO3)= 1.0x10^-2 mol N or 0.01 mol N.

[vanessanguyen3I]

I completely understand your thinking and I got the same answer too when I first tried it! Let me try to clear things up.

First, I think you are applying the concept that even if you dilute a solution, the amount of moles stays the same. This is because you are simply adding more solution, but the same amount of solvent stays in the container. When you add three liters to the solution, the amount of moles in the solution is still 0.2. However, when you pour 100 mL of the solution into the plant, you are now splitting up the solution, so the amount of moles is not the same anymore. As a result you have to use the 0.05 moles/L and find out how many moles there are in 100 mL of that solution. When you mind the amount of moles, then you multiply by 2 to find the amount of moles of N. Hope this helps!

[Stacey Phan 2I]

I completely understand your thinking and I got the same answer too when I first tried it! Let me try to clear things up.

First, I think you are applying the concept that even if you dilute a solution, the amount of moles stays the same. This is because you are simply adding more solution, but the same amount of solvent stays in the container. When you add three liters to the solution, the amount of moles in the solution is still 0.2. However, when you pour 100 mL of the solution into the plant, you are now splitting up the solution, so the amount of moles is not the same anymore. As a result you have to use the 0.05 moles/L and find out how many moles there are in 100 mL of that solution. When you mind the amount of moles, then you multiply by 2 to find the amount of moles of N. Hope this helps!

I didn't realize the amount of moles would change at first so thank you for clearing this up!