Homework Problem G.13 in Fundamentals

[somyapanchal1D]

How would you go about solving homework problem G.13 in Fundamentals Exercises? The question is also shown below:

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.

[David Zhang 1B]

You first have to find the concentration of the diluted solution. You can find the moles of the initial solution since they give you the molarity of the solution and an initial volume of 1 Liter. Since molarity is moles per volume, the initial solution has 0.20 moles.When the florist adds water, the volume increases by 3 L but the moles stay the same. Using the final solution, you then find 100 mL of the diluted solution by multiplying the final molarity by 0.100 L (100 mL). You would then multiple that answer by 2 since each NH4NO3 molecule has 2 N atoms.

[hannabarlow1A]

This problem can be solved as long as we know that even if a solution is diluted, the amount of solute stays the same. The variable for the amount of solute is n and n can be calculated by multiplying molarity (M) times volume (v). Thus, knowing that n stays the same, M times v also stays the same. We multiply the initial molarity (.2) and initial volume (1) and set it equal to the final molarity (x) times the final volume (4 because we added 3 liters to the initial 1), to solve for the final molarity. Thus, (.2) * (1) = 4x and x must equal .05 M. We are not done yet, since this answer is M, or moles per liter. To find our answer in moles, we multiple .05 M (aka .05 moles per liter) times 0.1 liters (the amount given to the plants) so that liters cancel out and we are left with 0.005 moles. Finally, since the question asks about nitrogen ions, we multiply this answer by 2 since there are two nitrogen ions in the molecules. Thus, the answer is .01 moles of nitrogen atoms.

[jlinwashington1B]

I'm also confused with how to solve this... When it says "how many moles of nitrogen", does that mean we have to find the mass of nitrogen and then multiply it by Avogadro's number?? Please help.