You dissolve 157.1 g of ammonium nitrate in a 250 mL volumetric flask and add water to the mark (call this solution A). You take 30 mL of solution A and place it in a 100 mL volumetric flask and add water to the mark (this is solution B). Next you take 50 mL of solution B and place it in a 500 mL volumetric flask and add water to the mark (this is solution C). Finally you take 10 mL of solution A, 10 mL of solution B and 10 mL of solution C and mix them to form solution D. What is the concentration (M) of solution D? (see problem 6 in Zumdahl test bank)
To find the concentration of solution D, we need to determine the amount of ammonium nitrate present in solution D and the volume of solution D.
Let's break down the steps and calculate the concentration step by step:
Step 1: Solution A
In solution A, we dissolve 157.1 g of ammonium nitrate in a 250 mL volumetric flask and then dilute it to the mark with water. The mass of ammonium nitrate and the volume of solution are given.
Step 2: Solution B
We take 30 mL of solution A and transfer it to a 100 mL volumetric flask, then dilute it to the mark with water. This creates solution B.
Step 3: Solution C
We take 50 mL of solution B and transfer it to a 500 mL volumetric flask, then dilute it to the mark with water. This creates solution C.
Step 4: Solution D
We take 10 mL each of solutions A, B, and C and mix them together to form solution D.
Now, let's calculate the amount of ammonium nitrate and the volume of solution D.
Step 1: Solution A
The mass of ammonium nitrate in solution A is 157.1 g.
Step 2: Solution B
To find the amount of ammonium nitrate in solution B, we need to use the concept of dilution. Since 30 mL of solution A was transferred to a 100 mL flask, the ratio of ammonium nitrate stays the same. Thus, the amount of ammonium nitrate in solution B is (30 mL / 250 mL) * 157.1 g.
Step 3: Solution C
Similarly, the amount of ammonium nitrate in solution C is (50 mL / 100 mL) * [(30 mL / 250 mL) * 157.1 g].
Step 4: Solution D
We take 10 mL each of solutions A, B, and C, so we have a total volume of 30 mL for solution D. The amount of ammonium nitrate in solution D is the sum of the amounts from solutions A, B, and C.
Finally, to find the concentration of solution D (Molarity, M), we divide the amount of ammonium nitrate in solution D by the volume of solution D and convert the units if necessary.
Note: Since the actual values of the volumes and masses were not provided, I cannot provide the exact concentration. You'll need to substitute the given values into the calculations.
To determine the concentration (M) of solution D, we will calculate the number of moles of ammonium nitrate (NH4NO3) in each solution and then divide by the volume of solution D.
1. Calculate the moles of ammonium nitrate in Solution A:
- Molar mass of NH4NO3 = 80.04 g/mol
- Moles of NH4NO3 = mass / molar mass = 157.1 g / 80.04 g/mol
2. Calculate the volume of Solution B (30 mL) in liters:
- Volume of Solution B = 30 mL / 1000 mL/L
3. Calculate the moles of ammonium nitrate in Solution B:
- Moles in Solution B = (Moles in Solution A) * (Volume of Solution B)
4. Calculate the volume of Solution C (50 mL) in liters:
- Volume of Solution C = 50 mL / 1000 mL/L
5. Calculate the moles of ammonium nitrate in Solution C:
- Moles in Solution C = (Moles in Solution B) * (Volume of Solution C)
6. Calculate the volume of Solution D (10 mL of each Solution A, B, and C) in liters:
- Volume of Solution D = (10 mL + 10 mL + 10 mL) / 1000 mL/L
7. Calculate the moles of ammonium nitrate in Solution D:
- Moles in Solution D = (Moles in Solution A) + (Moles in Solution B) + (Moles in Solution C)
8. Calculate the concentration of Solution D:
- Concentration of Solution D (M) = Moles in Solution D / Volume of Solution D
Performing these calculations will give us the concentration of solution D.