You extract the iron from a tablet and dilute that to 250.0 ml in a volumetric flask. You transfer 0.400 ml of this solution to a 25.0 ml volumetric flask and dilute this to volume. When you measure the concentration of this solution, you find that it is 3.27 ppm Fe. How many milligrams of Fe were in the tablet?
I think the easy way to do this is to convert 3.27 ppm in the last sample to mg in that sample. We know 3.27 ppm = 3.27 mg/L and since this in 25 mL, then 3.27 mg/L x 0.025 L = 0.08175 mg in the 25 mL. That's also the mg Fe in the 0.4 mL. If 0.08175 mg are in 0.4mL, then 0.08175 x (250/0.4) = ? mg in the original sample.
To solve this problem, we need to use the given information and follow a series of calculations to find the amount of iron (Fe) in milligrams present in the tablet. Let's break down the steps to find the answer.
Step 1: Calculate the concentration of the solution after the initial dilution
The concentration of the initially diluted solution is given as 3.27 ppm (parts per million) Fe. However, we need to convert this to milligrams per liter (mg/L) for easier calculations.
1 ppm = 1 mg/L
So, 3.27 ppm = 3.27 mg/L
Step 2: Calculate the amount of Fe in the initially diluted solution
We know that the volume of the initially diluted solution is 0.400 mL. To find the amount of Fe in this solution, we can use the formula:
Amount of Fe (in mg) = Concentration of Fe (in mg/L) × Volume (in L)
Concentration of Fe = 3.27 mg/L (from step 1)
Volume = 0.400 mL = 0.400 mL ÷ 1000 mL/L = 0.0004 L
Amount of Fe = 3.27 mg/L × 0.0004 L = 0.001308 mg
Step 3: Calculate the concentration of the final solution
Now, we have transferred a volume of 0.400 mL from the initially diluted solution to a 25.0 mL volumetric flask and diluted it to volume. So, the final volume is 25.0 mL.
To find the concentration of the final solution, we can use the equation:
Concentration of the final solution = (Amount of Fe transferred ÷ Final volume) × 1000000
Amount of Fe transferred = 0.001308 mg (from step 2)
Final volume = 25.0 mL = 25.0 mL ÷ 1000 mL/L = 0.025 L
Concentration of the final solution = (0.001308 mg ÷ 0.025 L) × 1000000 = 52.32 mg/L
Step 4: Calculate the amount of Fe in the tablet
Lastly, we need to calculate the amount of Fe in the original tablet. We can use the equation:
Amount of Fe in the tablet = Concentration of the final solution (in mg/L) × Volume of the final solution (in L)
Concentration of the final solution = 52.32 mg/L (from step 3)
Volume of the final solution = 0.025 L
Amount of Fe in the tablet = 52.32 mg/L × 0.025 L = 1.308 mg
Therefore, there are 1.308 milligrams of Fe in the tablet.
To find out how many milligrams of Fe were in the tablet, we can use the given concentration and the dilution factor.
Step 1: Calculate the dilution factor.
The dilution factor is the ratio of the final volume to the initial volume.
Initial volume = 250.0 ml
Final volume = 25.0 ml
Dilution factor = Final volume / Initial volume
Dilution factor = 25.0 ml / 0.400 ml
Dilution factor = 62.5
Step 2: Calculate the concentration of the original solution.
We know that the concentration of the final solution is 3.27 ppm Fe.
Concentration of the original solution = Concentration of the final solution * Dilution factor
Concentration of the original solution = 3.27 ppm * 62.5
Concentration of the original solution = 204.38 ppm Fe
Step 3: Calculate the mass of Fe in the original solution.
To convert ppm (parts per million) to milligrams, we use the fact that 1 ppm = 1 mg/L.
Mass of Fe = Concentration of the original solution * Volume
Mass of Fe = 204.38 ppm * 250.0 ml
Since 1 ppm = 1 mg/L, we can convert the volume from ml to L.
Mass of Fe = 204.38 mg/L * 0.250 L
Mass of Fe = 51.09 mg
Therefore, there were approximately 51.09 milligrams of Fe in the tablet.