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Chapter 13: Problem 18

The vitamin \(\mathrm{B}_{12}\) content of a multivitamin tablet is determined by the following procedure. A sample of 10 tablets is dissolved in water and diluted to volume in a 100 -mL volumetric flask. A 50.00 -mL portion is removed and \(0.500 \mathrm{mg}\) of radioactive vitamin \(\mathrm{B}_{12}\) having an activity of 572 cpm is added as a tracer. The sample and tracer are homogenized and the vitamin \(\mathrm{B}_{12}\) isolated and purified, producing \(18.6 \mathrm{mg}\) with an activity of 361 cpm. Calculate the milligrams of vitamin \(\mathrm{B}_{12}\) in a multivitamin tablet.

Short Answer

Expert verified
Each tablet contains approximately 0.587 mg of vitamin \(\mathrm{B}_{12}\).

Step by step solution

01

Understand the problem statement

We need to find out the amount of vitamin \(\mathrm{B}_{12}\) in a single tablet, given that 10 tablets were dissolved, the mixture was diluted and a portion of it was analyzed using a tracer with known activity.
02

Determine the total activity after purification

The activity after purification is 361 cpm. Since the tracer with known activity (572 cpm) was added, we must calculate the reduction in activity to determine the actual vitamin \(\mathrm{B}_{12}\) present before adding the tracer.
03

Use dilution ratio to find the original concentration

Because the tracer has 572 cpm and the result after isolation is 361 cpm, it shows the total activity. The ratio of these should attribute to the isolated vitamin \(\mathrm{B}_{12}\) and tracer, allowing us to calculate the untagged vitamin \(\mathrm{B}_{12}\) content. Thus, \[\frac{361 \text{ cpm}}{572 \text{ cpm}} = \frac{\text{Actual amount of vitamin }\mathrm{B}_{12}}{\text{Total after purification (18.6 mg)}}\]This ratio can be used to determine the original content before the tracer was added.
04

Calculate the mass of vitamin \(\mathrm{B}_{12}\)

Using the proportion derived in Step 3, the mass of the original vitamin \(\mathrm{B}_{12}\) is calculated as:\[\text{Original mass} = 18.6 \times \frac{361}{572} \text{ mg}\]Calculating this gives approximately 11.74 mg of vitamin \(\mathrm{B}_{12}\).
05

Adjust for sample size

Remember, the calculation from Step 4 was for the sample derived from 10 tablets and half of the flask content. Since only a 50 mL sample was taken from a 100 mL solution originally containing \(10\times \) tablets:\[\text{Original vitamin } \mathrm{B}_{12} \text{ per tablet} = \frac{\text{Original mass}}{10\times 2} = \frac{11.74}{10 \times 2} \]Therefore, approximately 0.587 mg per tablet.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Vitamin B12 analysis
Vitamin B12 is an essential nutrient commonly found in multivitamins, and accurate analysis of its content is vital for both nutritionists and consumers. When analyzing Vitamin B12 in multivitamin tablets, the sample undergoes several steps:
  • First, a batch of tablets is dissolved in water to create a homogeneous solution. This ensures that each component in the tablet is evenly distributed throughout the solution.
  • The solution is then diluted to a known volume, in this case, 100 mL. Dilution helps in managing and accurately measuring highly concentrated samples.
Once a uniform solution is prepared, a portion of it is used for further testing. By isolating this portion, it becomes easier to conduct sensitive tests like tracer technique analysis to determine the presence and quantity of Vitamin B12. Understanding the principles of solution preparation and homogenization is crucial for accurate Vitamin B12 analysis.
Radioactive tracer technique
The radioactive tracer technique is a powerful tool for analyzing the presence of specific substances within a mixture. It involves adding a known quantity of a radioactive isotope to the sample, which acts as a marker or tracer. The salient aspects of this method include:
  • After adding the tracer to the sample, its activity is measured in counts per minute (cpm). This allows for precise detection even at low concentrations.
  • The process involves purification and isolation of the specific substance of interest, in this case, vitamin B12, separated from other components after tracer addition.
  • The activity of both the sample and tracer is measured after purification, to compare against the initial known activity of the tracer.
By evaluating the reduction in activity from the initial tracer, it is possible to determine the amount of the target substance. This method is especially useful in complex mixtures, allowing for accurate and reliable results.
Calculation of concentrations
Calculating the concentration of Vitamin B12 using the radioactive tracer technique involves several logical and mathematical steps. It requires accounting for both the dilution and the activity counts before and after purification. Here is a simplified view of the calculation process:
  • We start by noting the initial concentration and activity of the radioactive tracer, which provides the baseline for comparison.
  • By comparing the activity before and after purification, a ratio is established, which indicates the proportion of tracer incorporated into the purified vitamin B12 sample.
  • This ratio reflects the change in activity due to the presence of the original Vitamin B12 content, allowing for the calculation of its actual amount.
The critical step then involves adjusting for the sample portion taken against the entire mixture (e.g., 50 mL from an initial 100 mL), and further accounting for the number of tablets used.
Ultimately, through calculation adjustments, the concentration of Vitamin B12 per tablet can be determined, ensuring consumers receive accurate nutritional information.

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