Naturally occurring iodine has an atomic mass of 126.9045 amu. A 12.3849 g sample of iodine is accidentally contaminated with an additional 1.00070 g of 129 I, a synthetic radioisotope of iodine used in the treatment of certain diseases of the thyroid gland. The mass of 129 I is 128.9050 amu. Find the apparent 'atomic mass' of the contaminated iodine.

Hello everyone today. We are being given the following parliament asked to solve for it. It says Cesium has one stable isotope which has an atomic mass of 0.9054 A. M. U. A synthetic radioisotopes. Cesium 1 37. With a mass of 1.2410 g was accidentally added to 13.2541 g of cesium sample. The atomic mass of 1 37 cesium is 136.9071 A. M. You what is the apparent molecular mass of the contaminated cesium? So first we have to take into account our total mass which is going to be the 1.02410 g From our Cesium 1 37. That's also going to be our 13. grams of our original sample. And this is going to give us a total of 14.278g of a sample of our total mess. And so to find the fraction of our original cesium We have to sort of find the fraction of our original cesium. We have to take our 13.2541 or our mass of that cesium and divided by the total amount that we have. This is going to give us 0.9-8. And to find the fraction Of our 1 37 cesium. We're gonna take that mass or 1.02410 g. And divide that by the total mass which is 14.278g. That is going to give us 0.07172 as our final answer for that. 3rdly, we want to calculate the atomic mass am I doing that? We're gonna go ahead and take our mass, our original mass of our original cesium. And we're gonna multiply that by the fraction. So you multiply that by the fraction of our isotope one. And we're going to add that to the mass of our contaminant or cesium 1 37. And multiply that by the fraction which is isotope too. And so that's going to look like our 1 32.9 A. M. U. Times our 0.9 to eight plus our 1 36.9071 A. M. You Multiplied by our 0.0717. And that is going to give us an atomic mass of 133.1 92 A. M. U. As our final answer, I hope this helps. And until next time

Ch.2 - Atoms & Elements

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Tro 4th Edition

Ch.2 - Atoms & Elements

Problem 100

Chapter 2, Problem 100

Naturally occurring iodine has an atomic mass of 126.9045 amu. A 12.3849 g sample of iodine is accidentally contaminated with an additional 1.00070 g of ¹²⁹I, a synthetic radioisotope of iodine used in the treatment of certain diseases of the thyroid gland. The mass of ¹²⁹I is 128.9050 amu. Find the apparent 'atomic mass' of the contaminated iodine.

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Calculate the total mass of the contaminated iodine sample by adding the mass of the naturally occurring iodine and the mass of the added 129I isotope.

Determine the number of moles of naturally occurring iodine (127I) using its given mass and atomic mass unit (amu). Use the formula: moles = mass (g) / atomic mass (amu).

Calculate the number of moles of the 129I isotope using its given mass and atomic mass unit (amu) with the same formula as in step 2.

Find the total moles of iodine in the sample by adding the moles of 127I and the moles of 129I.

Calculate the apparent atomic mass of the contaminated iodine sample by dividing the total mass of the sample by the total moles of iodine. Use the formula: apparent atomic mass = total mass (g) / total moles.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Atomic Mass

Atomic mass is the weighted average mass of an element's isotopes, measured in atomic mass units (amu). It reflects both the mass and the relative abundance of each isotope in a naturally occurring sample. For example, iodine has isotopes with different masses, and the atomic mass of 126.9045 amu accounts for the contributions of these isotopes based on their natural abundance.

Isotopes

Isotopes are variants of a chemical element that have the same number of protons but different numbers of neutrons, resulting in different atomic masses. For iodine, the stable isotope is 127I, while 129I is a radioactive isotope. Understanding isotopes is crucial for calculating the average atomic mass when a sample contains multiple isotopes, as in the case of the contaminated iodine.

Weighted Average Calculation

The weighted average calculation is used to determine the average atomic mass of an element when multiple isotopes are present. This involves multiplying the mass of each isotope by its relative abundance (in terms of mass) and summing these products. In the context of the contaminated iodine sample, this calculation will yield the apparent atomic mass by considering both the natural iodine and the added synthetic isotope.