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Chapter 2: Problem 71

Use fundamental definitions and statements from Chapters 1 and 2 to establish the fact that \(6.022 \times 10^{23} \mathrm{u}=1.000 \mathrm{g}\)

Short Answer

Expert verified
Knowing that 1 mole of any substance contains 6.022 x 10^23 entities (Avogadro's number) and the weight of 1 mole of that substance in grams is numerically equal to the atomic or molecular weight in u, we can establish that 6.022 x 10^23 u (Avogadro's number of atomic mass units) equals 1 gram.

Step by step solution

01

Define atomic mass unit (AMU)

One atomic mass unit (u) is defined as 1/12th the mass of a carbon-12 atom, which is approximately 1.66 x 10^-24 g.
02

Apply the concept of a mole

One mole of any element or compound contains 6.022 x 10^23 entities (usually atoms or molecules), which is also known as Avogadro's number.
03

Link AMU, grams and mole

When an element's atomic mass is expressed in u, it is almost the same number as the mass of one mole of that element in grams. For example, one mole of carbon-12 atoms has a mass of exactly 12 grams, because the atomic mass of carbon-12 is 12 u. Therefore, 1 u, as defined above, is equivalent to 1 g/mol.
04

Establish the relationship

Applying these principles, we can say that 6.022 x 10^23 u (Avogadro's number of atomic mass units) is equivalent to 1 gram, because 1 mole of 1-u atoms weighs 1 gram.

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Most popular questions from this chapter

Iodine-131 is a radioactive isotope that has important medical uses. Small doses of iodine-131 are used for treating hyperthyroidism (overactive thyroid) and larger doses are used for treating thyroid cancer. Iodine-131 is administered to patients in the form of sodium iodide capsules that contain \(^{131} \mathrm{I}^{-}\) ions. Determine the number of neutrons, protons, and electrons in a single \(^{131} \mathrm{I}^{-}\) ion.

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