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Chapter 2: Problem 44

\begin{tabular}{l} There are four naturally occurring isotopes of \\ \hline \end{tabular} chromium. Their masses and percent natural abundances are \(49.9461 \mathrm{u}, 4.35 \% ; 51.9405 \mathrm{u}, 83.79 \% ; 52.9407 \mathrm{u}\) \(9.50 \% ;\) and \(53.9389 \mathrm{u}, 2.36 \% .\) Calculate the weightedaverage atomic mass of chromium.

Short Answer

Expert verified
The weighted average atomic mass of chromium is approximately \(51.996 \mathrm{u}\)

Step by step solution

01

Understand the concept of weighted average

A weighted average is typically used when the average of a list of numbers must account for different levels of significance or importance of the numbers. In this case, the different masses of the isotopes are not all equally common, indicated by their different percent abundances.
02

Convert the percentages into decimals

Before proceeding, one should convert the percent natural abundances into decimal form. This is done by simply dividing each percentage by 100. Thus, these will become: 0.0435, 0.8379, 0.0950, and 0.0236, respectively.
03

Multiply each mass by its fraction and sum the products

To find the weighted average atomic mass of chromium, multiply each isotope's atomic mass by its abundance, then sum these products. The calculations are as follows: \((49.9461 \mathrm{u} * 0.0435) + (51.9405 \mathrm{u} * 0.8379) + (52.9407 \mathrm{u} * 0.0950) + (53.9389 \mathrm{u} * 0.0236)\)
04

Calculate

Performing these calculations gives a sum of \(51.996 \mathrm{u}\)

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Most popular questions from this chapter

The properties of magnesium will most resemble those of which of the following? (a) cesium; (b) sodium; (c) aluminum; (d) calcium; (e) manganese.

The four naturally occurring isotopes of strontium have the atomic masses 83.9134 u; 85.9093 u; 86.9089 u; and 87.9056 u. The percent natural abundance of the lightest isotope is \(0.56 \%\) and of the heaviest, \(82.58 \%\) Estimate the percent natural abundances of the other two. Why is this result only a rough approximation?

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.

Germanium has three major naturally occurring isotopes: \(^{70}\) Ge \((69.92425 \mathrm{u}, 20.85 \%),^{72} \mathrm{Ge}(71.92208 \mathrm{u},\) \(27.54 \%),^{74} \mathrm{Ge}(73.92118 \mathrm{u}, 36.29 \%) .\) There are also two minor isotopes: \(^{73}\) Ge \(\left(72.92346 \text { u) and }^{76} \mathrm{Ge}\right.\) (75.92140 u). Calculate the percent natural abundances of the two minor isotopes. Comment on the precision of these calculations.

Refer to the periodic table inside the front cover and identify (a) the element that is in group 14 and the fourth period (b) one element similar to and one unlike sulfur (c) the alkali metal in the fifth period (d) the halogen element in the sixth period
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