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Chapter 3: Problem 34

An element " \(\mathrm{X}\) " has five major isotopes, which are listed below along with their abundances. What is the element? $$ \begin{array}{|ccc|} \hline \text { Isotope } & \text { Percent Natural Abundance } & \text { Mass (amu) } \\ \hline{ }^{46} \mathrm{X} & 8.00 \% & 45.95269 \\ { }^{47} \mathrm{X} & 7.30 \% & 46.951764 \\ { }^{45} \mathrm{X} & 73.80 \% & 47.947947 \\ { }^{49} \mathrm{X} & 5.50 \% & 48.947841 \\ { }^{50} \mathrm{X} & 5.40 \% & 49.944792 \\ \hline \end{array} $$

Short Answer

Expert verified
The element X is \(\textbf{Titanium}\), with an average atomic mass of approximately \(47.88amu\).

Step by step solution

01

Calculate the mass contribution of each isotope

Multiply the percent abundance of each isotope by its mass to find the contribution to the average atomic mass. 1. \(46X: \: 8.00\% * 45.95269 = 3.6762152\) 2. \(47X: \: 7.30\% * 46.951764 = 3.427286472\) 3. \(45X: \: 73.80\% * 47.947947 = 35.39210566\) 4. \(49X: \: 5.50\% * 48.947841 = 2.69153125\) 5. \(50X: \: 5.40\% * 49.944792 = 2.69677896\)
02

Calculate the average atomic mass

Add up the mass contributions calculated in Step 1: Average atomic mass = \(3.6762152 + 3.427286472 + 35.39210566 + 2.69153125 + 2.69677896 = 47.884¢01054\)
03

Identify the element using the periodic table

Using the average atomic mass calculated in Step 2, refer to the periodic table and find the element with atomic mass close to the calculated value, which is \(47.88401054amu\). The element with an atomic mass close to \(47.88401054amu\) is \(\textbf{Titanium}\) with an atomic mass of approximately \(47.87amu\). Therefore, the element X is \(\textbf{Titanium}\).

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Most popular questions from this chapter

A common demonstration in chemistry courses involves adding a tiny speck of manganese(IV) oxide to a concentrated hydrogen peroxide \(\left(\mathrm{H}_{2} \mathrm{O}_{2}\right)\) solution. Hydrogen peroxide decomposes quite spectacularly under these conditions to produce oxygen gas and steam (water vapor). Manganese(IV) oxide is a catalyst for the decomposition of hydrogen peroxide and is not consumed in the reaction. Write the balanced equation for the decomposition reaction of hydrogen peroxide.

Consider the following balanced chemical equation: $$ A+5 B \longrightarrow 3 C+4 D $$ a. Equal masses of \(\mathrm{A}\) and \(\mathrm{B}\) are reacted. Complete each of the following with either "A is the limiting reactant because \(" ;{ }^{\prime *} \mathrm{~B}\) is the limiting reactant because \("\) or "we cannot determine the limiting reactant because i. If the molar mass of \(\mathrm{A}\) is greater than the molar mass of B, then ii. If the molar mass of \(\mathrm{B}\) is greater than the molar mass of A, then b. The products of the reaction are carbon dioxide (C) and water (D). Compound \(\mathrm{A}\) has the same molar mass as carbon dioxide. Compound \(\mathrm{B}\) is a diatomic molecule. Identify \(\mathrm{com}-\) pound \(\mathrm{B}\) and support your answer. c. Compound \(\mathrm{A}\) is a hydrocarbon that is \(81.71 \%\) carbon by mass. Detemine its empirical and molecular formulas.

A sample of a hydrocarbon (a compound consisting of only carbon and hydrogen) contains \(2.59 \times 10^{2.3}\) atoms of hydrogen and is \(17.3 \%\) hydrogen by mass. If the molar mass of the hydrocarbon is between 55 and \(65 \mathrm{~g} / \mathrm{mol}\), what amount (moles) of compound is present, and what is the mass of the sample?

Determine the molecular formulas to which the following empirical formulas and molar masses pertain. a. SNH \((188.35 \mathrm{~g} / \mathrm{mol})\) b. \(\mathrm{NPCl}_{2}(347.64 \mathrm{~g} / \mathrm{mol})\) c. \(\mathrm{CoC}_{4} \mathrm{O}_{4}(341.94 \mathrm{~g} / \mathrm{mol})\) d. SN \((184.32 \mathrm{~g} / \mathrm{mol})\)

The compound \(\mathrm{As}_{2} \mathrm{I}_{4}\) is synthesized by reaction of arsenic metal with arsenic triiodide. If a solid cubic block of arsenic \((d=5.72\) \(\mathrm{g} / \mathrm{cm}^{3}\) ) that is \(3.00 \mathrm{~cm}\) on edge is allowed to react with \(1.01 \times 10^{24}\) molecules of arsenic triiodide, what mass of \(\mathrm{As}_{2} \mathrm{I}_{4}\) can be prepared? If the percent yield of \(\mathrm{As}_{2} \mathrm{I}_{4}\) was \(75.6 \%\), what mass of \(\mathrm{As}_{2} \mathrm{I}_{4}\) was actually isolated?
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