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Chapter 3: Problem 136

Boron consists of two isotopes, 10 \(\mathrm{B}\) and 11 \(\mathrm{B}\) . Chlorine also has two isotopes, 35 \(\mathrm{Cl}\) and 37 \(\mathrm{Cl}\) . Consider the mass spectrum of \(\mathrm{BCl}_{3}\) . How many peaks would be present, and what approximate mass would each peak correspond to in the BCl_ mass spectrum?

Short Answer

Expert verified
There would be 8 peaks in the mass spectrum of BCl₃, with corresponding approximate masses of 115, 116, 117, 118, 119, 120, 121, and 122.

Step by step solution

01

List all possible combinations of boron and chlorine isotopes in BCl₃

For each boron isotope, there are three possible chlorine isotopes. So, for both boron isotopes, we have: - B⁽¹⁰⁾Cl₃ - B⁽¹¹⁾Cl₃ For each BCl₃, there are 3 chlorine atoms with two possible isotopes each (35Cl and 37Cl), resulting in 2³ = 8 combinations. Therefore, we have: - B⁽¹⁰⁾Cl₃: 8 combinations - B⁽¹¹⁾Cl₃: 8 combinations Total possible combinations: 8 + 8 = 16
02

Find the number of unique approximate masses

Now, we'll look for unique masses by considering the mass of each combination. The approximate mass of BCl₃ is the sum of the mass of the boron isotope and the three chlorine isotopes. For B⁽¹⁰⁾Cl₃: 1. 10 + 3(35) = 115 2. 10 + 2(35) + 37 = 117 3. 10 + 35 + 2(37) = 119 4. 10 + 3(37) = 121 For B⁽¹¹⁾Cl₃: 1. 11 + 3(35) = 116 2. 11 + 2(35) + 37 = 118 3. 11 + 35 + 2(37) = 120 4. 11 + 3(37) = 122 The unique approximate masses are 115, 116, 117, 118, 119, 120, 121, and 122.
03

Determine the number of peaks and their corresponding approximate masses

We have 8 unique approximate masses, which means there will be 8 peaks in the mass spectrum of BCl₃. The approximate masses corresponding to these peaks are: - 115 - 116 - 117 - 118 - 119 - 120 - 121 - 122 So, there would be 8 peaks in the mass spectrum of BCl₃, with approximate masses of 115, 116, 117, 118, 119, 120, 121, and 122.

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Most popular questions from this chapter

Zinc and magnesium metal each reacts with hydrochloric acid to make chloride salts of the respective metals, and hydrogen gas. A 10.00 -g mixture of zinc and magnesium produces 0.5171 g of hydrogen gas upon being mixed with an excess of hydrochloric acid. Determine the percent magnesium by mass in the original mixture.

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Some bismuth tablets, a medication used to treat upset stomachs, contain 262 \(\mathrm{mg}\) of bismuth subsalicylate, $\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{BiO}_{4},$ per tablet. Assuming two tablets are digested, calculate the mass of bismuth consumed.

The aspirin substitute, acetaminophen $\left(\mathrm{C}_{8} \mathrm{H}_{9} \mathrm{O}_{2} \mathrm{N}\right),$ is produced by the following three-step synthesis: $$ \mathrm{I} . \quad \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{3} \mathrm{N}(s)+3 \mathrm{H}_{2}(g)+\mathrm{HCl}(a q) \longrightarrow $$ $$ \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{ONCl}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) $$ $$ \mathrm{II}\quad \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{ONCl}(s)+\mathrm{NaOH}(a q) \longrightarrow $$ $$ \mathrm{C}_{6} \mathrm{H}_{7} \mathrm{ON}(s)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{NaCl}(a q) $$ $$ \mathrm{III.} \quad \mathrm{C}_{6} \mathrm{H}_{7} \mathrm{ON}(s)+\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3}(l) \longrightarrow $$ $$ \mathrm{C}_{8} \mathrm{H}_{9} \mathrm{O}_{2} \mathrm{N}(s)+\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(l) $$ The first two reactions have percent yields of 87\(\%\) and 98\(\%\) by mass, respectively. The overall reaction yields 3 moles of acetaminophen product for every 4 moles of \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{3} \mathrm{N}\) reacted. a. What is the percent yield by mass for the overall process? b. What is the percent yield by mass of Step III?
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