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Chapter 3: Problem 34

Hydrogen has two stable isotopes, \({ }_{1}^{1} \mathrm{H}\) and \({ }_{1}^{2} \mathrm{H},\) and sulfur has four stable isotopes, \({ }_{16}^{32} \mathrm{~S},{ }_{16}^{33} \mathrm{~S},{ }_{16}^{34} \mathrm{~S},\) and \({ }_{16}^{36} \mathrm{~S}\). How many peaks would you observe in the mass spectrum of the positive ion of hydrogen sulfide, \(\mathrm{H}_{2} \mathrm{~S}^{+}\) ? Assume no decomposition of the ion into smaller fragments.

Short Answer

Expert verified
You would observe 6 peaks in the mass spectrum of the positive ion of hydrogen sulfur, \(\mathrm{H}_{2} \mathrm{~S}^{+}\).

Step by step solution

01

Identify Isotopes

First, identify the stable isotopes of both hydrogen (H) and sulfur (S). Hydrogen has two stable isotopes: \({ }_{1}^{1} \mathrm{H}\) and \({ }_{1}^{2}\mathrm{H}\). Sulfur has four stable isotopes: \({ }_{16}^{32} \mathrm{S}\), \({ }_{16}^{33} \mathrm{S}\), \({ }_{16}^{34} \mathrm{S}\), and \({ }_{16}^{36}\mathrm{S}\).
02

Calculate Combinations

Hydrogen sulfide has the formula \(\mathrm{H}_{2} \mathrm{~S}^{+}\). This means it consists of 2 hydrogen atoms and one sulfur atom. For each hydrogen atom we have 2 possible isotopes, and for the sulfur atom we have 4 different isotopes. The total number of combinations of these isotopes that can form hydrogen sulfide, then, is the product of the number of isotopes: \(2 \times 2 \times 4 = 16\). It means there are 16 different isotopic combinations that can form \(\mathrm{H}_{2} \mathrm{~S}^{+}\).
03

Determine Unique Masses

However, not all of these combinations will result in a unique mass. Therefore, count the number of unique masses. Here, considering the masses of isotopes: 1. Hydrogen sulfide can have the hydrogen atoms either of mass 1 or 2. This contributes to 2 mass varies: \(2 \times 1 = 2\) and \(2 \times 2 = 4\). 2. For sulfur atom, there are 4 isotopes of mass 32, 33, 34, 36 each. It means when counting unique masses, one might end up with hydrogen sulfide of masses \(32+2=34, 32+4=36, 33+2=35, 33+4=37, 34+2=36, 34+4=38, 36+2=38, 36+4=40\). After removing the duplicate mass, one gets: 34, 35, 36, 37, 38, and 40. This are 6 unique masses.

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Most popular questions from this chapter

Nitrous oxide \(\left(\mathrm{N}_{2} \mathrm{O}\right)\) is also called "laughing gas." \(\mathrm{It}\) can be prepared by the thermal decomposition of ammonium nitrate \(\left(\mathrm{NH}_{4} \mathrm{NO}_{3}\right)\). The other product is \(\mathrm{H}_{2} \mathrm{O} .\) (a) Write a balanced equation for this reaction. (b) How many grams of \(\mathrm{N}_{2} \mathrm{O}\) are formed if 0.46 mole of \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) is used in the reaction?

The annual production of sulfur dioxide from burning coal and fossil fuels, auto exhaust, and other sources is about 26 million tons. The equation for the reaction is $$ \mathrm{S}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g) $$ How much sulfur (in tons), present in the original materials, would result in that quantity of \(\mathrm{SO}_{2} ?\)

Describe how you would determine the isotopic abundance of an element from its mass spectrum.

The depletion of ozone \(\left(\mathrm{O}_{3}\right)\) in the stratosphere has been a matter of great concern among scientists in recent years. It is believed that ozone can react with nitric oxide (NO) that is discharged from the high-altitude jet plane, the SST. The reaction is $$ \mathrm{O}_{3}+\mathrm{NO} \longrightarrow \mathrm{O}_{2}+\mathrm{NO}_{2} $$ If \(0.740 \mathrm{~g}\) of \(\mathrm{O}_{3}\) reacts with \(0.670 \mathrm{~g}\) of \(\mathrm{NO}\), how many grams of \(\mathrm{NO}_{2}\) will be produced? Which compound is the limiting reagent? Calculate the number of moles of the excess reagent remaining at the end of the reaction.

Carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) is the gas that is mainly responsible for global warming (the greenhouse effect). The burning of fossil fuels is a major cause of the increased concentration of \(\mathrm{CO}_{2}\) in the atmosphere. Carbon dioxide is also the end product of metabolism (see Example 3.13). Using glucose as an example of food, calculate the annual human production of \(\mathrm{CO}_{2}\) in grams, assuming that each person consumes \(5.0 \times 10^{2} \mathrm{~g}\) of glucose per day. The world's population is 6.5 billion, and there are 365 days in a year.
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