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Chapter 3: Problem 129

In using a mass spectrometer, a chemist sees a peak at a mass of \(30.0106\). Of the choices \({ }^{12} \mathrm{C}_{2}{ }^{1} \mathrm{H}_{6},{ }^{12} \mathrm{C}^{1} \mathrm{H}_{2}{ }^{16} \mathrm{O}\), and \({ }^{14} \mathrm{~N}^{16} \mathrm{O}\), which is responsible for this peak? Pertinent masses are \({ }^{1} \mathrm{H}, 1.007825\); \({ }^{16} \mathrm{O}, 15.994915 ;\) and \({ }^{14} \mathrm{~N}, 14.003074 .\)

Short Answer

Expert verified
The molecule responsible for the observed peak in the mass spectrometer at 30.0106 units is \({ }^{12} \mathrm{C}^{1} \mathrm{H}_{2}{ }^{16} \mathrm{O}\), as its total mass of 30.010565 is the closest match to the given mass in the peak.

Step by step solution

01

First, find the total mass of this molecule, considering that carbon has a mass of 12 units: Total mass = 2 (mass of carbon) + 6 (mass of hydrogen) = 2 * 12 + 6 * 1.007825 = 24 + 6.04695 = 30.04695 #Step 2: Calculate mass of \({ }^{12} \mathrm{C}^{1} \mathrm{H}_{2}{ }^{16} \mathrm{O}\)

Now find the total mass of this molecule: Total mass = 1 (mass of carbon) + 2 (mass of hydrogen) + 1 (mass of oxygen) = 12 + 2 * 1.007825 + 15.994915 = 12 + 2.01565 + 15.994915 = 30.010565 #Step 3: Calculate mass of \({ }^{14} \mathrm{~N}^{16} \mathrm{O}\)
02

Find the total mass of this last molecule: Total mass = 1 (mass of nitrogen) + 1 (mass of oxygen) = 14.003074 + 15.994915 = 29.997989 #Step 4: Identify the molecule responsible for the peak

Compare the total masses calculated in steps 1-3 with the observed peak of the spectrometer at 30.0106: The total mass of the molecules: * \({ }^{12} \mathrm{C}_{2}{ }^{1} \mathrm{H}_{6}:\) 30.04695 * \({ }^{12} \mathrm{C}^{1} \mathrm{H}_{2}{ }^{16} \mathrm{O}:\) 30.010565 * \({ }^{14} \mathrm{~N}^{16} \mathrm{O}:\) 29.997989 The mass that is closest to the peak is 30.010565 (for the molecule \({ }^{12} \mathrm{C}^{1} \mathrm{H}_{2}{ }^{16} \mathrm{O}\)). Therefore, this molecule is responsible for the observed peak.

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Most popular questions from this chapter

Arrange the following substances in order of increasing mass percent of carbon. a. caffeine, \(\mathrm{C}_{\mathrm{s}} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{O}_{2}\) b. sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) c. ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\)

Bacterial digestion is an economical method of sewage treatment. The reaction \(5 \mathrm{CO}_{2}(g)+55 \mathrm{NH}_{4}^{+}(a q)+76 \mathrm{O}_{2}(g)\) \(\mathrm{C}_{5} \mathrm{H}_{7} \mathrm{O}_{2} \mathrm{~N}(s)+54 \mathrm{NO}_{2}^{-}(a q)+52 \mathrm{H}_{2} \mathrm{O}(l)+109 \mathrm{H}^{+}(a q)\)

A compound that contains only carbon, hydrogen, and oxygen is \(48.64 \% \mathrm{C}\) and \(8.16 \% \mathrm{H}\) by mass. What is the empirical formula of this substance?

Consider the following unbalanced equation: \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{CaSO}_{4}(s)+\mathrm{H}_{3} \mathrm{PO}_{4}(a q)\) What masses of calcium sulfate and phosphoric acid can be produced from the reaction of \(1.0 \mathrm{~kg}\) calcium phosphate with \(1.0\) \(\mathrm{kg}\) concentrated sulfuric acid \(\left(98 \% \mathrm{H}_{2} \mathrm{SO}_{4}\right.\) by \(\left.\mathrm{mass}\right)\) ?

A sample of urea contains \(1.121 \mathrm{~g} \mathrm{~N}, 0.161 \mathrm{~g} \mathrm{H}, 0.480 \mathrm{~g} \mathrm{C}\), and \(0.640 \mathrm{~g} \mathrm{O} .\) What is the empirical formula of urea?
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