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Chapter 3: Problem 135

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 peak at a mass of 30.0106 in the mass spectrometer is \(^{12}C^1H_2^{16}O\).

Step by step solution

01

Choice 1: \(^{12}C_2^1H_6\)

Calculate the mass of \(^{12}C_2^1H_6\) by multiplying the mass of \(^{12}C\) by 2 and the mass of \(^{1}H\) by 6 and adding the results: \[Mass (^{12}C_2^1H_6) = 2(12.000) + 6(1.007825)\]
02

Choice 2: \(^{12}C^1H_2^{16}O\)

Calculate the mass of \(^{12}C^1H_2^{16}O\) by adding the mass of \(^{12}C\), multiplying the mass of \(^{1}H\) by 2, and adding the mass of \(^{16}O\): \[Mass (^{12}C^1H_2^{16}O) = 12.000 + 2(1.007825) + 15.994915\]
03

Choice 3: \(^{14}N^{16}O\)

Calculate the mass of \(^{14}N^{16}O\) by adding the mass of \(^{14}N\) and \(^{16}O\): \[Mass (^{14}N^{16}O) = 14.003074 + 15.994915\] #Step 2: Comparing calculated masses to the given peak# Compare the calculated masses from Step 1 to the given peak mass of 30.0106 to determine which is responsible for the peak.
04

Choice 1: \(^{12}C_2^1H_6\)

Calculate the mass of \(^{12}C_2^1H_6\): \[Mass (^{12}C_2^1H_6) = 2(12.000) + 6(1.007825) = 24.000 + 6.04695 = 30.04695\]
05

Choice 2: \(^{12}C^1H_2^{16}O\)

Calculate the mass of \(^{12}C^1H_2^{16}O\): \[Mass (^{12}C^1H_2^{16}O) = 12.000 + 2(1.007825) + 15.994915 = 12.000 + 2.01565 + 15.994915 = 30.010565\]
06

Choice 3: \(^{14}N^{16}O\)

Calculate the mass of \(^{14}N^{16}O\): \[Mass (^{14}N^{16}O) = 14.003074 + 15.994915 = 29.997989\] #Step 3: Determine the responsible molecule# Based on the calculations in Step 2, the mass of \(^{12}C^1H_2^{16}O\), 30.010565, is the closest to the given peak at a mass of 30.0106.
07

Conclusion

The molecule responsible for the peak at a mass of 30.0106 in the mass spectrometer is \(^{12}C^1H_2^{16}O\).

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Most popular questions from this chapter

A gas contains a mixture of \(\mathrm{NH}_{3}(g)\) and $\mathrm{N}_{2} \mathrm{H}_{4}(g),\( both of which react with \)\mathrm{O}_{2}(g)$ to form \(\mathrm{NO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g) .\) The gaseous mixture (with an initial mass of 61.00 \(\mathrm{g}\) ) is reacted with 10.00 \(\mathrm{moles}\) \(\mathrm{O}_{2},\) and after the reaction is complete, 4.062 moles of \(\mathrm{O}_{2}\) remains. Calculate the mass percent of \(\mathrm{N}_{2} \mathrm{H}_{4}(g)\) in the original gaseous mixture.

Cumene is a compound containing only carbon and hydrogen that is used in the production of acetone and phenol in the chemical industry. Combustion of 47.6 \(\mathrm{mg}\) cumene produces some \(\mathrm{CO}_{2}\) and 42.8 \(\mathrm{mg}\) water. The molar mass of cumene is between 115 and 125 $\mathrm{g} / \mathrm{mol}$ . Determine the empirical and molecular formulas.

There are two binary compounds of mercury and oxygen. Heating either of them results in the decomposition of the compound, with oxygen gas escaping into the atmosphere while leaving a residue of pure mercury. Heating 0.6498 g of one of the compounds leaves a residue of 0.6018 g. Heating 0.4172 g of the other compound results in a mass loss of 0.016 g. Determine the empirical formula of each compound.

Silicon is produced for the chemical and electronics industries by the following reactions. Give the balanced equation for each reaction. a. \(\mathrm{SiO}_{2}(s)+\mathrm{C}(s)\) $\frac{\text { Electric }}{\text { are furnace }}\( \)\mathrm{Si}(s)+\mathrm{CO}(g)$ b. Liquid silicon tetrachloride is reacted with very pure solid magnesium, producing solid silicon and solid magnesium chloride. c. $\mathrm{Na}_{2} \mathrm{SiF}_{6}(s)+\mathrm{Na}(s) \rightarrow \mathrm{Si}(s)+\mathrm{NaF}(s)$

A compound contains 47.08\(\%\) carbon, 6.59\(\%\) hydrogen, and 46.33\(\%\) chlorine by mass; the molar mass of the compound is 153 g/mol. What are the empirical and molecular formulas of the compound?
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