Chemistry

Problem

A research team discovers a synthetic element, temporarily named Q, and analyzes a purified sample using time-of-flight mass spectrometry. The detector registers singly charged ions at

m/z

values of 281.0, 282.0, 283.0, 284.0, and 285.0. The integrated peak areas (already corrected for background) are listed below.

$m/z$ (amu)	Integrated peak area (counts)
281.0	$3.25\times10^{4}$
282.0	$7.80\times10^{4}$
283.0	$1.15\times10^{5}$
284.0	$8.60\times10^{4}$
285.0	$2.20\times10^{4}$

Assume the peak at each

m/z

corresponds to a distinct isotope of element Q and all other possible charge states are negligible. (a) Calculate the percentage abundance of each isotope to two significant figures. (b) Determine the weighted average atomic mass of element Q in amu, reporting the value to four significant figures. (c) Convert the average atomic mass obtained in part (b) to units of

\text{g}\cdot\text{mol}^{-1}

. State any assumptions or conventions used in the conversion. (d) Using your result from part (c), estimate the mass in grams of a

1.50\,\text{mol}

sample of element Q. Show all steps, including unit analysis.

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