Gallium consists of two naturally occurring isotopes: (isotopic mass = ) and…

CHEMISTRY · Multi-part · AP · Chemistry · Atomic Structure and Properties · Atomic Structure and Properties

Problem

Gallium consists of two naturally occurring isotopes:

^{69}\text{Ga}

(isotopic mass =

68.9256\,\text{amu}

) and

^{71}\text{Ga}

(isotopic mass =

70.9247\,\text{amu}

). A physical sample of gallium weighing

3.500\,\text{g}

is analyzed and found to contain

4.41\times10^{22}

total atoms. The accepted natural abundances of the two isotopes are

60.11\%

for

^{69}\text{Ga}

and

39.89\%

for

^{71}\text{Ga}

. Avogadro’s constant is

N_A = 6.022\times10^{23}\,\text{mol}^{-1}

. (a) Calculate the average atomic mass of gallium based on the accepted isotopic abundances. (b) Determine the experimental molar mass of the gallium sample using the measured mass and atom count. (c) Compute the percent deviation of the experimental molar mass (part b) from the accepted value (part a). (d) Evaluate whether the isotopic composition of the sample is likely to match naturally occurring gallium, citing quantitative evidence from your calculations.

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