Respuesta :
Answer:
69.7231 u to 4 decimal places.
Explanation:
Gallium is composed of two natural occuring isotopes that is Ga-69(60.108%) with mass of 68.9256 amu and Ga-71(39.892%) with mas of 70.9247 amu. The ratio of their masses are 1.0290. The relative abundance of Ga-69 is 60.11% and Ga-71 is 39.89%.
Calculate average atomic mass of Ga-69 :
Ga-69 = 60.108% = 0.60108.
GA-71 = 39.892% = 0.39892.
Atomic mass of Ga = (68.9256⋅0.60108)+(70.9247⋅0.39892)
AM(Ga)=69.7231 u to 4 decimal places.
The mass of Ga-69 is [tex]\boxed{68.926{\text{ u}}}[/tex]
Further explanation:
Isotopes are the atoms of the same element with same atomic number but different atomic masses. The number of protons is the same in these but the number of neutrons is different.
Relative Atomic Mass:
The average mass of an atom of the element compared to 1/12th of the mass of carbon-12 atom is termed as the relative atomic mass. It is generally denoted by [tex]{{\text{A}}_{\text{r}}}[/tex]. The formula to calculate the relative atomic mass of an element is as follows:
[tex]{{\text{A}}_{\text{r}}} = \dfrac{{\sum {\left\{ {\left( {{\text{Relative isotopic mass}}} \right)\left( {{\text{\% abundance}}} \right)} \right\}} }}{{100}}[/tex]
Here, [tex]{{\text{A}}_{\text{r}}}[/tex] is the relative atomic mass.
We are provided with the information that gallium (Ga) is composed of two isotopes, namely Ga-69 and Ga-71. The relative abundance of Ga-69 is 60.108 %.
The expression to calculate the relative abundance is as follows:
[tex]{\text{Relative abundance of Ga - 69}} + {\text{Relative abundance of Ga - 71}} = 100{\text{ \% }}[/tex] …… (1)
Rearrange equation (1) to calculate the relative abundance of Ga-71.
[tex]{\text{Relative abundance of Ga - 71}} = 100{\text{ \% }} - {\text{Relative abundance of Ga - 69}}[/tex] …… (2)
Substitute 60.108 % for the relative abundance of Ga-69 in equation (2).
[tex]\begin{aligned}{\text{Relative abundance of Ga - 71}}&= 100{\text{ \% }} - 60.108{\text{ \% }}\\&= {\text{39}}{\text{.892 \% }}\\\end{aligned}[/tex]
The formula to evaluate the relative atomic mass of Ga is as follows:
[tex]{{\text{A}}_{\text{r}}}{\text{ of Ga}} &= \dfrac{{\left[ \begin{aligned}\left( {{\text{Mass of Ga - 69}}} \right)\left( {{\text{\% abundance of Ga - 69}}} \right) + \hfill\\\left( {{\text{Mass of Ga - 71}}} \right)\left( {{\text{\% abundance of Ga - 71}}} \right) \hfill \\\end{aligned} \right]}}{{100}}[/tex] …… (3)
The ratio of the masses of two isotopes is 1.0290. Consider the mass of Ga-69 to be x. So the mass of Ga-71 becomes 1.0290.
Substitute x for the mass of Ga-69, 1.0290x for the mass of Ga-71, 60.108 % for % abundance of Ga-69, 39.892 % for % abundance of Ga-71 and 69.723 u for the relative mass of Ga in equation (3).
[tex]{\text{69}}{\text{.723}} = \dfrac{{\left[ {\left( {\text{x}} \right)\left( {{\text{60}}{\text{.108 \% }}} \right) + \left( {{\text{1}}{\text{.0290x}}} \right)\left( {{\text{39}}{\text{.892 \% }}} \right)} \right]}}{{100}}[/tex]
Solve for x,
[tex]x = 68.926[/tex]
Therefore the mass of Ga-69 is 68.926 u.
Learn more:
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Answer details:
Grade: Middle School
Subject: Chemistry
Chapter: Mole Concept
Keywords: percentage abundance, Ga-69, Ga-71, mass, relative atomic mass, x, 1.0290, 1.0290x, 68.926 u, relative abundance, 60.108 %, 39.892 %.
