Solved on Nov 21, 2023

Find the percent abundance of Cu-63 (62.9296 u) and Cu-65 (64.9278 u) given copper's atomic weight of $63.546 u$ .

STEP 1

Assumptions1. Copper is made up of two isotopes, Cu-63 and Cu-65. . The atomic mass of Cu-63 is62.9296 u and that of Cu-65 is64.9278 u.
3. The atomic weight of copper is63.546 u.
4. The percent abundance of Cu-63 is x and that of Cu-65 is (1-x).

STEP 2

The atomic weight of an element is the weighted average of the atomic masses of its isotopes. The weights are the percent abundances of the isotopes. Therefore, we can write the equation for the atomic weight of copper as follows $63.546 =62.9296x +64.9278(1-x)$

STEP 3

We can simplify this equation by distributing the64.9278 to the terms inside the parenthesis.
$63.546 =62.9296x +64.9278 -64.9278x$

STEP 4

Combine like terms.
$63.546 = (62.9296 -64.9278)x +64.9278$

STEP 5

implify the equation.
$63.546 = -1.9982x +64.9278$

STEP 6

Subtract64.9278 from both sides of the equation to isolate the term with x.
$63.546 -64.9278 = -1.9982x$

STEP 7

implify the left side of the equation.
$-1.381 = -1.9982x$

STEP 8

Divide both sides of the equation by -1.9982 to solve for x.
$x = \frac{-1.3818}{-1.9982}$

STEP 9

Calculate the value of x.
$x =.6915$

STEP 10

To find the percent abundance of Cu-63, multiply x by100.
$Percent\, abundance\, of\, Cu-63 =0.6915 \\times100$

STEP 11

Calculate the percent abundance of Cu-63.
$Percent\, abundance\, of\, Cu-63 =69.15\%$

STEP 12

The percent abundance of Cu-65 is (-x), so subtract x from.
$Percent\, abundance\, of\, Cu-65 = -0.6915$

STEP 13

Calculate the percent abundance of Cu-65.
$Percent\, abundance\, of\, Cu-65 =0.3085$

STEP 14

To find the percent abundance of Cu-65, multiply the result by100.
$Percent\, abundance\, of\, Cu-65 =0.308 \\times100$

STEP 15

Calculate the percent abundance of Cu-65.
$Percent\, abundance\, of\, Cu-65 =30.85\%$ The percent abundance of Cu-63 is69.15% and that of Cu-65 is30.85%.

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Find the percent abundance of Cu-63 (62.9296 u) and Cu-65 (64.9278 u) given copper's atomic weight of $63.546 u$ .

STEP 1

Assumptions1. Copper is made up of two isotopes, Cu-63 and Cu-65. . The atomic mass of Cu-63 is62.9296 u and that of Cu-65 is64.9278 u.
3. The atomic weight of copper is63.546 u.
4. The percent abundance of Cu-63 is x and that of Cu-65 is (1-x).

STEP 2

The atomic weight of an element is the weighted average of the atomic masses of its isotopes. The weights are the percent abundances of the isotopes. Therefore, we can write the equation for the atomic weight of copper as follows $63.546 =62.9296x +64.9278(1-x)$

STEP 3

We can simplify this equation by distributing the64.9278 to the terms inside the parenthesis.
$63.546 =62.9296x +64.9278 -64.9278x$

STEP 4

Combine like terms.
$63.546 = (62.9296 -64.9278)x +64.9278$

STEP 5

implify the equation.
$63.546 = -1.9982x +64.9278$

STEP 6

Subtract64.9278 from both sides of the equation to isolate the term with x.
$63.546 -64.9278 = -1.9982x$

STEP 7

implify the left side of the equation.
$-1.381 = -1.9982x$

STEP 8

Divide both sides of the equation by -1.9982 to solve for x.
$x = \frac{-1.3818}{-1.9982}$

STEP 9

Calculate the value of x.
$x =.6915$

STEP 10

To find the percent abundance of Cu-63, multiply x by100.
$Percent\, abundance\, of\, Cu-63 =0.6915 \\times100$

STEP 11

Calculate the percent abundance of Cu-63.
$Percent\, abundance\, of\, Cu-63 =69.15\%$

STEP 12

The percent abundance of Cu-65 is (-x), so subtract x from.
$Percent\, abundance\, of\, Cu-65 = -0.6915$

STEP 13

Calculate the percent abundance of Cu-65.
$Percent\, abundance\, of\, Cu-65 =0.3085$

STEP 14

To find the percent abundance of Cu-65, multiply the result by100.
$Percent\, abundance\, of\, Cu-65 =0.308 \\times100$

STEP 15

Calculate the percent abundance of Cu-65.
$Percent\, abundance\, of\, Cu-65 =30.85\%$ The percent abundance of Cu-63 is69.15% and that of Cu-65 is30.85%.

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Find the percent abundance of Cu-63 (62.9296 u) and Cu-65 (64.9278 u) given copper's atomic weight of 63.546u63.546 u63.546u.

STEP 1

Assumptions1. Copper is made up of two isotopes, Cu-63 and Cu-65. . The atomic mass of Cu-63 is62.9296 u and that of Cu-65 is64.9278 u.3. The atomic weight of copper is63.546 u.4. The percent abundance of Cu-63 is x and that of Cu-65 is (1-x).

STEP 2

STEP 3

We can simplify this equation by distributing the64.9278 to the terms inside the parenthesis.63.546=62.9296x+64.9278−64.9278x63.546 =62.9296x +64.9278 -64.9278x63.546=62.9296x+64.9278−64.9278x

STEP 4

Combine like terms.63.546=(62.9296−64.9278)x+64.927863.546 = (62.9296 -64.9278)x +64.927863.546=(62.9296−64.9278)x+64.9278

STEP 5

implify the equation.63.546=−1.9982x+64.927863.546 = -1.9982x +64.927863.546=−1.9982x+64.9278

STEP 6

Subtract64.9278 from both sides of the equation to isolate the term with x.63.546−64.9278=−1.9982x63.546 -64.9278 = -1.9982x63.546−64.9278=−1.9982x

STEP 7

implify the left side of the equation.−1.381=−1.9982x-1.381 = -1.9982x−1.381=−1.9982x

STEP 8

Divide both sides of the equation by -1.9982 to solve for x.x=−1.3818−1.9982x = \frac{-1.3818}{-1.9982}x=−1.9982−1.3818​

STEP 9

Calculate the value of x.x=.6915x =.6915x=.6915

STEP 10

To find the percent abundance of Cu-63, multiply x by100.Percent abundance of Cu−63=0.6915times100Percent\, abundance\, of\, Cu-63 =0.6915 \\times100PercentabundanceofCu−63=0.6915times100

STEP 11

Calculate the percent abundance of Cu-63.Percent abundance of Cu−63=69.15%Percent\, abundance\, of\, Cu-63 =69.15\%PercentabundanceofCu−63=69.15%

STEP 12

The percent abundance of Cu-65 is (-x), so subtract x from.Percent abundance of Cu−65=−0.6915Percent\, abundance\, of\, Cu-65 = -0.6915PercentabundanceofCu−65=−0.6915

STEP 13

Calculate the percent abundance of Cu-65.Percent abundance of Cu−65=0.3085Percent\, abundance\, of\, Cu-65 =0.3085PercentabundanceofCu−65=0.3085

STEP 14

To find the percent abundance of Cu-65, multiply the result by100.Percent abundance of Cu−65=0.308times100Percent\, abundance\, of\, Cu-65 =0.308 \\times100PercentabundanceofCu−65=0.308times100

STEP 15

Calculate the percent abundance of Cu-65.Percent abundance of Cu−65=30.85%Percent\, abundance\, of\, Cu-65 =30.85\%PercentabundanceofCu−65=30.85%The percent abundance of Cu-63 is69.15% and that of Cu-65 is30.85%.

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Find the percent abundance of Cu-63 (62.9296 u) and Cu-65 (64.9278 u) given copper's atomic weight of $63.546 u$ .

Assumptions1. Copper is made up of two isotopes, Cu-63 and Cu-65. . The atomic mass of Cu-63 is62.9296 u and that of Cu-65 is64.9278 u.
3. The atomic weight of copper is63.546 u.
4. The percent abundance of Cu-63 is x and that of Cu-65 is (1-x).

We can simplify this equation by distributing the64.9278 to the terms inside the parenthesis.
$63.546 =62.9296x +64.9278 -64.9278x$

Combine like terms.
$63.546 = (62.9296 -64.9278)x +64.9278$

implify the equation.
$63.546 = -1.9982x +64.9278$

Subtract64.9278 from both sides of the equation to isolate the term with x.
$63.546 -64.9278 = -1.9982x$

implify the left side of the equation.
$-1.381 = -1.9982x$

Divide both sides of the equation by -1.9982 to solve for x.
$x = \frac{-1.3818}{-1.9982}$

Calculate the value of x.
$x =.6915$

To find the percent abundance of Cu-63, multiply x by100.
$Percent\, abundance\, of\, Cu-63 =0.6915 \\times100$

Calculate the percent abundance of Cu-63.
$Percent\, abundance\, of\, Cu-63 =69.15\%$

The percent abundance of Cu-65 is (-x), so subtract x from.
$Percent\, abundance\, of\, Cu-65 = -0.6915$

Calculate the percent abundance of Cu-65.
$Percent\, abundance\, of\, Cu-65 =0.3085$

To find the percent abundance of Cu-65, multiply the result by100.
$Percent\, abundance\, of\, Cu-65 =0.308 \\times100$

Calculate the percent abundance of Cu-65.
$Percent\, abundance\, of\, Cu-65 =30.85\%$ The percent abundance of Cu-63 is69.15% and that of Cu-65 is30.85%.