QuestionCalculate the % abundance of ${ }^{87} \mathrm{Rb}$ if Rubidium's atomic mass is 85.47 amu, with isotopes ${ }^{85} \mathrm{Rb}$ and ${ }^{87} \mathrm{Rb}$ .

Studdy Solution

STEP 1

Assumptions1. There are two isotopes of Rubidium, ${ }^{85} \mathrm{Rb}$ and ${ }^{87} \mathrm{Rb}$ . . The mass of ${ }^{85} \mathrm{Rb}$ is $84.911789 \mathrm{amu}$ .
3. The mass of ${ }^{87} \mathrm{Rb}$ is $86.909183 \mathrm{amu}$ .
4. The atomic mass of Rubidium is $85.47 \mathrm{amu}$ .
5. The atomic mass of Rubidium is the weighted average of the masses of its isotopes.

STEP 2

Let's denote the percentage abundance of ${ }^{87} \mathrm{Rb}$ as $x$ . Then, the percentage abundance of ${ }^{85} \mathrm{Rb}$ is $100\% - x$ .

STEP 3

We can write the equation for the atomic mass of Rubidium as a weighted average of the masses of its isotopes $85.47 = \frac{{84.911789 \times (100 - x) +86.909183 \times x}}{100}$

STEP 4

Multiply each side of the equation by100 to simplify $8547 =8491.1789 -84.911789x +86.909183x$

STEP 5

Combine like terms $8547 =8491.1789 +1.997394x$

STEP 6

Subtract8491.1789 from each side of the equation $55.8211 =1.997394x$

STEP 7

Divide each side of the equation by1.997394 to solve for $x$ $x = \frac{55.8211}{1.997394}$

STEP 8

Calculate the value of $x$ $x =27.97\%$ The isotope abundance of ${ }^{87} \mathrm{Rb}$ is approximately27.97%.

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QuestionCalculate the % abundance of ${ }^{87} \mathrm{Rb}$ if Rubidium's atomic mass is 85.47 amu, with isotopes ${ }^{85} \mathrm{Rb}$ and ${ }^{87} \mathrm{Rb}$ .

Studdy Solution

STEP 1

STEP 2

Let's denote the percentage abundance of ${ }^{87} \mathrm{Rb}$ as $x$ . Then, the percentage abundance of ${ }^{85} \mathrm{Rb}$ is $100\% - x$ .

STEP 3

We can write the equation for the atomic mass of Rubidium as a weighted average of the masses of its isotopes $85.47 = \frac{{84.911789 \times (100 - x) +86.909183 \times x}}{100}$

STEP 4

Multiply each side of the equation by100 to simplify $8547 =8491.1789 -84.911789x +86.909183x$

STEP 5

Combine like terms $8547 =8491.1789 +1.997394x$

STEP 6

Subtract8491.1789 from each side of the equation $55.8211 =1.997394x$

STEP 7

Divide each side of the equation by1.997394 to solve for $x$ $x = \frac{55.8211}{1.997394}$

STEP 8

Calculate the value of $x$ $x =27.97\%$ The isotope abundance of ${ }^{87} \mathrm{Rb}$ is approximately27.97%.

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QuestionCalculate the % abundance of 87Rb{ }^{87} \mathrm{Rb}87Rb if Rubidium's atomic mass is 85.47 amu, with isotopes 85Rb{ }^{85} \mathrm{Rb}85Rb and 87Rb{ }^{87} \mathrm{Rb}87Rb.

Studdy Solution

STEP 1

STEP 2

Let's denote the percentage abundance of 87Rb{ }^{87} \mathrm{Rb}87Rb as xxx. Then, the percentage abundance of 85Rb{ }^{85} \mathrm{Rb}85Rb is 100%−x100\% - x100%−x.

STEP 3

We can write the equation for the atomic mass of Rubidium as a weighted average of the masses of its isotopes85.47=84.911789×(100−x)+86.909183×x10085.47 = \frac{{84.911789 \times (100 - x) +86.909183 \times x}}{100}85.47=10084.911789×(100−x)+86.909183×x​

STEP 4

Multiply each side of the equation by100 to simplify8547=8491.1789−84.911789x+86.909183x8547 =8491.1789 -84.911789x +86.909183x8547=8491.1789−84.911789x+86.909183x

STEP 5

Combine like terms8547=8491.1789+1.997394x8547 =8491.1789 +1.997394x8547=8491.1789+1.997394x

STEP 6

Subtract8491.1789 from each side of the equation55.8211=1.997394x55.8211 =1.997394x55.8211=1.997394x

STEP 7

Divide each side of the equation by1.997394 to solve for xxxx=55.82111.997394x = \frac{55.8211}{1.997394}x=1.99739455.8211​

STEP 8

Calculate the value of xxxx=27.97%x =27.97\%x=27.97%The isotope abundance of 87Rb{ }^{87} \mathrm{Rb}87Rb is approximately27.97%.

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QuestionCalculate the % abundance of ${ }^{87} \mathrm{Rb}$ if Rubidium's atomic mass is 85.47 amu, with isotopes ${ }^{85} \mathrm{Rb}$ and ${ }^{87} \mathrm{Rb}$ .

Let's denote the percentage abundance of ${ }^{87} \mathrm{Rb}$ as $x$ . Then, the percentage abundance of ${ }^{85} \mathrm{Rb}$ is $100\% - x$ .

We can write the equation for the atomic mass of Rubidium as a weighted average of the masses of its isotopes $85.47 = \frac{{84.911789 \times (100 - x) +86.909183 \times x}}{100}$

Multiply each side of the equation by100 to simplify $8547 =8491.1789 -84.911789x +86.909183x$

Combine like terms $8547 =8491.1789 +1.997394x$

Subtract8491.1789 from each side of the equation $55.8211 =1.997394x$

Divide each side of the equation by1.997394 to solve for $x$ $x = \frac{55.8211}{1.997394}$

Calculate the value of $x$ $x =27.97\%$ The isotope abundance of ${ }^{87} \mathrm{Rb}$ is approximately27.97%.