iridium has two isotopes. with mass numbers 191 and 193, and its average relative atomic mass is 192.23.calculate the relative abundances of the two isotopes
191x + 193(1-x) = 192.23
x = .385
so,
38.5% Ir191
61.5% Ir193
or, since 192.23 is about 5/8 of the way from 191 to 193, 5/8 will be Ir193, or 62.5%. Fairly close ...
ridium has two stable isotopes: 191Ir and 193Ir with masses of 190.9605940 amu and 192.9629264 amu. If the fractional abundance of 191Ir is 0.373 on Earth, complete the expression below that can be used to calculate the average atomic mass.
Why did the chicken join the circus? Because it wanted to become an "iridium balancing" act! Now, let's calculate the relative abundances of the two isotopes of iridium, shall we?
Let's assume the relative abundance of the isotope with mass number 191 is x, and the relative abundance of the isotope with mass number 193 is y.
Since the average relative atomic mass of iridium is given as 192.23, we can set up the following equation:
(191x) + (193y) = 192.23
Now, let's solve this equation and find the values of x and y:
191x + 193y = 192.23
We know that x + y = 1, as the sum of the relative abundances should be equal to 100%. So, we can solve for x in terms of y:
x = 1 - y
Substituting this back into the equation:
191(1-y) + 193y = 192.23
191 - 191y + 193y = 192.23
2y = 1.23
y = 0.615
Now, we can calculate the value of x:
x = 1 - 0.615
x = 0.385
Therefore, the relative abundances of the two isotopes of iridium are approximately 38.5% for isotope 191 and 61.5% for isotope 193.
To calculate the relative abundances of the two isotopes of iridium, we can use the following formula:
Relative abundance = (Isotopic mass × Relative atomic mass) / Average relative atomic mass
Let's calculate the relative abundance of the first isotope with mass number 191:
Relative abundance of isotopic mass 191 = (191 × 192.23) / 192.23
= 191 / 1
= 191
Now, let's calculate the relative abundance of the second isotope with mass number 193:
Relative abundance of isotopic mass 193 = (193 × 192.23) / 192.23
= 193 / 1
= 193
Therefore, the relative abundances of the two isotopes of iridium are 191 and 193, respectively.
To calculate the relative abundances of the two isotopes of iridium, we can use the following formula:
Average atomic mass = (mass1 × abundance1) + (mass2 × abundance2)
We know that:
- Iridium has two isotopes with mass numbers 191 and 193.
- The average relative atomic mass of iridium is 192.23.
Let's assign the following variables:
m1 = mass1 = 191
m2 = mass2 = 193
a1 = abundance1 (relative abundance of the isotope with mass number 191)
a2 = abundance2 (relative abundance of the isotope with mass number 193)
Using the given information, we can set up the equation:
192.23 = (191 × a1) + (193 × a2)
Now, we need to solve this equation to find the values of a1 and a2.
Since we have two unknowns (a1 and a2), we will need another equation to solve the system of equations.
Luckily, there is a relationship between the relative abundances of isotopes. Since the total relative abundance of all isotopes adds up to 1 (or 100%), we have the equation:
a1 + a2 = 1
Now, we have a system of equations to solve:
192.23 = (191 × a1) + (193 × a2)
a1 + a2 = 1
We can solve this system using various methods, such as substitution or elimination. Let's use substitution:
Rearrange the second equation to express a1 in terms of a2:
a1 = 1 - a2
Substitute the value of a1 in the first equation:
192.23 = (191 × (1 - a2)) + (193 × a2)
Simplify the equation:
192.23 = 191 - 191a2 + 193a2
Combine like terms:
192.23 = 191 + 2a2
Rearrange the equation:
2a2 = 192.23 - 191
Simplify:
2a2 = 1.23
Divide both sides by 2:
a2 = 0.615
Now, substitute the value of a2 back into the second equation to find a1:
a1 + 0.615 = 1
Subtract 0.615 from both sides:
a1 = 1 - 0.615
a1 = 0.385
Therefore, the relative abundances of the two isotopes of iridium are approximately:
Isotope with mass number 191: 38.5%
Isotope with mass number 193: 61.5%