Bromine has two natural occurring isotopes (Br-79 and Br-81) and has an atomic mass of 79.904 amu. The mass of Br-81 is 80.9163 amu, and its natural abundance is 49.31%. Calculate the mass and natural abundance of Br-79.
My teacher said the answer is 78.92 amu and 50.69%. But i keep getting 81.13amu and i don't know how to get the percentage.
Br-79 & Br-81 have a total amu of 79.904
Br-81 = 80.9163amu & 49.31% abundance
100-49.31=50.69 which would be the abundance of Br-79
Convert the % into decimals.
50.69%=0.5069 49.31%= 0.4931
x= total amu of Br-79
0.5069(x) + 0.4931(80.9163)= 79.904
0.5069x + 39.89982753 = 79.904
0.5069x = 40.00417247
x= 78.92 amu
Do you see in my post where I have 100-0.4931? That is where you get the 0.5069 = 50.69%.
Post your work and I'll find your error.
Your teacher is right. The correct answer is 78.92.
(79.904)=(80.9163)(0.4931) + x(0.4931)
79.904=39.90 + 0.4931x
40.004=0.4931x
x=81.13amu
My first response was:
80.916(0.4931) + x(100-49.31) = 79.904. Solve for x.
(79.904)=(80.9163)(0.4931) + x(0.4931)
Note that I made a typo. It should have been 1.00-0.4931 (and not 100-49.31), then you should have
79.904 = (80.9163) + x(0.5069) and go from there.
79.904=39.90 + 0.4931x
Should be
79.904 = 39.900 + 0.5069x etc.
40.004=0.4931x
x=81.13amu
oh okay i get it now, thank you! Why did you subtract 1.00 from the abundance though? how do you know?
There are two Br isotopes. One is 49.31% so the other one must be 100%-49.31% = 50.69% or 0.5069 as a fraction.
To solve this problem, we can set up a system of equations based on the given information. Let's denote the mass of Br-79 as x and its natural abundance as y.
From the problem, we know the following information:
1. Atomic mass of bromine (Br) = 79.904 amu.
2. Mass of Br-81 = 80.9163 amu.
3. Natural abundance of Br-81 = 49.31%.
Now, we can set up the equations:
1. Mass equation:
(mass of Br-79 * natural abundance of Br-79) + (mass of Br-81 * natural abundance of Br-81) = atomic mass of bromine
(x * y) + (80.9163 * 0.4931) = 79.904
2. Natural abundance equation:
natural abundance of Br-79 + natural abundance of Br-81 = 100%
y + 49.31% = 100%
Now, we can solve the equations:
1. Rearrange the mass equation:
xy + 39.8439533 = 79.904
2. Simplify the natural abundance equation:
y + 0.4931 = 1.0
3. Solve for y (natural abundance of Br-79):
y = 1.0 - 0.4931
y = 0.5069
4. Substitute y into the mass equation:
x * 0.5069 + 39.8439533 = 79.904
5. Solve for x (mass of Br-79):
x * 0.5069 = 79.904 - 39.8439533
x * 0.5069 = 40.0600467
x = 40.0600467 / 0.5069
x = 78.9949 amu
Therefore, the mass of Br-79 is approximately 78.9949 amu, and its natural abundance is approximately 50.69%.
If 81 has abundance of 49.31%, then Br79 must be 100-49.31. Then
80.916(0.4931) + x(100-49.31) = 79.904. Solve for x.