Zinc has three major and two minor isotopes. For this problem, assume that the only isotopes of zinc are the major ones, zinc-64, zinc-66, and zinc-68. The atomic mass of zinc-64 is 63.9291 Da, that of zinc-66 is 65.9260 Da, and that of zinc-68 is 67.9248 Da. Calculate the atomic mass of zinc from the relative peak intensities in the following spectrum.
Peaks: At Zn-64=100, Zn-66=57.4, Zn-68=38.6
thanks!
I would change the intensities to percent.
100 + 57.4 + 38.6 = 196
Then 100/196 = about 51% but you need to do these more accurately.
57.4/196 = about 29%
38.6/196 = about 19%
Then
(0.51)(mass Zn64) + (0.29)(mass Zn66) + (0.19)(mass Zn68) = Avg mass Zn. I obtained 65.294 but you need another place.
Great Answer
To calculate the atomic mass of zinc from the relative peak intensities, we need to find the weighted average of the atomic masses of the three isotopes using their respective intensities.
Step 1: Convert the relative peak intensities into fraction form.
The relative peak intensities given are:
Zn-64 = 100
Zn-66 = 57.4
Zn-68 = 38.6
Step 2: Calculate the sum of the peak intensities.
Sum = 100 + 57.4 + 38.6 = 196
Step 3: Convert the peak intensities into fractions by dividing each intensity by the sum.
Fraction of Zn-64 = 100/196 = 0.5102
Fraction of Zn-66 = 57.4/196 = 0.2929
Fraction of Zn-68 = 38.6/196 = 0.1969
Step 4: Calculate the weighted average.
Weighted average = (Fraction of Zn-64 * Atomic mass of Zn-64) + (Fraction of Zn-66 * Atomic mass of Zn-66) + (Fraction of Zn-68 * Atomic mass of Zn-68)
Using the given atomic masses:
Weighted average = (0.5102 * 63.9291) + (0.2929 * 65.926) + (0.1969 * 67.9248)
Simplifying the calculation:
Weighted average = 32.60541492 + 19.2518404 + 13.39093512
Final calculation:
Weighted average = 65.24819044
Therefore, the atomic mass of zinc from the given spectrum is approximately 65.25 Da.
To calculate the atomic mass of zinc, we can use the relative peak intensities and the atomic masses of the three major isotopes of zinc.
First, let's convert the percentages of the peak intensities to ratios. We can do this by dividing each percentage by 100:
- Zn-64: 100/100 = 1
- Zn-66: 57.4/100 = 0.574
- Zn-68: 38.6/100 = 0.386
Next, we need to find the total sum of these ratios. Adding them together, we get:
1 + 0.574 + 0.386 = 1.96
This sum tells us that the total peak intensity corresponds to 1.96 units.
The next step is to normalize these ratios by dividing each one by the total sum:
- Zn-64: 1/1.96 ≈ 0.5102
- Zn-66: 0.574/1.96 ≈ 0.2939
- Zn-68: 0.386/1.96 ≈ 0.1970
These normalized ratios represent the relative abundance of each isotope in the sample.
Finally, to calculate the atomic mass of zinc, we can multiply each normalized ratio by the atomic mass of the corresponding isotope and sum them up:
(0.5102 x 63.9291) + (0.2939 x 65.9260) + (0.1970 x 67.9248)
= 32.6169 + 19.3796 + 13.4045
= 65.401 Da
Therefore, the atomic mass of zinc, based on the given peak intensities, is approximately 65.401 Da.