By knowing the natural abundance of minor isotopes, it's possible to calculate the relative heights of M+ and M+1 peaks. If natural abundances are 12C - 98.9% and 13C - 1.10%, what are the relative heights, to the nearest 0.1%, of the M+ and M+1 peaks in the mass spectrum of ribose, C5H10O5?
Ignore the contributions of isotopes like 2H (deuterium; 0.015% natural abundance) and 17O (0.04% natural abundance) that are small.
I added up the different masses and got 103% but that isn't correct.
To calculate the relative heights of the M+ and M+1 peaks in the mass spectrum of ribose, you need to consider the natural abundances of the isotopes and their contributions.
First, let's determine the total percentage contribution of the M+ and M+1 peaks:
M+ peak: Contribution of 12C isotope = 98.9%
M+1 peak: Contribution of 13C isotope = 1.10%
Now we can calculate the relative heights of the peaks. The M+ peak will have a height of 98.9 divided by the total contribution, and the M+1 peak will have a height of 1.10 divided by the total contribution.
Total contribution = 98.9% + 1.10% = 100%
Relative height of M+ peak = (98.9% / 100%) * 100% = 98.9%
Relative height of M+1 peak = (1.10% / 100%) * 100% = 1.10%
Therefore, the relative heights of the M+ and M+1 peaks in the mass spectrum of ribose are approximately 98.9% and 1.10%, respectively (rounded to the nearest 0.1%).
To calculate the relative heights of the M+ and M+1 peaks in the mass spectrum of ribose, we need to consider the natural abundances of the carbon isotopes 12C and 13C.
The M+ peak represents the molecular ion with only carbon-12 (12C) isotopes, while the M+1 peak contains one carbon-13 (13C) isotope.
To determine the relative heights, we need to calculate the ratio of the number of molecules with M+1 peak to the number of molecules with only M+ peak.
First, let's calculate the ratio of carbon-13 to carbon-12 using the natural abundances provided:
Ratio of 13C to 12C = (1.10% natural abundance of 13C) / (98.9% natural abundance of 12C)
= 0.011 / 0.989
≈ 0.0111
This ratio represents the expected probability of finding a carbon-13 isotope in a ribose molecule.
Next, let's consider the formula of ribose, C5H10O5. We have 5 carbon atoms in ribose, so the number of combinations of carbon-13 isotopes in the molecule will vary from 0 to 5.
Now, we can calculate the relative heights of the M+ and M+1 peaks:
M+ peak: The number of carbon-12 isotopes (12C) = 5 - (number of carbon-13 isotopes)
M+1 peak: The number of carbon-13 isotopes (13C) = (number of carbon-13 isotopes)
We can calculate the relative heights based on the probabilities of each combination:
Relative height of M+ peak = (Probability of finding M+ peak) * 100
= (Probability of having 5 carbon-12 isotopes) * 100
≈ (0.989)^5 * 100
Relative height of M+1 peak = (Probability of finding M+1 peak) * 100
= (Probability of having 1 carbon-13 isotope) * 100
≈ (0.0111) * (Number of combinations with 1 carbon-13 isotope) * 100
To find the total relative heights, we need to calculate the sum of the relative heights of the M+ peak and the M+1 peak.
Total relative heights = Relative height of M+ peak + Relative height of M+1 peak
Note: Since the question asks for the relative heights to the nearest 0.1%, you can round the values to the nearest 0.1% after calculating them.
Using these calculations, you should be able to find the correct relative heights of the M+ and M+1 peaks in the mass spectrum of ribose.