Question

the mass spectrum of an organic compound shows the relative abundances of m to be 61.89% and M+1 to be 16.07%. Assuming the peaks are caused by ¹²C and ¹³C isotopes, determine the number of carbon atoms in the compound. The natural abundance of ¹²C is 98.93%, and the natural abundance of ¹³C is 1.07%. number of carbon atoms:

Answer 1

The number of carbon atoms in the compound is determined by using the relative abundances of m to M+1, corresponding to 12C to 13C isotopes, and is found to be approximately 3 carbon atoms after calculation.

Step-by-step explanation:

The mass spectrum of an organic compound can reveal the number of carbon atoms based on the relative intensities of the M (due to 12C) and M+1 (due to 13C) peaks. To find the number of carbon atoms, we set up the following equation, where n is the number of carbon atoms, I(M) is the intensity of the M peak, and I(M+1) is the intensity of the M+1 peak:

I(M+1)/I(M) = (n * natural abundance of 13C) / (natural abundance of 12C)

Inserting the given values into the equation:

0.1607 / 0.6189 = (n * 0.0107) / 0.9893

Solving for n yields the number of carbon atoms in the compound:

n = (0.1607 / 0.6189) * (0.9893 / 0.0107)

Calculate n to find the number of carbon atoms.

With given percentages, we calculate:

n = (0.1607 / 0.6189) * (0.9893 / 0.0107)

≈ 2.52

Since the number of carbon atoms cannot be a fraction, we round to the nearest whole number. Therefore, the number of carbon atoms in the compound is approximately 3.