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Chapter 2: Problem 35

Explain how a mass spectrometer, capable of distinguishing between ions with \(\mathrm{m} / \mathrm{e}\) values differing by 1 part in 50,000 , could be used to tell whether an ion of mass 29 is \(\mathrm{C}_{2} \mathrm{H}_{5} \oplus\) or \(\mathrm{CHO}^{\oplus}\)

Short Answer

Expert verified
The mass-to-charge ratios of \(C_2H_5^+\) and \(CHO^+\) ions are 29.048 and 29.018, respectively. The mass difference between them is 0.03. Given the mass spectrometer's resolution of 1 part in 50,000, its minimum mass difference that it can resolve is about \(5.81 \times 10^{-4}\), which is smaller than the mass difference between the two ions. Therefore, the mass spectrometer can distinguish between the \(C_2H_5^+\) and \(CHO^+\) ions.

Step by step solution

01

Calculate the mass-to-charge ratios of the ions

To determine whether the mass spectrometer can differentiate these ions, first, we need to find their respective mass-to-charge ratios. Here are the atomic masses of each element: - Carbon (C): 12.01 u - Hydrogen (H): 1.008 u - Oxygen (O): 16.00 u - Charge (e): 1 (since both ions have a charge of +1) Now, we can calculate the mass-to-charge ratio for each ion: - \( C_2H_5^+ \): mass = (2)(12.01) + (5)(1.008) = 29.048 u; m/e = 29.048 - \( CHO^+ \): mass = 12.01 + 1.008 + 16.00 = 29.018 u; m/e = 29.018
02

Calculate the mass difference between the ions

Next, we need to find the mass difference between the two ions. To do this, we will take the absolute difference between their m/e values: \( \Delta m = |m_{C_2H_5^+} - m_{CHO^+}| = |29.048 - 29.018| = 0.03 \)
03

Determine if the mass spectrometer can resolve the ions

We are given that the mass spectrometer can distinguish between ions with m/e values that differ by 1 part in 50,000. The minimum mass difference the instrument can resolve can be found by dividing the ion's mass by 50,000: \( \Delta m_{min} = \frac{m_{C_2H_5^+}}{50,000} = \frac{29.048}{50,000} \approx 5.81 \times 10^{-4} \)
04

Compare the calculated mass difference with the instrument's resolving power

Now, we need to compare the mass difference we calculated in Step 2 with the instrument's resolving power calculated in Step 3: \( 0.03 > 5.81 \times 10^{-4} \) Since the mass difference between the two ions (0.03) is much greater than the minimum mass difference the mass spectrometer can resolve (5.81 x 10^-4), the instrument is capable of distinguishing between the \( C_2H_5^+ \) and \( CHO^+ \) ions.

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