Mass spectrometry is an analytical technique used to identify elements and compounds. It determines the relative abundance of isotopes in a sample, helping us calculate relative atomic mass (Ar) and identify molecular structures.
🔑 Key Principle
A mass spectrometer works by converting atoms or molecules into positive gaseous ions, accelerating them to the same kinetic energy, and measuring their travel time down a flight tube. Lighter ions travel faster and arrive at the detector first.
How a TOF Mass Spectrometer Works
The entire instrument is kept under a **high vacuum** to prevent the moving ions from colliding with air molecules. The process consists of four main stages:
Stage 1: Ionisation
The sample must be ionised to form positive 1+ ions so they can be accelerated by an electric field and detected. There are two main methods of ionisation:
A. Electron Impact (Hard Ionisation)
Used for elements and low-mass molecular samples. The vaporised sample is injected into the spectrometer. An electron gun fires high-energy electrons at the sample, knocking off an electron from each atom/molecule to form a 1+ ion.
Equation: X(g) → X⁺(g) + e⁻
Tip: This can cause larger molecules to fragment.
B. Electrospray Ionisation (Soft Ionisation)
Used for high-mass molecules like proteins. The sample is dissolved in a volatile solvent and injected through a fine hypodermic needle connected to a high voltage supply. The droplets gain a proton (H⁺) from the solvent as they exit, forming a 1+ ion.
Equation: M(g) + H⁺ → MH⁺(g)
Tip: The m/z value of the peak will be 1 unit higher than the actual molecular mass due to the added H⁺.
Stage 2: Acceleration
The positive ions are accelerated by an electric field. The electric field is calibrated so that all ions are given the exact same kinetic energy (KE).
Since \( KE = \frac{1}{2}mv^2 \), the velocity of an ion depends solely on its mass. Lighter ions will travel at a higher velocity, while heavier ions travel slower.
Stage 3: Ion Drift (Flight Tube)
The ions enter a region with no electric field, known as the drift region or flight tube. They drift down the tube toward the detector. Because they have different velocities, they separate:
- Lighter ions travel faster and reach the detector first.
- Heavier ions travel slower and reach the detector later.
Stage 4: Detection
When the positive ions reach the detector, they hit a negatively charged plate. On contact, the positive ions gain electrons from the detector. This movement of electrons generates an electric current.
The size of the current is directly proportional to the **abundance** (number) of the ions hitting the detector. A computer records the times of flight and the current to generate a mass spectrum.
When describing how a TOF mass spectrometer works, make sure to detail all four stages in sequence: ionisation, acceleration to constant kinetic energy, drift/separation in a flight tube based on velocity, and detection where ions gain electrons to produce a current. In recent years, AQA questions focus on the physics equations underlying this: \( v = \sqrt{\frac{2KE}{m}} \) and \( t = \frac{d}{v} = d\sqrt{\frac{m}{2KE}} \).
The Mass Spectrum
A mass spectrum is a graph plotted with **relative abundance** (y-axis) against **mass-to-charge ratio (m/z)** (x-axis).
Because the charge on the ions is almost always 1+, the m/z value on the x-axis corresponds directly to the mass of the isotope or molecule. For example, a peak at m/z = 35 represents an isotope with a mass of 35.
Calculating Relative Atomic Mass (Ar)
From the peaks in a mass spectrum, you can calculate the relative atomic mass using the relative abundance. The formula is:
Step 1: Multiply each isotopic mass by its percentage abundance:
\[ (35 \times 75.0) + (37 \times 25.0) = 2625 + 925 = 3550 \]
Step 2: Divide by the total abundance (which is 100%):
\[ A_r = \frac{3550}{100} = 35.5 \]
Therefore, the relative atomic mass of chlorine is 35.5.
Step 1: Calculate the total relative abundance of all isotopes:
\[ \text{Total abundance} = 7.9 + 1.0 + 1.1 = 10.0 \]
Step 2: Apply the formula:
\[ A_r = \frac{(24 \times 7.9) + (25 \times 1.0) + (26 \times 1.1)}{10.0} \]
\[ A_r = \frac{189.6 + 25.0 + 28.6}{10.0} = \frac{243.2}{10.0} = 24.32 \]
Rounding to 1 decimal place gives 24.3. Looking at the periodic table, the element with an Ar of 24.3 is Magnesium (Mg).
TOF Calculations and Physics
You may be asked to calculate the mass, distance, velocity, or flight time of an ion in a flight tube. The relationships are based on two classical physics equations:
By substituting velocity (\(v\)) into the kinetic energy equation, we get the time of flight (\(t\)):
Where:
- \(KE\) = kinetic energy in Joules (\(\text{J}\))
- \(m\) = mass of **one single ion** in kilograms (\(\text{kg}\))
- \(v\) = velocity of the ion in meters per second (\(\text{m s}^{-1}\))
- \(d\) = distance of the flight tube in meters (\(\text{m}\))
- \(t\) = time of flight in seconds (\(\text{s}\))
Step 1: Calculate the mass of a single selenium-82 ion in kg.
Mass of 1 mole of \(^{82}\text{Se}\) atoms = 82 g = \(0.082\text{ kg}\).
Mass of 1 single ion: \[ m = \frac{0.082}{6.022 \times 10^{23}} = 1.362 \times 10^{-25}\text{ kg} \]
Step 2: Calculate the velocity of the ion.
\[ KE = \frac{1}{2}mv^2 \implies v = \sqrt{\frac{2KE}{m}} \]
\[ v = \sqrt{\frac{2 \times (1.00 \times 10^{-16})}{1.362 \times 10^{-25}}} = \sqrt{1.468 \times 10^9} = 38320\text{ m s}^{-1} \]
Step 3: Calculate the flight time.
\[ t = \frac{d}{v} = \frac{1.00}{38320} = 2.61 \times 10^{-5}\text{ s} \]
The time of flight for the selenium-82 ion is \(2.61 \times 10^{-5}\text{ s}\) (or 26.1 μs).
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