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A sample of titanium was ionised by electron impact in a time of flight (TOF) mass spectrometer - AQA - A-Level Chemistry - Question 4 - 2017 - Paper 1
Question 4
A sample of titanium was ionised by electron impact in a time of flight (TOF) mass spectrometer. Information from the mass spectrum about the isotopes of titanium in... show full transcript
Worked Solution & Example Answer:A sample of titanium was ionised by electron impact in a time of flight (TOF) mass spectrometer - AQA - A-Level Chemistry - Question 4 - 2017 - Paper 1
Step 1
Calculate the relative atomic mass of titanium in this sample
Answer
To find the relative atomic mass, we use the abundances and m/z values from Table 2:
Relative atomic mass (Ar) = ( \frac{(46 \times 1.9) + (47 \times 7.8) + (48 \times 74.6) + (49 \times 8.5)}{100} )
Calculating this gives: ( Ar = \frac{(87.4 + 366.6 + 3579.2 + 416.5)}{100} = \frac{4420.7}{100} = 47.2 )
Thus, the relative atomic mass of titanium is 47.2.
Step 2
Write an equation, including state symbols, to show how an atom of titanium is ionised by electron impact and give the m/z value of the ion that would reach the detector first.
Answer
The equation for ionisation by electron impact is:
[ \text{Ti(g)} + e^- \rightarrow \text{Ti}^+ \text{(g)} + 2e^- ]
The m/z value of the ion that would reach the detector first, which is ( ext{Ti}^+ ) (mass 48), is 48.
Step 3
Step 4
Calculate the time of flight of the ⁴Ti²⁺ ion.
Answer
To calculate the time of flight using the equation:
[ t = d \sqrt{\frac{m}{2E}} ]
Given ( d = 1.54 \text{ m} ), ( m = 4 imes 10^{-27} \text{ kg} ), and ( E = 1.013 \times 10^{-3} \text{ J} ):
First, we need to find the mass of the ⁴Ti²⁺ ion. Since the mass of ⁴Ti is approximately (4 imes 10^{-27}), the mass of ⁴Ti²⁺ will be half: ( m = \frac{4 \times 10^{-27}}{2} = 2 \times 10^{-27} \text{ kg} ) Then: [ t = 1.54 \sqrt{\frac{2 \times 10^{-27}}{2 \times 1.013 \times 10^{-3}}} \approx 4.78 \times 10^{-7} \text{ s} ]