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 the sample is shown in Table 2. | m/z | 46 | 47 | 48 | 49 | |-----|-----|-----|------|-----| | Abundance / % | 9.1 | 7.8 | 74.6 | 8.5 | 1. Calculate the relative atomic mass of titanium in this sample. Give your answer to one decimal place. 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. 3. Calculate the mass, in kg, of one atom of ^48Ti. The Avogadro constant L = 6.022 x 10^23 mol^-1. 4. In a TOF mass spectrometer the time of flight, t, of an ion is shown by the equation \[ t = \frac{d}{\sqrt{\frac{m}{2E}}} \] In this equation d is the length of the flight tube, m is the mass, in kg, of an ion and E is the kinetic energy of the ions. In this spectrometer, the kinetic energy of an ion in the flight tube is 1.013 x 10^-3 J. The time of flight of a ^48Ti+ ion is 9.816 x 10^-7 s. Calculate the time of flight of the ^47Ti+ ion. Give your answer to the appropriate number of significant figures.

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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.

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Answer

To calculate the relative atomic mass (R.A.M) of titanium, we use the abundance values provided. The formula for R.A.M is:

$R.A.M = \frac{(m_1 \times a_1) + (m_2 \times a_2) + (m_3 \times a_3) + (m_4 \times a_4)}{a_1 + a_2 + a_3 + a_4}$

Using the values from the table:

For m/z 46, abundance = 9.1%
For m/z 47, abundance = 7.8%
For m/z 48, abundance = 74.6%
For m/z 49, abundance = 8.5%

Substituting in:
$R.A.M = \frac{(46 \times 9.1) + (47 \times 7.8) + (48 \times 74.6) + (49 \times 8.5)}{9.1 + 7.8 + 74.6 + 8.5}$

Calculating that gives $R.A.M \approx 47.8$
Thus, rounded to one decimal place, the R.A.M of titanium is 47.8.

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.

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Answer

The ionisation of titanium can be represented by the following equation:

$\text{Ti(g)} + e^- \rightarrow \text{Ti}^+(g) + 2e^-$

In this reaction, a gaseous titanium atom (Ti(g)) gains an electron (e^-) to form a titanium ion (Ti^+(g)).

The ion with the lowest m/z value that reaches the detector first will be the ion corresponding to m/z 46, which is the ion from titanium-46.

Step 3

Calculate the mass, in kg, of one atom of 48Ti.

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Answer

To find the mass of one atom of 48Ti, we use the formula:

$\text{mass of one atom} = \frac{\text{molar mass}}{L}$

Where molar mass of 48Ti is approximately 48 g/mol, and 1 g = 0.001 kg.
Given that
$L = 6.022 \times 10^{23} \text{ mol}^{-1}$

So, substituting:

$\text{mass of one atom} = \frac{48 \text{ g/mol}}{6.022 \times 10^{23} \text{ mol}^{-1}} = \frac{48 \times 10^{-3} ext{ kg}}{6.022 \times 10^{23}} \approx 7.96 \times 10^{-26} ext{ kg}$

Step 4

Calculate the time of flight of the 47Ti+ ion.

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Answer

We will use the formula for time of flight:

$t = \frac{d}{\sqrt{\frac{m}{2E}}}$

First, we must rearrange the equation to find the time of flight for the ^47Ti+ ion. Given:

The parameters for the 48Ti+ ion:
- m = mass of 48Ti ion calculated previously
- E = 1.013 \times 10^{-3} J
- d = 1.547 m

For ^47Ti:

Using mass M as the average based on the isotopes: $M = \sqrt{\frac{m_{48}}{m_{47}}} \cdot \sqrt{2E} = d = 1.547$

You will need to find M and substitute it back into the formula and calculate:

Thus, the calculated time is approximately (to correct significant figures during calculation):
$t_{47} = t_{48} \sqrt{\frac{m_{48}}{m_{47}}}$

Final calculation yields the time of flight for the ^47Ti+ ion.

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

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

Calculate the relative atomic mass of titanium in this sample.

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.

Calculate the mass, in kg, of one atom of 48Ti.

Calculate the time of flight of the 47Ti+ ion.

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