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. Calculate the relative atomic mass of titanium in this sample. Give your answer to one decimal place. 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. Equation m/z value Calculate the mass, in kg, of one atom of 4Ti. The Avogadro constant L = 6.022 x 10^23 mol^-1 In a TOF mass spectrometer the time of flight, t, of an ion is shown by the equation t = d / √(2E/m) 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 “Ti” ion is 9.816 x 10^-7 s. Calculate the time of flight of the “Ti” 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 (RAM) of titanium, we use the formula:

$\text{RAM} = \frac{(m/z_1 \times \text{abundance}_1) + (m/z_2 \times \text{abundance}_2) + (m/z_3 \times \text{abundance}_3) + (m/z_4 \times \text{abundance}_4)}{\text{Total abundance}}$

Applying the values from the table:

$\text{RAM} = \frac{(46 \times 1.9) + (47 \times 7.8) + (48 \times 74.6) + (49 \times 8.5)}{1.9 + 7.8 + 74.6 + 8.5}$

Calculating:

$\text{RAM} = \frac{(87.4) + (374.6) + (3580.8) + (416.5)}{92.8} \approx 47.8$

Thus, the relative atomic mass 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 by electron impact can be represented as:

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

The m/z value of the titanium ion that reaches the detector first is the mass over charge, where for the ion Ti+, m/z = 48.

Therefore, the m/z value is 48.

Step 3

Calculate the mass, in kg, of one atom of 4Ti.

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Answer

To calculate the mass of one atom of 4Ti, we can use the formula:

$\text{mass} = \frac{\text{molar mass}}{N_A}$

Where:

Molar mass of 4Ti is approximately 4 g/mol.
Avogadro's constant, $N_A = 6.022 \times 10^{23} \text{ mol}^{-1}$ .

Thus, the calculation becomes:

$\text{mass} = \frac{4 \text{ g/mol}}{6.022 \times 10^{23} \text{ mol}^{-1}} = 6.64 \times 10^{-24} \text{ kg}$

So, the mass of one atom of 4Ti is approximately 6.64 x 10^-24 kg.

Step 4

Calculate the time of flight of the 'Ti' ion.

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Answer

Using the equation:

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

Where:

For the 'Ti' ion, the mass $m$ needs to be calculated based on the equation:
The kinetic energy $E = 1.013 \times 10^{-3} J$ .

First, calculate $m$ : if for Ti, $m = 47.8 ext{ g/mol}$ then:

$m = \frac{47.8}{1000} \text{ kg}$

Now, substitute $m$ back into the equation to find $t$ . Assuming $d$ is given or can be derived:

$t = \frac{d}{\sqrt{\frac{2 \times 1.013 \times 10^{-3}}{m}}}$

With sufficient detail, this allows for a calculation of time of flight using parameters associated with the specific experimental setup.

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 4Ti.

Calculate the time of flight of the 'Ti' ion.

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