No questions found
This investigation looks at the structure of models of molecules.
Molecules called alkanes contain carbon atoms (C) and hydrogen atoms (H) arranged in a pattern.
These diagrams show the first three alkanes.
(a) Draw a diagram to show the next alkane which contains four carbon atoms.
(b) (i) Complete this table to show the number of hydrogen atoms $(h)$ for different numbers of carbon atoms $(c)$.
[Table_1]
(ii) What is the value of $h$ when $c$ is 12?
........................................................
(iii) Find a formula for $h$ in terms of $c$.
$h = .........................................................$
(iv) What is the value of $c$ when $h$ is 100?
........................................................
560
500
518
Alkanes can be made into alcohols by adding one oxygen atom (O).
For example
(a) Complete the table below for an alcohol with 3 carbon atoms.
[Table_1]
| Number of carbon atoms $c$ | Number of hydrogen atoms $h$ | Number of oxygen atoms $o$ | Total number of atoms $t$ |
|-----------------------------|------------------------------|----------------------------|----------------------------|
| 1 | 4 | 1 | 6 |
| 2 | 6 | 1 | 9 |
| 3 | | | |
(b) Find a formula for $t$ in terms of $c$.
$t = \text{........................................................}$
514
580
576
Chemists use small spheres and rods to make models of molecules. These diagrams show a sequence of molecules of height 1.
[Image_1: Molecule 1, Molecule 2, Molecule 3]
(a) Draw the next two molecules in this sequence.
(b) Complete this table for molecules of height 1.
[Table_1]
| Molecule m | Number of spheres s | Number of rods r |
|------------|---------------------|-----------------|
| 1 | 1 | 0 |
| 2 | 2 | 1 |
| 3 | 3 | 2 |
| 4 | | |
| 5 | | |
| 6 | | |
(c) Write down a formula for $s$ in terms of $m$.
$s = \text{......................................................}$
(d) A molecule of height 1 has 97 spheres.
How many rods does this molecule have?
...............................................................
580
584
586
These diagrams show a sequence of molecules of height 2.
[Image_1: Molecule diagrams]
(a) Complete this table for molecules of height 2.
[Table_1]
| Molecule \( m \) | Number of spheres \( s \) | Number of rods \( r \) |
|------------------|----------------------|------------------|
| 1 | 2 | 1 |
| 2 | 4 | 4 |
| 3 | 6 | 7 |
| 4 | | |
| 5 | | |
| 6 | | |
(b) Find, in terms of \( m \), a formula for
(i) \( s \),
\( s = \text{...................................................} \)
(ii) \( r \).
\( r = \text{...................................................} \)
(c) A molecule of height 2 has 100 spheres.
How many rods does this molecule have?
\( \text{..........................................................} \)
534
558
538
(a) Use your answers to questions 3(c) and 4(b) to help you complete the table for molecules of height $h$.
[Table]
| Height $(h)$ | Number of spheres $(s)$ in terms of $m$ | Number of rods $(r)$ in terms of $m$ |
|-------------|-------------------------------------|----------------------------------|
| 1 | | $m - 1$ |
| 2 | | |
| 3 | $3m$ | $5m - 3$ |
| 4 | | |
| 5 | $5m$ | $9m - 5$ |
| 6 | | |
(b) Find, in terms of $m$ and $h$, a formula for
(i) $s$,
$s = \text{............................................................}$
(ii) $r$.
$r = \text{............................................................}$
540
533
560
