Side of cube / mm 4 6 8 10 12 Depth dye penetrated / mm 3 3 3 3 3 Length of uncoloured core / mm 0 0 6 Cubes of plain agar of five different sizes were each...
Question 1 Report
| Side of cube / mm | 4 | 6 | 8 | 10 | 12 |
|---|---|---|---|---|---|
| Depth dye penetrated / mm | 3 | 3 | 3 | 3 | 3 |
| Length of uncoloured core / mm | 0 | 0 | 6 |
Cubes of plain agar of five different sizes were each soaked for the same time in a purple acidic dye. The dye diffused inwards a fixed depth of 3 mm into every cube, leaving an uncoloured core at the centre of the larger cubes. Each cube was then cut open and the length of the uncoloured core was measured. The results are recorded in Table 7.1.
Fig. 7.1 shows the specimen used.
(a) State the independent variable. [1]
(b) The dye diffused 3 mm into every cube. Complete Table 7.1 by calculating the length of the uncoloured core for the 8 mm cube and the 10 mm cube. [2]
(c) Name the apparatus used to measure the side of each cube. [1]
(d) Calculate the percentage of the 12 mm cube, by volume, that remained uncoloured. Show your working. [3]
(e) Plot a graph of the length of the uncoloured core on the y-axis against the side of the cube on the x-axis on the grid provided. [3]
(f) Measure from your graph the length of the uncoloured core for a cube of side 9 mm. [1]
(g) Measure from your graph the smallest cube side that would still leave an uncoloured core. [1]
(h) Describe how the size of the cube affects the fraction of it that becomes coloured. [2]
(i) Explain, using surface area to volume ratio and diffusion, why the largest cubes keep an uncoloured centre. [3]
(j) Suggest why cubes are used rather than irregular lumps of agar. [2]
(k) State the process by which the dye enters the agar. [1]
Answer Details
This question tests surface area to volume ratio and diffusion: completing a table, a volume percentage, plotting and reading a graph, and explaining why large cubes keep an uncoloured centre.
(a) The independent variable is the size / side length of the cube. [1]
(b) The dye enters 3 mm from every face, so it eats 3 mm off each side, that is \(2\times 3 = 6\) mm off the side length. Uncoloured core \(= \text{side} - 6\): for the 8 mm cube, \(8-6=2\) mm [1]; for the 10 mm cube, \(10-6=4\) mm [1]. Completed table: [2]
| Side of cube / mm | 4 | 6 | 8 | 10 | 12 |
|---|---|---|---|---|---|
| Depth dye penetrated / mm | 3 | 3 | 3 | 3 | 3 |
| Length of uncoloured core / mm | 0 | 0 | 2 | 4 | 6 |
(c) The side of each cube is measured with a (millimetre) ruler. [1]
(d) For the 12 mm cube the uncoloured core is a cube of side \(12-6=6\) mm. Compare volumes: \[\frac{6^3}{12^3}=\frac{216}{1728}=0.125=12.5\%\] core side [1]; volume ratio [1]; answer 12.5 % [1]. [3]
(e) The graph of uncoloured core length (y) against cube side (x) is plotted below, with labelled axes, a suitable scale, and the points joined. [3]
Axes correctly labelled with units [1]; suitable scale [1]; accurate points joined with a line [1]. [3]
(f) Read up from a side of 9 mm to the line: the uncoloured core is about 3 mm (accept 2.5 to 3.5). [1]
(g) The line meets the axis (core = 0) at about a side of 6 mm, so any cube larger than this keeps an uncoloured centre (accept 6 to 7). [1]
(h) Smaller cubes become completely coloured [1], while larger cubes keep an uncoloured centre, so a smaller fraction of a large cube is coloured [1]. [2]
(i) The dye can only diffuse a fixed distance (3 mm) in the time allowed [1]; a large cube has a low surface area to volume ratio and a greater distance from surface to centre [1]; so the dye does not reach the middle before the time is up, leaving an uncoloured core [1]. [3]
(j) Cubes are used because they have known, equal dimensions, so their surface area to volume ratio can be calculated and compared fairly, and they are easy to measure. [2]
(k) The dye enters the agar by diffusion. [1]
Exam tip: a fixed diffusion depth means small objects colour right through, but as size grows the centre stays clear, which is exactly why real cells stay small to keep a high surface area to volume ratio.
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