Scientific calculations - simple compound measures of rate
Example results
For the potato cylinder placed in distilled water - a sucrose concentration of 0 mol dm-3 - the following results were obtained.
| Concentration of sucrose | Mass of potato cylinder at start (g) | Mass of potato cylinder at end (g) | Change in mass (g) |
| 0 | 2.22 | 2.81 | + 0.59 |
| Concentration of sucrose | 0 |
|---|---|
| Mass of potato cylinder at start (g) | 2.22 |
| Mass of potato cylinder at end (g) | 2.81 |
| Change in mass (g) | + 0.59 |
The increase in mass is the result of water being taken up by osmosis.
The rate of water uptake
In this experiment, 0.59 grams of water were taken up by the potato cylinder.
This took place over 40 minutes, so the water uptake in an hour, assuming that the rate was constant, would be:
Water uptake in 1 hour =
\({change~in~mass}\times \frac{60~minutes}{period~of~time~measured~in~minutes}\)
Water uptake in 1 hour =
\(0.59 \times \frac{60}{40} = 0.89~g\)
The rate of water uptake is therefore 0.89 g/hour.
Percentage change in mass
There is some variation in mass between the potato cylinders at the beginning of the experiment as it would be impractical to prepare the cylinders so that they were identical in mass.
To compare changes in mass of different potato cylinders, calculate the percentage change in mass.
\(change\; in\; mass\: =\: \frac{mass\; at\; end\, -\, mass\; at\; start}{mass\; at\; start}\; \times 100\)
Some of the values obtained for percentage change in mass will be positive, some will be negative.
For the potato cylinder in the distilled water:
\(change\; in\; mass\: =\: \frac{mass\; at\; end\, -\, mass\; at\; start}{mass\; at\; start}\; \times 100\)
\(change\; in\; mass\: =\:\frac{2.81-2.22}{2.22}\, \times 100\; or\; \frac{0.59}{2.22}\, \times 100\,\)
\(change\; in\; mass\: =\frac{0.59}{2.22}\, \times 100\, =\, 26.6\%\)
The changes in mass, as percentages, must be calculated for each potato cylinder.
Question
For the potato cylinder placed in a sucrose concentration of 0.2 mol dm-3, the following results were obtained:
| Concentration of sucrose | Mass of potato cylinder at start (g) | Mass of potato cylinder at end (g) |
| 0.2 | 2.42 | 2.54 |
| Concentration of sucrose | 0.2 |
|---|---|
| Mass of potato cylinder at start (g) | 2.42 |
| Mass of potato cylinder at end (g) | 2.54 |
Calculate the change in mass as a percentage to the nearest whole number.
\(change \: in \: mass =\: \frac{mass\: at \: end \; - \: mass\: at\: start}{mass\: at \: start} \times 100\)
\( = \frac{2.54 - 2.42}{2.42} \times 100\)
\( = \frac{0.12}{2.42} \times 100 = {4.7}\%\)
\(change \: in \: mass\: \: =\: +5\%\)