Maths - Simple compound measures of rate
Example results
For a potato cylinder placed in distilled water with a sucrose concentrationThe concentration of a solution tells us how much of a substance is dissolved in water. The higher the concentration, the more particles of the substance are present. 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 | 2.52 | +0.30 |
| Concentration of sucrose % | 0 |
|---|---|
| Mass of potato cylinder at start (g) | 2.22 |
| Mass of potato cylinder at end (g) | 2.52 |
| Change in mass (g) | +0.30 |
The increase in massThe amount of matter an object contains. Mass is measured in kilograms (kg) or grams (g). is the result of water being taken up by osmosisThe movement of water molecules across a selectively permeable membrane from a region of higher water concentration to a region of lower water concentration..
Rate of water uptake
In this experiment, 0.30 grams of water were taken up by the potato cylinder.
This took place over 20 minutes, so the water uptake in an hour, assuming that the rate was constant, would be:
\(\text{water uptake in 1 hour} = \text{change in mass}\times\frac{60~\text{minutes}}{\text{length of experiment in minutes}}\)
\(\text{water uptake in 1 hour} = 0.30 \times \frac{60}{20} = 0.90~\text{grams}\)
The rate of water uptake is therefore 0.90 g h−1.
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.
So that we can compare changes in mass of different potato cylinders, it is necessary to calculate the percentage change in mass.
\(\text{change in mass}=\frac{\text{mass at end}-\text{mass at start}}{\text{mass at start}} \times 100\)
Some of the values we obtain for percentage change in mass will be positive, some will be negative.
For the potato cylinder in the distilled water:
\(\text{change in mass}=\frac{2.52-2.22}{2.22} \times 100\)
\(\frac{0.30}{2.22} \times 100 = 13.5\%\)
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 | 2.42 | 2.54 |
| Concentration of sucrose % | 0 |
|---|---|
| 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.
\(\text{change in mass}=\frac{\text{mass at end}-\text{mass at start}}{\text{mass at start}} \times 100\)
\(\text{change in mass}=\frac{2.54-2.42}{2.42} \times 100\)
\(\frac{0.12}{2.42} \times 100 = 5\%\)
