# 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 (mol dm−3)Mass of potato cylinder at start (g)Mass of potato cylinder at end (g)Change in mass (g)
02.222.81+0.59

The increase in mass is the result of water being taken up by osmosis.

## 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:

$\text{water uptake in 1 hour} = \text{change in mass} \times \frac{\text{60 minutes}}{\text{period of time measured in minutes}}$

$\text{water uptake in 1 hour} = 0.59 \times \frac{60}{40} = 0.89~\text{g}$

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.

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:

$\text{change in mass} = \frac{\text{mass at end} - \text{mass at start}}{\text{mass at start}} \times 100$

$$\text{change in mass} = \frac{2.81 - 2.22}{2.22} \times 100$$ or $$\frac{0.59}{2.22} \times 100$$

$\text{change in mass} = \frac{0.59}{2.22} \times 100 = 26.6%$

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 (mol dm−3)Mass of potato cylinder at start (g)Mass of potato cylinder at end (g)
02.422.54

Calculate the change in mass as a percentage.

$\text{change in mass} = \frac{\text{mass at end} - \text{mass at start}}{\text{mass at start}} \times 100$

$\text{change in mass} = \frac{2.54 - 2.42}{2.42} \times 100 = \frac{0.12}{2.42} \times 100 = 5%$

The change in mass is therefore +5%