Question

You must investigate the uncertainty that arises during the preparation of three standard solutions (0.1g/L, 0.05 g/L and 0.01 g/L) based on a stock solution. The stock solution is prepared by dissolving 1.0 +/- 0.01 g of substance in a 1000 +/- 0.4 ml volumetric flask. The standard solutions are prepared by adding x +/- 0.1 ml stock solution (x is the volume you need) to a 100 +/- 0.1 ml volumetric flask, then top up with water to the mark.

a) Calculate the relative uncertainty in concentration for the three standard solutions. Hint calculate ey/y.
b) Calculate the absolute uncertainty in concentration for the three standard solutions. Hint calculate ey.

Answer 1

a) The relative uncertainty in concentration for the three standard solutions can be calculated using the formula ey/y, where ey is the absolute uncertainty and y is the nominal value of the concentration.

For the 0.1 g/L solution:
- Nominal value of concentration (y) = 0.1 g/L
- Absolute uncertainty (ey) = (0.01 g / 1.0 g) * 1000 mL = 0.1 mL
- Relative uncertainty (ey/y) = (0.1 mL / 100 mL) * 100% = 0.1%

For the 0.05 g/L solution:
- Nominal value of concentration (y) = 0.05 g/L
- Absolute uncertainty (ey) = (0.01 g / 1.0 g) * x mL + (0.4 mL / 1000 mL) * 100 mL = 0.01x + 0.004 mL
- Relative uncertainty (ey/y) = (0.01x + 0.004 mL) / (0.05 g/L * 100 mL) * 100%

For the 0.01 g/L solution:
- Nominal value of concentration (y) = 0.01 g/L
- Absolute uncertainty (ey) = (0.01 g / 1.0 g) * x mL + (0.4 mL / 1000 mL) * 100 mL = 0.01x + 0.004 mL
- Relative uncertainty (ey/y) = (0.01x + 0.004 mL) / (0.01 g/L * 100 mL) * 100%

b) The absolute uncertainty in concentration for the three standard solutions can be calculated using the formula ey, where ey is the absolute uncertainty.

For the 0.1 g/L solution:
- Absolute uncertainty (ey) = (0.01 g / 1.0 g) * 1000 mL = 0.1 mL

For the 0.05 g/L solution:
- Absolute uncertainty (ey) = (0.01 g / 1.0 g) * x mL + (0.4 mL / 1000 mL) * 100 mL = 0.01x + 0.4 mL

For the 0.01 g/L solution:
- Absolute uncertainty (ey) = (0.01