Help! The concentration of a solution of hydrochloric acid is 1•00 ± 0•05 mol dm−3 and the volume is 10•0 ± 0•1 cm3. Calculate the number of moles and state the absolute uncertainty.
To calculate the number of moles in this solution, you need to multiply the concentration by the volume.
Given:
Concentration = 1.00 ± 0.05 mol dm^-3
Volume = 10.0 ± 0.1 cm^3
Step 1: Calculate the number of moles
Number of moles = concentration x volume
Using the given values, we have:
Number of moles = (1.00 mol dm^-3) x (10.0 cm^3)
To ensure consistent units, we need to convert the volume from cm^3 to dm^3. There are 1000 cm^3 in 1 dm^3, so we divide the volume by 1000:
Number of moles = (1.00 mol dm^-3) x (10.0 cm^3 ÷ 1000 cm^3/dm^3)
Number of moles = 0.0100 mol
Thus, the number of moles in the solution is 0.0100 mol.
Step 2: Calculate the absolute uncertainty
To determine the absolute uncertainty, we need to consider the absolute uncertainties for both the concentration and the volume.
For concentration: ±0.05 mol dm^-3
For volume: ±0.1 cm^3
The absolute uncertainty for number of moles can be calculated by adding the absolute uncertainties of concentration and volume in quadrature (square root of the sum of squares):
Absolute uncertainty = √(concentration uncertainty^2 + volume uncertainty^2)
Absolute uncertainty = √((0.05 mol dm^-3)^2 + (0.1 cm^3)^2)
Absolute uncertainty = √(0.0025 mol^2 dm^-6 + 0.01 cm^2)
Absolute uncertainty = √(0.0025 mol^2 dm^-6 + 0.01 mol cm^3 dm^-6)
Absolute uncertainty = √(0.0025 + 0.01) mol dm^-3
Absolute uncertainty = √(0.0125) mol dm^-3
Absolute uncertainty = 0.111 mol dm^-3
Therefore, the number of moles in the solution is 0.0100 ± 0.111 mol, stating the absolute uncertainty.