You have a bottle labeled “53.4 (±0.4) % w/w NaOH” with a density of 1.52 (±0.01) g/mL. You use 16.7 (± 0.2) mL of the NaOH to prepare 2.00 (±0.02) L of 0.169M NaOH. Report the absolute error for the 0.169M of NaOH. You may assume negligible error in the NaOH molar mass.

Question

You have a bottle labeled “53.4 (±0.4) % w/w NaOH” with a density of 1.52 (±0.01) g/mL. You use 16.7 (± 0.2) mL of the NaOH to prepare 2.00 (±0.02) L of 0.169M NaOH. Report the absolute error for the 0.169M of NaOH. You may assume negligible error in the NaOH molar mass.

Answer 1

To calculate the absolute error for the 0.169M NaOH solution, we need to consider the errors associated with the volume and concentration of the NaOH used.

1. Volume Error:
Given that you used 16.7 ± 0.2 mL of NaOH, the absolute error is ± 0.2 mL.

2. Concentration Error:
To calculate the concentration of the NaOH solution, we need to determine the number of moles of NaOH present in the volume used (16.7 ± 0.2 mL).

First, calculate the mass of NaOH used:
Mass (g) = Volume (mL) × Density (g/mL)
Mass (g) = (16.7 ± 0.2 mL) × (1.52 ± 0.01 g/mL)

The uncertainty in the mass can be determined using the following formula:
Absolute Error (g) = (Volume × Density) × √((Relative Error in Volume)^2 + (Relative Error in Density)^2)

Absolute Error (g) = (16.7 mL × 1.52 g/mL) × √((0.2/16.7)^2 + (0.01/1.52)^2)

Next, calculate the moles of NaOH used:
Moles = Mass (g) ÷ Molar Mass (g/mol)
Molar Mass of NaOH = 22.99 (g/mol) + 16 (g/mol) + 1.008 (g/mol) = 39.008 (g/mol)

The uncertainty in moles can be determined using the following formula:
Absolute Error (mol) = (Mass (g) ÷ Molar Mass (g/mol)) × Relative Error in Mass

Absolute Error (mol) = [(Mass ± Absolute Error (g)) ÷ Molar Mass (g/mol)] - (Mass ÷ Molar Mass (g/mol))

Now, calculate the concentration of the NaOH:
Concentration (M) = Moles ÷ Volume (L)
Concentration (M) = (Moles ± Absolute Error (mol)) ÷ (2.00 ± 0.02 L)

Finally, calculate the absolute error for the concentration:
Absolute Error (M) = (Concentration (M) × Relative Error in Concentration) + (Absolute Error (mol) ÷ Volume (L))

Absolute Error (M) = [(Concentration ± Absolute Error (M)) × (0.169/100)] + (Absolute Error (mol) ÷ (2.00 L))

By following these steps, you can calculate the absolute error for the 0.169M NaOH solution given the provided uncertainties in volume and concentration.