The molar mass of an unknown organic liquid (M~100) is determined by placing 5 mL of the liquid in a weighed 125-mL conical flask fitted with a piece of Al foil with a pin hole in it. The flask is heated in a boiling water bath until the liquid evaporates to expel the air and fill the flask with the unknown vapor at atmospheric pressure. After cooling to room temperature the flask and its contents are reweighed. The uncertainty in which piece of apparatus causes the largest percentage error in the molar mass?
A) balance (±0.01 g)
B) Barometer (±0.2 mm Hg)
C) Flask (±1.0 mL)
D) thermometer (±0.2°C)
Answer is A. No clue how to figure it out. Please explain(:
To determine the uncertainty caused by each piece of apparatus, we need to consider how each measurement affects the calculation of the molar mass. The molar mass can be determined by using the ideal gas equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
Let's analyze the impact of the uncertainty in each piece of apparatus on the calculation:
A) Balance (±0.01 g):
The mass of the flask and its contents before and after the evaporation process is measured using a balance. The uncertainty of ±0.01 g in the balance reading will directly affect the determination of the mass of the liquid. Since the molar mass is calculated by dividing the mass of the liquid by its volume, any error in mass will lead to an error in the molar mass. Therefore, the balance measurement causes the largest percentage error.
B) Barometer (±0.2 mm Hg):
The pressure of the unknown vapor is assumed to be equal to the atmospheric pressure. However, variations in atmospheric pressure due to weather conditions or altitude can affect the barometer reading. While this could introduce a small error, it will have a negligible impact on the calculation of the molar mass compared to the balance measurement.
C) Flask (±1.0 mL):
The volume of the flask is used to calculate the volume of the unknown vapor. An uncertainty of ±1.0 mL in the flask reading will affect the determination of the unknown vapor's volume. The molar mass calculation involves dividing the mass by volume, so any error in the volume will lead to an error in the molar mass. However, the flask uncertainty is relatively larger than the balance uncertainty, making the balance the larger contributor to the percentage error.
D) Thermometer (±0.2°C):
The temperature of the flask and its contents is monitored to ensure that the liquid completely evaporates. However, the temperature plays a minor role in the determination of molar mass as it is cancelled out in the ideal gas equation. Therefore, the uncertainty in the thermometer reading has a negligible impact on the molar mass calculation.
Based on these considerations, the balance (option A) causes the largest percentage error in the molar mass determination compared to the other apparatus.