Exercises: Determining Relative Molecular Mass from a Vapour

At room temperature and pressure, one mole of any gas occupies approximately $24\ \text{L}$. A sample of a gas has a volume of $0.060\ \text{L}$ at room temperature and pressure. Calculate the number of moles.

A volatile liquid is vaporised in a graduated gas syringe. State the measurements needed to calculate its relative molecular mass, and name the equation used.

Convert each temperature to kelvin:

1. a) $20\ ^\circ\text{C}$
2. b) $100\ ^\circ\text{C}$
3. c) $-10\ ^\circ\text{C}$

A student vaporises $0.152\ \text{g}$ of a volatile liquid. The vapour occupies $60.0\ \text{mL}$ at $373\ \text{K}$ and $1.01\times10^{5}\ \text{Pa}$. Using $R = 8.31\ \text{J K}^{-1}\text{mol}^{-1}$, calculate:

1. a) the number of moles of vapour
2. b) the relative molecular mass of the liquid

A sample of propanone vapour of mass $0.116\ \text{g}$ occupies $50.0\ \text{mL}$ at $373\ \text{K}$ and $1.00\times10^{5}\ \text{Pa}$.

1. a) Calculate the relative molecular mass.
2. b) Compare it with the value calculated from the formula $\mathrm{C_3H_6O}$ $(A_r$: C = 12.0, H = 1.0, O = 16.0$)$ and calculate the percentage error.

In an experiment a small mass of volatile liquid is injected into a gas syringe in a heated oven. State two precautions that should be taken to ensure the result is reliable, and explain why each one matters.

A student injects $0.250\ \text{g}$ of a volatile liquid into a gas syringe held at $353\ \text{K}$ and $1.013\times10^{5}\ \text{Pa}$. The final vapour volume is $97.7\ \text{mL}$.

1. a) Calculate the relative molecular mass.
2. b) The liquid is known to contain $64.9\%$ carbon, $13.5\%$ hydrogen and $21.6\%$ oxygen by mass. Determine its empirical formula and molecular formula.
3. c) Suggest whether the vapour behaves as an ideal gas under these conditions and justify your answer.

In an experiment to find the relative molecular mass of a liquid, a student failed to allow for the fact that a small portion of the liquid had not fully vaporised.

1. a) State, with reasoning, whether the calculated relative molecular mass would be too high or too low.
2. b) The student also read the syringe volume while the oven was cooling slightly. State the effect of this error on the result.
3. c) Suggest one improvement to the procedure.

A $0.480\ \text{g}$ sample of a volatile liquid fully vaporises to give $150\ \text{mL}$ of gas at $400\ \text{K}$ and $1.00\times10^{5}\ \text{Pa}$.

1. a) Calculate the relative molecular mass.
2. b) The compound is a hydrocarbon. Deduce its molecular formula, given that it has a molecular mass close to your answer and contains only C and H.
3. c) Explain why the result is only an approximation of the true value for a real gas.