A sample of an unknown gas from a cylinder is collected over water in the apparatus shown above. [VI — States of Matter Chemistry Question

STEPS:

1. Understand the target variable: To calculate the molar mass ($M$) of the unknown gas, we must use the relationship:
$$M = \frac{m}{n}$$
where $m$ is the mass of the collected gas sample and $n$ is the number of moles of that gas.
2. Determine how to find the mass ($m$): The unknown gas is released directly from a pressurized cylinder into the collection tube. The mass of the gas sample collected is determined by measuring the difference between the initial mass of the cylinder before the gas is released and the final mass of the cylinder after collection is complete (Option D).
3. Determine how to find the moles ($n$): To find the number of moles of the collected gas, we use the ideal gas law equation:
$$n = \frac{P_{\text{gas}}V}{RT}$$
* The volume ($V$) of the gas is read directly from the graduated markings on the gas-collection tube (Option C).
* The absolute temperature ($T$) of the gas is assumed to be equal to the temperature of the water bath once thermal equilibrium is reached, which is measured with a thermometer (Option B).
* $R$ is the standard molar gas constant.
4. Determine how to find the dry gas pressure ($P_{\text{gas}}$): Because the gas is collected over water, it is saturated with water vapor. By Dalton's Law of Partial Pressures, the total pressure inside the tube is:
$$P_{\text{total}} = P_{\text{gas}} + P_{\text{H}_2\text{O}}$$
Adjusting the tube so that the water levels inside and outside are equalized ensures that the total pressure inside the tube is exactly equal to the barometric atmospheric pressure outside ($P_{\text{total}} = P_{\text{atm}}$). Thus:
$$P_{\text{gas}} = P_{\text{atm}} - P_{\text{H}_2\text{O}}$$
To calculate $P_{\text{gas}}$, we must measure the atmospheric pressure using a laboratory barometer (Option A) and look up the equilibrium vapor pressure of water ($P_{\text{H}_2\text{O}}$) at the measured water temperature (Option B).
5. Identify the unnecessary measurement: The mass of the water in the apparatus (Option E) does not affect the mass of the gas released, the volume of gas collected, the temperature, or any of the pressure calculations. Therefore, this measurement is completely unnecessary to calculate the molar mass, making Option E the correct answer to this "EXCEPT" question.

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WHY_OTHERS_WRONG:

• A is incorrect: Measuring atmospheric pressure is absolutely necessary because when the water levels are equilibrated, the total pressure inside the tube is equal to the atmospheric pressure. Without this, the partial pressure of the dry gas cannot be isolated.
• B is incorrect: Measuring the temperature of the water is necessary for two reasons: it acts as the temperature of the gas ($T$) in the ideal gas equation, and it allows the student to look up the correct temperature-dependent vapor pressure of water ($P_{\text{H}_2\text{O}}$) to subtract from the total pressure.
• C is incorrect: Measuring the volume of gas in the gas-collection tube is necessary because $V$ is a direct variable in the ideal gas law equation ($PV = nRT$) used to calculate the number of moles of gas.
• D is incorrect: Measuring the initial and final mass of the gas cylinder is necessary because the difference between these two masses ($\Delta m$) directly gives the actual mass ($m$) of the gas sample that was collected.