Final answer:
To calculate the atomic mass of the unknown metal (X), we apply ideal gas laws to the volume of hydrogen gas collected and use stoichiometric relationships from the balanced chemical equation. Moles of gas is determined with the formula PV = nRT, and atomic mass is obtained by dividing the mass of the sample by the moles of metal calculated.
Step-by-step explanation:
The determination of the atomic mass of an unknown metal (X) reacting with hydrochloric acid involves the application of ideal gas laws, molar ratios from the balanced chemical equation, and stoichiometry to calculate the moles of gas produced. According to the stoichiometry of the given reaction 2X(s) + 6 HCl(aq) → 2XCl₃(aq) + 3 H₂(g), one mole of the unknown metal produces 1.5 moles of hydrogen gas.
To calculate the moles of hydrogen gas, we first need to correct the measured volume for the vapor pressure of water at 20°C and convert the pressure to atmospheres. Using the ideal gas law PV = nRT, with R being the gas constant of 0.0821 L·atm/K·mol and T being the temperature in Kelvin, we can solve for n, the number of moles of hydrogen. After determining the moles of hydrogen, we can use the stoichiometric relationship from the equation to find the moles of the unknown metal.
Finally, by dividing the mass of the unknown metal sample by its moles, we will find the atomic mass of the metal. During this process, we ensure that all units are appropriately converted to match, such as milliliters to liters for volume and degrees Celsius to Kelvin for temperature.