Ideal Gas Law Problem: Determining Pressure, Temperature, and Mass of Vapor
Given Data:
A student weighs an empty flask and stopper and finds the mass to be 55.844 g. She then adds about 5 mL of an unknown liquid and heats the flask in a boiling water bath at 99.7 degrees C. After all the liquid is vaporized, she removes the flask from the bath, stoppers it, and lets it cool. After it is cool, she momentarily removes the stopper, then replaces it and weighs the flask and condensed vapor, obtaining a mass of 56.101 g. The volume of the flask is known to be 248.1 mL. The barometric pressure in the laboratory is 752 mm Hg. a. What was the pressure of the vapor in the flask atm? P = ______ atm b. What was the temperature of the vapor in K? the volume of the flask in liters? T =______K, V=______ L c. What was the mass of vapor that was present in the flask? g = ___________grams d. How many moles of vapor are present? n =___________grams e. What is the mass of one mole of vapor? MM=___________g/mole
Answer:
(a) The pressure of the vapor in the flask in atm is 0.989 atm
(b) The temperature of the vapor in the flask in Kelvin is 372.7 K. The volume of the flask in liters is 0.2481 L
(c) The mass of vapor present in the flask was 0.257 g
(d) The number of moles of vapor present are 0.00802 mole
(e) The mass of one mole of vapor is 32.0 g/mole
Explanation: Given, the mass of the empty flask and stopper, volume of the liquid, temperature, and mass of the flask and condensed vapor, we can use the ideal gas law to calculate the pressure, temperature, volume, mass, and moles of the vapor present in the flask. To find the pressure, we use the barometric pressure in the laboratory, converting mm Hg to atm. The temperature in Kelvin and volume in liters are calculated based on the given data. The mass of the vapor is determined by subtracting the mass of the empty flask and stopper from the mass of the entire flask and condensed vapor.
Using the ideal gas law equation PV = nRT, we can calculate the number of moles of vapor present by rearranging the formula and plugging in the values for pressure, volume, and temperature. Finally, the mass of one mole of vapor is found by dividing the mass of the vapor present by the number of moles of vapor. This comprehensive problem-solving approach demonstrates the application of the ideal gas law in determining various properties of a vapor in a closed container.