Textbook Question
(a) Calculate the density of NO2 gas at 0.970 atm and 35 °C.
Ch.10 - Gases
Chapter 10, Problem 53
In the Dumas-bulb technique for determining the molarmass of an unknown liquid, you vaporize the sample of aliquid that boils below 100 °C in a boiling-water bath anddetermine the mass of vapor required to fill the bulb. Fromthe following data, calculate the molar mass of the unknownliquid: mass of unknown vapor, 1.012 g; volume of bulb,354 cm3; pressure, 98.93 kPa; temperature, 99 °C.
Verified step by step guidance1
Convert the temperature from Celsius to Kelvin by adding 273.15 to the given temperature in Celsius.
Convert the volume from cm³ to liters by dividing the volume in cm³ by 1000.
Use the ideal gas law equation, PV = nRT, to solve for the number of moles (n) of the vapor. Here, P is the pressure in kPa, V is the volume in liters, R is the ideal gas constant (8.314 L·kPa/mol·K), and T is the temperature in Kelvin.
Rearrange the ideal gas law equation to solve for n: n = PV / RT.
Calculate the molar mass of the unknown liquid by dividing the mass of the vapor by the number of moles calculated in the previous step.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Ideal Gas Law
The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. In this context, it allows us to calculate the number of moles of vapor produced from the known pressure, volume, and temperature, which is essential for determining the molar mass of the unknown liquid.
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Ideal Gas Law Formula
Molar Mass Calculation
Molar mass is defined as the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To find the molar mass of the unknown liquid, we use the formula: Molar Mass = mass of vapor (g) / moles of vapor (mol), where moles are derived from the Ideal Gas Law.
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Vaporization and Boiling Point
Vaporization is the process of converting a liquid into vapor, which occurs at the boiling point of the liquid. In the Dumas-bulb technique, the sample is vaporized in a boiling-water bath, ensuring that the temperature remains constant at the boiling point, which is crucial for accurate measurements of pressure and volume in the gas phase.
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Related Practice
Textbook Question
(b) Calculate the molar mass of a gas if 2.50 g occupies 0.875 L at 685 torr and 35 °C
Textbook Question
(b) Calculate the molar mass of a vapor thathas a density of 7.135 g>L at 12 °C and 99.06 kPa.
Textbook Question
The molar mass of a volatile substance was determined bythe Dumas-bulb method described in Exercise 10.53. Theunknown vapor had a mass of 2.55 g; the volume of thebulb was 500 mL, pressure 101.33 kPa, and temperature37 °C.Calculate the molar mass of the unknown vapor.
Textbook Question
Magnesium can be used as a 'getter' in evacuated enclosuresto react with the last traces of oxygen. (The magnesium isusually heated by passing an electric current through a wireor ribbon of the metal.) If an enclosure of 5.67 L has a partialpressure of O2 of 7.066 mPa at 30 °C, what mass of magnesiumwill react according to the following equation?2 Mg1s2 + O21g2¡2 MgO1s2
Textbook Question
Calcium hydride, CaH2, reacts with water to form hydrogengas:CaH21s2 + 2 H2O1l2¡Ca1OH221aq2 + 2 H21g2This reaction is sometimes used to inflate life rafts, weatherballoons, and the like, when a simple, compact means ofgenerating H2 is desired. How many grams of CaH2 areneeded to generate 145 L of H2 gas if the pressure of H2 is110 kPa at 21 °C?