Textbook Question
(b) Calculate the molar mass of a gas if 2.50 g occupies 0.875 L at 685 torr and 35 °C
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Ch.10 - Gases
Chapter 10, Problem 54
The molar mass of a volatile substance was determined by the Dumas-bulb method described in Exercise 10.53. The unknown vapor had a mass of 2.55 g; the volume of the bulb was 500 mL, pressure 101.33 kPa, and temperature 37 °C.Calculate the molar mass of the unknown vapor.
Verified step by step guidance1
Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature.
Convert the volume from milliliters to liters by dividing by 1000.
Use the ideal gas law equation, PV = nRT, to solve for the number of moles (n) of the gas. 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 by dividing the mass of the vapor (2.55 g) by the number of moles (n) 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. This law is essential for calculating the molar mass of gases, as it allows us to determine the number of moles (n) from the known values of pressure (P), volume (V), and temperature (T), using the ideal gas constant (R).
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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 calculate the molar mass of a gas using the Ideal Gas Law, we can rearrange the equation to find n (moles) and then use the formula: Molar Mass = mass (g) / n (moles). This allows us to derive the molar mass from the mass of the gas and the conditions under which it was measured.
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Dumas Method
The Dumas method is a technique used to determine the molar mass of volatile substances by measuring the mass of vapor produced in a controlled environment. In this method, the vapor is collected in a bulb, and its properties (mass, volume, pressure, and temperature) are measured to apply the Ideal Gas Law, facilitating the calculation of the substance's molar mass.
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Related Practice
Textbook Question
(b) Calculate the molar mass of a vapor that
has a density of 7.135 g>L at 12 °C and 99.06 kPa.
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Textbook Question
In the Dumas-bulb technique for determining the molar
mass of an unknown liquid, you vaporize the sample of a
liquid that boils below 100 °C in a boiling-water bath and
determine the mass of vapor required to fill the bulb. From
the following data, calculate the molar mass of the unknown
liquid: mass of unknown vapor, 1.012 g; volume of bulb,
354 cm3; pressure, 98.93 kPa; temperature, 99 °C.
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Textbook Question
Magnesium can be used as a 'getter' in evacuated enclosures
to react with the last traces of oxygen. (The magnesium is
usually heated by passing an electric current through a wire
or ribbon of the metal.) If an enclosure of 5.67 L has a partial
pressure of O2 of 7.066 mPa at 30 °C, what mass of magnesium
will react according to the following equation?
2 Mg1s2 + O21g2¡2 MgO1s2
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Textbook Question
Calcium hydride, CaH2, reacts with water to form hydrogen
gas:
CaH21s2 + 2 H2O1l2¡Ca1OH221aq2 + 2 H21g2
This reaction is sometimes used to inflate life rafts, weather
balloons, and the like, when a simple, compact means of
generating H2 is desired. How many grams of CaH2 are
needed to generate 145 L of H2 gas if the pressure of H2 is
110 kPa at 21 °C?
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Open Question
The metabolic oxidation of glucose, C6H12O6, in our bodies produces CO2, which is expelled from our lungs as a gas: C6H12O6(aq) + 6 O2(g) → 6 CO2(g) + 6 H2O(l). (a) Calculate the volume of dry CO2 produced at normal body temperature, 37 °C, and 101.33 kPa when 10.0 g of glucose is consumed in this reaction. (b) Calculate the volume of oxygen you would need, at 100 kPa and 298 K, to completely oxidize 15.0 g of glucose.