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.

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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).

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.

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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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

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.

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.

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

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?