Ch.5 - Gases

Tro - Chemistry: A Molecular Approach 4th Edition

Tro4th EditionChemistry: A Molecular ApproachISBN: 9780134112831Not the one you use?Change textbook

Tro 4th Edition

Ch.5 - Gases

Problem 59

Chapter 5, Problem 59

A sample of gas has a mass of 38.8 mg. Its volume is 224 mL at a temperature of 55 °C and a pressure of 886 torr. Find the molar mass of the gas.

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Convert the mass of the gas from milligrams to grams by dividing by 1000.

Convert the temperature from Celsius to Kelvin by adding 273.15.

Convert the pressure from torr to atmospheres by dividing by 760.

Use the Ideal Gas Law equation \( PV = nRT \) to solve for the number of moles \( n \). Here, \( P \) is the pressure in atm, \( V \) is the volume in liters, \( R \) is the ideal gas constant \( 0.0821 \text{ L atm mol}^{-1} \text{ K}^{-1} \), and \( T \) is the temperature in Kelvin.

Calculate the molar mass of the gas by dividing the mass of the gas in grams 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 is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law allows us to calculate the behavior of gases under various conditions, which is essential for solving problems involving gas samples.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all the atoms in a molecule. In the context of gas calculations, determining the molar mass is crucial for converting between mass and moles, which is necessary for applying the Ideal Gas Law and finding the identity of the gas.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another set of units. In gas calculations, it is often necessary to convert measurements such as pressure (from torr to atm), volume (from mL to L), and temperature (from Celsius to Kelvin) to ensure consistency with the units used in the Ideal Gas Law. Mastery of unit conversion is essential for accurate calculations in chemistry.

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Conversion Factors

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Textbook Question

A gas mixture with a total pressure of 745 mmHg contains each of the following gases at the indicated partial pressures: CO₂, 125 mmHg; Ar, 214 mmHg; and O₂, 187 mmHg. The mixture also contains helium gas. What is the partial pressure of the helium gas? What mass of helium gas is present in a 12.0-L sample of this mixture at 273 K?

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Textbook Question

A 248-mL gas sample has a mass of 0.433 g at a pressure of 745 mmHg and a temperature of 28 °C. What is the molar mass of the gas?

A sample of N₂O gas has a density of 2.85 g/L at 298 K. What is the pressure of the gas (in mmHg)?

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Textbook Question

What is the density (in g/L) of hydrogen gas at 20.0 °C and a pressure of 1655 psi?

A sample of gas has a mass of 0.555 g. Its volume is 117 mL at a temperature of 85 °C and a pressure of 753 mmHg. Find the molar mass of the gas.

A gas mixture contains each of the following gases at the indicated partial pressures: N₂, 215 torr; O₂, 102 torr; and He, 117 torr. What is the total pressure of the mixture? What mass of each gas is present in a 1.35-L sample of this mixture at 25.0 °C?

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