Ch.5 - Gases

Tro - Chemistry: A Molecular Approach 4th Edition

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Tro 4th Edition

Ch.5 - Gases

Problem 58

Chapter 5, Problem 58

A 113-mL gas sample has a mass of 0.171 g at a pressure of 721 mmHg and a temperature of 32 °C. What is the molar mass of the gas?

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Convert the temperature from degrees Celsius to Kelvin using the formula: \( T(K) = T(°C) + 273.15 \).

Convert the pressure from mmHg to atm using the conversion factor: \( 1 \text{ atm} = 760 \text{ mmHg} \).

Convert the volume from mL to L by dividing by 1000, since \( 1 \text{ L} = 1000 \text{ mL} \).

Use the ideal gas law equation \( PV = nRT \) to solve for the number of moles \( n \), where \( P \) is the pressure in atm, \( V \) is the volume in L, \( R \) 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 using the formula: \( \text{Molar Mass} = \frac{\text{mass of gas (g)}}{\text{number of moles (mol)}} \).

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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. Here, 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 is fundamental for calculating properties of gases under various conditions.

Molar Mass

Molar mass is defined as the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It can be calculated by dividing the mass of the gas sample by the number of moles present. Understanding molar mass is crucial for converting between mass and moles in chemical calculations.

Gas Properties and Units

Gas properties such as pressure (measured in mmHg or atm), volume (in liters or mL), and temperature (in Celsius or Kelvin) are essential for gas calculations. It is important to convert these units appropriately to ensure consistency in calculations, especially when applying the Ideal Gas Law.

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