Ch.5 - Gases

Tro - Chemistry: A Molecular Approach 4th Edition

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Tro 4th Edition

Ch.5 - Gases

Problem 37a

Chapter 5, Problem 37a

What volume is occupied by 0.118 mol of helium gas at a pressure of 0.97 atm and a temperature of 305 K?

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Identify the ideal gas law equation: \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is temperature.

Rearrange the ideal gas law equation to solve for volume \( V \): \( V = \frac{nRT}{P} \).

Substitute the given values into the equation: \( n = 0.118 \text{ mol} \), \( P = 0.97 \text{ atm} \), \( T = 305 \text{ K} \), and \( R = 0.0821 \text{ L atm/mol K} \).

Calculate the volume \( V \) by plugging the values into the rearranged equation: \( V = \frac{0.118 \times 0.0821 \times 305}{0.97} \).

Simplify the expression to find the volume \( V \) in liters.

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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 volume occupied by a gas under specific conditions.

Units of Measurement

Understanding the units of measurement is crucial in gas calculations. Pressure is often measured in atmospheres (atm), volume in liters (L), and temperature in Kelvin (K). In the Ideal Gas Law, consistency in units is essential; for example, the ideal gas constant R can be expressed in different units depending on the pressure and volume units used, which affects the final calculations.

Gas Behavior at Different Conditions

Gases behave differently under varying conditions of pressure and temperature. According to the kinetic molecular theory, gas particles are in constant motion and their behavior can be predicted based on these conditions. For instance, increasing temperature typically increases the volume of a gas if pressure is held constant, illustrating the relationship between these variables in the context of the Ideal Gas Law.

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