Q: Problem 1: Pressure Calculation

Given: ##n=1.0\ \text{mol}##, ##V=22.4\ \text{L}##, ##T=273\ \text{K}##. Find ##P##.

Q: Problem 2: Temperature Calculation

Given: ##n=0.5\ \text{mol}##, ##V=11.2\ \text{L}##, ##P=1\ \text{atm}##. Find ##T##.

Q: Problem 3: Mole Calculation

Given: ##P=2\ \text{atm}##, ##V=5\ \text{L}##, ##T=300\ \text{K}##. Find ##n##.

Q: Problem 4: Volume Calculation

Given: ##n=0.25\ \text{mol}##, ##P=2\ \text{atm}##, ##T=300\ \text{K}##. Find ##V##.

Question 1

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Understanding the Ideal Gas Law

The ideal gas law, represented by the equation ##PV = nRT##, is a cornerstone of thermodynamics. It elegantly links pressure, volume, number of moles, the gas constant, and temperature. This law is a powerful tool for understanding how gases behave under different conditions, enabling you to predict changes in volume, pressure, or temperature when other variables are altered. It provides a simplified model of gas behavior.

The Components of the Ideal Gas Law

Accepted Answer

The ideal gas law comprises several key components. 'P' represents pressure, measured in atmospheres (atm) or Pascals (Pa). 'V' stands for volume, typically measured in liters (L) or cubic meters (m³). 'n' is the number of moles of the gas, a measure of the amount of substance. 'R' is the ideal gas constant, with a value of 0.0821 L·atm/(mol·K) or 8.314 J/(mol·K), and 'T' is the temperature in Kelvin (K).

Question 2

Assumptions and Limitations

Accepted Answer

The ideal gas law is built on certain assumptions, such as that gas molecules have negligible volume and experience no intermolecular forces. While useful, these assumptions limit its accuracy, especially at high pressures or low temperatures, where real gases deviate from ideal behavior. Real gases exhibit more complex behavior. Understanding these limitations is crucial for using the ideal gas law effectively.

Question 3

Step-by-Step Solution

Accepted Answer

First, identify the known variables: n = 2 moles, T = 27°C = 300 K, P = 3 atm, and R = 0.0821 L·atm/(mol·K). The ideal gas law equation is ##PV = nRT##. To find the volume (V), rearrange the equation to ##V = \frac{{nRT}}{P}##. Ensure all units are consistent, and substitute the known values into the equation for accurate calculations.

Question 4

Calculation and Result

Accepted Answer

Substitute the values into the rearranged equation: ##V = \frac{{(2 	ext{ moles}) 	imes (0.0821 	ext{ L·atm/(mol·K)}) 	imes (300 	ext{ K})}}{3 	ext{ atm}}##. Solving this yields V ≈ 16.42 liters. Therefore, 2 moles of this ideal gas will occupy approximately 16.42 liters under the given conditions. This calculation shows the practical utility of the ideal gas law.

Question 5

Units and Conversions

Accepted Answer

It is essential to maintain consistent units when using the ideal gas law. Always ensure that pressure is in atmospheres (atm), volume in liters (L), temperature in Kelvin (K), and the gas constant (R) is used with the appropriate units. Conversion factors may be needed to convert between different units. Correct unit conversion is critical for obtaining accurate results.

Question 6

Problem 1: Pressure Calculation

Accepted Answer

Given: ##n=1.0\ ext{mol}##, ##V=22.4\ ext{L}##, ##T=273\ ext{K}##. Find ##P##.

Question 7

Problem 2: Temperature Calculation

Accepted Answer

Given: ##n=0.5\ ext{mol}##, ##V=11.2\ ext{L}##, ##P=1\ ext{atm}##. Find ##T##.

Question 8

Problem 3: Mole Calculation

Accepted Answer

Given: ##P=2\ ext{atm}##, ##V=5\ ext{L}##, ##T=300\ ext{K}##. Find ##n##.

Question 9

Problem 4: Volume Calculation

Accepted Answer

Given: ##n=0.25\ ext{mol}##, ##P=2\ ext{atm}##, ##T=300\ ext{K}##. Find ##V##.

Question 10

Problem 5: Combined Gas Law

Accepted Answer

If the volume of a gas is doubled while the temperature is held constant, what happens to the pressure?

Question 11

Problem 5: Combined Gas Law (Isothermal Change)

Accepted Answer

Given: Volume doubles at constant temperature (and moles). For an isothermal ideal gas, ###PV= ext{constant}###, so ###P\propto\dfrac{1}{V}###.

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