Exploring the Ideal Gas Law Worksheet 14.4 can be a great way to understand and apply one of the fundamental principles in chemistry and physics: the ideal gas law. This law, summarized by the equation PV = nRT, relates the pressure (P), volume (V), and temperature (T) of an ideal gas with the number of moles (n) and the gas constant (R). Here, we will provide detailed answers to the exercises in this worksheet, delve into the theoretical background, and share practical examples to aid in mastering this crucial topic.
The Ideal Gas Law Equation
The equation for the ideal gas law is:
[ PV = nRT ]
- P stands for pressure, typically measured in atmospheres (atm), Pascal (Pa), or mmHg.
- V represents volume in liters (L) or cubic meters (m³).
- n is the amount of substance in moles.
- R is the universal gas constant, which is approximately 0.08206 L·atm·K-1·mol-1 for calculations involving liters and atmospheres, or 8.314 J·mol-1·K-1 when using SI units.
- T denotes temperature in Kelvin (K).
🧪 Note: The ideal gas law is an approximation that assumes no intermolecular forces between the gas particles.
Worksheet 14.4: Ideal Gas Law Problems
Problem 1: Calculating Volume
Calculate the volume of 2.50 moles of an ideal gas at a pressure of 1.00 atm and a temperature of 300 K. Use the ideal gas law.
- Given: n = 2.50 mol, P = 1.00 atm, T = 300 K, R = 0.08206 L·atm·K-1·mol-1
- Step 1: Rearrange the equation to solve for V:
- Step 2: Plug in the values:
- Step 3: Calculate:
\[ V = \frac{nRT}{P} \]
\[ V = \frac{2.50 \times 0.08206 \times 300}{1.00} \]
\[ V \approx 61.55 \text{ L} \]
⚠️ Note: Always ensure temperatures are in Kelvin when using the ideal gas law.
Problem 2: Finding Pressure
Find the pressure exerted by 4.00 grams of Helium in a 3.00 L container at 25°C.
- Given: m = 4.00 g, V = 3.00 L, T = 25°C + 273.15 = 298.15 K
- Step 1: Convert mass to moles using the molar mass of Helium (He):
- Step 2: Use the ideal gas law to solve for pressure:
- Step 3: Plug in the values:
- Step 4: Calculate:
\[ n = \frac{m}{MM} = \frac{4.00}{4.00} = 1.00 \text{ mol} \]
\[ P = \frac{nRT}{V} \]
\[ P = \frac{1.00 \times 0.08206 \times 298.15}{3.00} \]
\[ P \approx 8.28 \text{ atm} \]
Problem 3: Determining Moles
Determine the number of moles of gas contained in a 22.4 L container at standard temperature and pressure (STP).
- Given: V = 22.4 L, P = 1 atm, T = 273.15 K (STP conditions)
- Step 1: Rearrange the ideal gas law to solve for n:
- Step 2: Plug in the values:
- Step 3: Calculate:
\[ n = \frac{PV}{RT} \]
\[ n = \frac{1.00 \times 22.4}{0.08206 \times 273.15} \]
\[ n \approx 1.00 \text{ mol} \]
Problem 4: Temperature Conversion
Convert 50°C to Kelvin for use in the ideal gas law.
[ T = 50 + 273.15 = 323.15 \text{ K} ]
The above answers to Worksheet 14.4 provide practical examples of how the ideal gas law can be applied. Whether calculating volume, pressure, moles, or converting temperature, understanding this law allows for predictions of gas behavior under different conditions.
Common Mistakes in Ideal Gas Law Calculations
Here are some common errors to avoid:
- Not converting temperature to Kelvin.
- Misusing the gas constant R for different units.
- Forgetting to account for significant figures.
- Incorrectly converting mass to moles or vice versa.
In summary, the ideal gas law is a powerful tool in understanding gas behavior, allowing us to predict how gases will respond to changes in temperature, pressure, and volume. Remember to use the correct units, pay attention to significant figures, and always convert temperature to Kelvin for accuracy. The examples provided in the worksheet give a practical application of these principles, reinforcing the importance of mastering this fundamental law in the study of gases.
Why is it important to use the ideal gas law?
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The ideal gas law provides a simple and direct relationship between four variables, allowing chemists and engineers to predict and manipulate gas behavior in various applications, from industrial processes to everyday phenomena.
What are real gases and how do they differ from ideal gases?
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Real gases differ from ideal gases because they have molecular volume and exhibit intermolecular forces. Ideal gases are an approximation assuming no intermolecular forces and negligible molecular volume.
How do you handle problems where the gas is not at STP?
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When gases are not at STP, use the provided values for pressure and temperature, ensuring that the temperature is in Kelvin and the pressure is consistent with the volume units.
