worksheet combined gas law answers

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03-02-2025

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This worksheet provides answers and detailed explanations for common Combined Gas Law problems. The Combined Gas Law, expressed as $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$, relates the pressure, volume, and temperature of a gas under two different sets of conditions, assuming the amount of gas remains constant. Remember that temperature must always be in Kelvin (K). To convert Celsius to Kelvin, add 273.15.

Let's tackle some example problems:

Example Problems & Solutions

Problem 1: A gas occupies 4.3 L at 25°C and 740 mmHg. What volume will it occupy at STP (Standard Temperature and Pressure: 0°C and 760 mmHg)?

Solution:

1. Convert to Kelvin: T₁ = 25°C + 273.15 = 298.15 K; T₂ = 0°C + 273.15 = 273.15 K

2. List knowns:

   • P₁ = 740 mmHg
   • V₁ = 4.3 L
   • T₁ = 298.15 K
   • P₂ = 760 mmHg
   • T₂ = 273.15 K
   • V₂ = ? (This is what we need to find)

3. Apply the Combined Gas Law: $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

4. Solve for V₂: Rearrange the equation to solve for V₂: $V_2 = \frac{P_1V_1T_2}{T_1P_2}$

5. Plug in values and calculate: $V_2 = \frac{(740 mmHg)(4.3 L)(273.15 K)}{(298.15 K)(760 mmHg)}$

6. Answer: V₂ ≈ 3.7 L. The gas will occupy approximately 3.7 liters at STP.

Problem 2: A sample of gas at 1.00 atm and 20.0°C occupies a volume of 10.0L. If the gas is compressed to a volume of 2.50 L at a pressure of 4.00 atm, what will its new temperature be in °C?

Solution:

1. Convert to Kelvin: T₁ = 20.0°C + 273.15 = 293.15 K

2. List knowns:

   • P₁ = 1.00 atm
   • V₁ = 10.0 L
   • T₁ = 293.15 K
   • P₂ = 4.00 atm
   • V₂ = 2.50 L
   • T₂ = ? (This is what we need to find)

3. Apply the Combined Gas Law: $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

4. Solve for T₂: Rearrange the equation to solve for T₂: $T_2 = \frac{P_2V_2T_1}{P_1V_1}$

5. Plug in values and calculate: $T_2 = \frac{(4.00 atm)(2.50 L)(293.15 K)}{(1.00 atm)(10.0 L)}$

6. Answer: T₂ ≈ 293.15 K. Convert back to Celsius: 293.15 K - 273.15 = 20.0°C. The new temperature will be 20.0°C. Notice that the temperature remains constant in this scenario, which is not always the case with the combined gas law.

Problem 3 (More Challenging): A balloon filled with helium gas has a volume of 12.0 L at 27°C and 1.00 atm. The balloon rises to an altitude where the pressure is 0.65 atm and the temperature is -23°C. What is the new volume of the balloon?

Solution: Follow the same steps as above, remembering to convert temperatures to Kelvin. The answer will reveal a larger volume due to the decrease in pressure and slight decrease in temperature.

Tips for Solving Combined Gas Law Problems

• Always convert Celsius to Kelvin: This is crucial for accurate calculations.
• Identify your knowns and unknowns: Clearly list what you are given and what you need to find.
• Rearrange the equation: Solve for the unknown variable before plugging in values.
• Use consistent units: Make sure all your units are consistent (e.g., all pressures in atm, all volumes in liters).
• Check your answer: Does your answer make sense in the context of the problem?

By understanding these examples and following these tips, you'll be well-equipped to tackle any combined gas law problem. Remember that practice is key to mastering this important concept in chemistry.