Introducing the Mixed Gas Laws Worksheet Answer Key, a comprehensive guide that unlocks the secrets of gas mixtures, empowering you to navigate the complexities of this fascinating scientific realm.
Delve into the intricacies of partial pressure, explore the relationship between volume, pressure, and temperature, and discover the practical applications of mixed gas laws in diverse fields such as scuba diving, medicine, and industry.
Understanding the Mixed Gas Laws
Mixed gas laws describe the behavior of gas mixtures, which are combinations of two or more gases. Understanding these laws is crucial in various fields, including chemistry, physics, and engineering.
Partial Pressure
Partial pressure is the pressure exerted by each individual gas in a mixture. It is directly proportional to the mole fraction of that gas. The total pressure of the mixture is the sum of the partial pressures of all gases present.
- The partial pressure of gas A in a mixture is given by P A= X A– P total, where X Ais the mole fraction of gas A and P totalis the total pressure of the mixture.
- Partial pressure helps predict the behavior of gases in mixtures, such as solubility and reactivity.
Volume, Pressure, and Temperature Relationship
The relationship between volume, pressure, and temperature in gas mixtures is described by the combined gas law:
P1V 1/T 1= P 2V 2/T 2
- This law states that the product of pressure and volume is directly proportional to the absolute temperature.
- It can be used to predict the changes in volume, pressure, or temperature of a gas mixture when one of these variables changes.
Applications of Mixed Gas Laws: Mixed Gas Laws Worksheet Answer Key
Mixed gas laws find diverse applications in various fields, including scuba diving, medical settings, and industrial processes.
Scuba Diving, Mixed gas laws worksheet answer key
In scuba diving, mixed gas laws are crucial for determining the composition of breathing gases used at different depths. As divers descend, the pressure increases, affecting the partial pressures of gases in the breathing mixture. Mixed gas laws help calculate the optimal proportions of oxygen, nitrogen, and helium in the breathing gas to prevent decompression sickness and other diving-related hazards.
Medical Settings
In medical settings, mixed gas laws are used in oxygen therapy, where controlled mixtures of oxygen and other gases are administered to patients with respiratory conditions. By adjusting the partial pressure of oxygen in the breathing mixture, medical professionals can optimize oxygen delivery to the body’s tissues.
Industrial Processes
In industrial processes, mixed gas laws are applied in various applications, such as welding, metalworking, and chemical manufacturing. By controlling the composition of gas mixtures used in these processes, industries can optimize efficiency, safety, and product quality.
Solving Mixed Gas Laws Problems
Solving mixed gas laws problems involves applying the ideal gas law and the relationships between pressure, volume, temperature, and the number of moles of a gas. The following steps provide a structured approach to solving these problems:
Step-by-Step Procedure
- Identify the given and unknown variables in the problem.
- Choose the appropriate gas law equation based on the given variables.
- Substitute the given values into the equation and solve for the unknown variable.
- Check the units of the answer to ensure they are correct.
Ideal Gas Law Equation
The ideal gas law equation, also known as the combined gas law, is a fundamental equation that relates the pressure (P), volume (V), temperature (T), and number of moles (n) of a gas:
PV = nRT
Where:
- P is the pressure in Pascals (Pa)
- V is the volume in cubic meters (m³)
- n is the number of moles in moles (mol)
- R is the ideal gas constant, which is 8.314 J/(mol·K)
- T is the temperature in Kelvin (K)
Formulas and Units
The following table summarizes the formulas and units used in mixed gas laws calculations:
| Formula | Units |
|---|---|
| Pressure (P) | Pascals (Pa) |
| Volume (V) | Cubic meters (m³) |
| Temperature (T) | Kelvin (K) |
| Number of moles (n) | Moles (mol) |
| Ideal gas constant (R) | 8.314 J/(mol·K) |
Worksheet Answer Key
This section provides comprehensive solutions to the problems presented in the Mixed Gas Laws worksheet. Each problem is categorized and addressed with detailed explanations.
Dalton’s Law of Partial Pressures
Dalton’s Law states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of each individual gas.
- Problem 1:A mixture of oxygen and nitrogen gases has a total pressure of 760 mmHg. The partial pressure of oxygen is 152 mmHg. What is the partial pressure of nitrogen?
- Solution:According to Dalton’s Law, the partial pressure of nitrogen is equal to the total pressure minus the partial pressure of oxygen. Therefore, the partial pressure of nitrogen is 760 mmHg – 152 mmHg = 608 mmHg.
Gay-Lussac’s Law
Gay-Lussac’s Law describes the relationship between the pressure and temperature of a gas at constant volume. It states that the pressure of a gas is directly proportional to its absolute temperature.
- Problem 2:A gas sample has a pressure of 2 atm at a temperature of 273 K. What will be its pressure at a temperature of 373 K, assuming the volume remains constant?
- Solution:Using Gay-Lussac’s Law, we can write: P1/T1 = P2/T 2. Substituting the given values, we get: 2 atm / 273 K = P2 / 373 K. Solving for P2, we find that the pressure at 373 K is 2.71 atm.
Charles’s Law
Charles’s Law describes the relationship between the volume and temperature of a gas at constant pressure. It states that the volume of a gas is directly proportional to its absolute temperature.
- Problem 3:A balloon filled with helium gas has a volume of 10 liters at a temperature of 20°C. What will be its volume at a temperature of 40°C, assuming the pressure remains constant?
- Solution:Using Charles’s Law, we can write: V1/T1 = V2/T 2. Substituting the given values, we get: 10 liters / 293 K = V2 / 313 K. Solving for V2, we find that the volume at 40°C is 10.68 liters.
Combined Gas Law
The Combined Gas Law combines Boyle’s Law, Charles’s Law, and Gay-Lussac’s Law to relate the pressure, volume, and temperature of a gas sample under different conditions.
- Problem 4:A sample of hydrogen gas has a pressure of 1.5 atm, a volume of 2 liters, and a temperature of 25°C. What will be its pressure if the volume is decreased to 1 liter and the temperature is increased to 50°C?
- Solution:Using the Combined Gas Law, we can write: (P1 – V1) / T1 = (P2 – V2) / T 2. Substituting the given values, we get: (1.5 atm – 2 liters) / 298 K = (P2 – 1 liter) / 323 K.
Solving for P2, we find that the pressure is 2.25 atm.
FAQ Resource
What is partial pressure?
Partial pressure refers to the pressure exerted by a specific gas within a mixture of gases, as if it were the only gas present.
How are mixed gas laws applied in scuba diving?
Mixed gas laws are crucial in determining the optimal gas mixtures for scuba divers, ensuring their safety and comfort at various depths.
What are the common applications of mixed gas laws in industry?
Mixed gas laws find applications in industrial processes such as welding, food processing, and chemical manufacturing.
