Chapter 3: Problem 53
Four one litre flasks are separately filled with the gases \(\mathrm{O}_{2}, \mathrm{~F}_{2}, \mathrm{CH}_{4}\) and \(\mathrm{CO}_{2}\) under same conditions. The ratio of the number of molecules in these gases are (a) \(2: 2: 4: 3\) (b) \(1: 1: 1: 1\) (c) \(1: 2 ; 3 ; 4\) (d) \(2: 2 ; 3: 4\)
Short Answer
Expert verified
The ratio of the number of molecules is \(1: 1: 1: 1\).
Step by step solution
01
Understand Equal Gas Conditions
The gases are filled in identical 1-litre flasks under the same temperature and pressure conditions. According to Avogadro's Law, equal volumes of gases at the same temperature and pressure contain an equal number of molecules.
02
Apply Avogadro's Law
Because the conditions are identical (same temperature and pressure), Avogadro's Law tells us that each flask will contain the same number of molecules regardless of the type of gas.
03
Ratio of Molecules
As a result of Avogadro's Law, the ratio of the number of gas molecules in the flasks for the gases \(\mathrm{O}_{2}, \mathrm{F}_{2}, \mathrm{CH}_{4}\), and \(\mathrm{CO}_{2}\) is equal. This makes the ratio \(1: 1: 1: 1\).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Ideal Gas Law
The Ideal Gas Law is a fundamental equation in chemistry and physics that describes how gases behave under different conditions. The law is expressed as \( PV = nRT \), where \( P \) is the pressure of the gas, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin. This formula helps scientists understand how gas molecules interact in a container and how changes in conditions like temperature or pressure can affect them.
The Ideal Gas Law combines several earlier gas laws, including Boyle's Law (relationship between pressure and volume), Charles's Law (relationship between volume and temperature), and Avogadro's Law (relationship between volume and moles), into a single equation. It's important to remember that this law assumes ideal behavior, meaning that it doesn't take into account interactions between molecules or the volume of the molecules themselves. Despite this simplification, it provides a useful approximation for real gases under many conditions.
The Ideal Gas Law combines several earlier gas laws, including Boyle's Law (relationship between pressure and volume), Charles's Law (relationship between volume and temperature), and Avogadro's Law (relationship between volume and moles), into a single equation. It's important to remember that this law assumes ideal behavior, meaning that it doesn't take into account interactions between molecules or the volume of the molecules themselves. Despite this simplification, it provides a useful approximation for real gases under many conditions.
Gas Molecules
Gas molecules, unlike those in liquids and solids, are free to move quickly and collide with each other and the walls of their container. This random movement is what causes gases to expand and fill the available space. Gas molecules are typically far apart compared to molecules in solid or liquid states, which means they have lower density.
The behavior of gas molecules was crucial in developing the kinetic molecular theory of gases, which provides insight into the motion of molecules and how they result in gas properties like pressure and temperature. According to this theory, temperature is proportional to the average kinetic energy of gas molecules, and pressure is the result of collisions between gas molecules and the walls of the container.
Understanding gas molecules is key to applying gas laws, including Avogadro's Law, by emphasizing how they distribute themselves in a given volume and how changes in physical conditions can influence their distribution and number.
The behavior of gas molecules was crucial in developing the kinetic molecular theory of gases, which provides insight into the motion of molecules and how they result in gas properties like pressure and temperature. According to this theory, temperature is proportional to the average kinetic energy of gas molecules, and pressure is the result of collisions between gas molecules and the walls of the container.
Understanding gas molecules is key to applying gas laws, including Avogadro's Law, by emphasizing how they distribute themselves in a given volume and how changes in physical conditions can influence their distribution and number.
Equal Volumes of Gases
Avogadro's Law is the principle that states equal volumes of gases at the same temperature and pressure will contain the same number of molecules. This insight is fundamental in understanding how different gases will behave under identical conditions.
The importance of Avogadro's Law is highlighted in calculations involving gases, especially in scenarios where we compare the amount of substance in different containers. Regardless of their chemical identity, gases like \( \text{O}_2 \), \( \text{F}_2 \), \( \text{CH}_4 \), and \( \text{CO}_2 \) will all have the same number of molecules if kept at the same pressure and temperature in equal volumes.
This concept helps simplify many chemical calculations and is a basis for more complex equations such as the Ideal Gas Law, which builds on the same premise of equivalence across conditions.
The importance of Avogadro's Law is highlighted in calculations involving gases, especially in scenarios where we compare the amount of substance in different containers. Regardless of their chemical identity, gases like \( \text{O}_2 \), \( \text{F}_2 \), \( \text{CH}_4 \), and \( \text{CO}_2 \) will all have the same number of molecules if kept at the same pressure and temperature in equal volumes.
This concept helps simplify many chemical calculations and is a basis for more complex equations such as the Ideal Gas Law, which builds on the same premise of equivalence across conditions.
Temperature and Pressure Conditions
Temperature and pressure are critical factors that determine how a gas behaves. The standard conditions for temperature and pressure (often abbreviated as STP) are 0 degrees Celsius and 1 atm pressure. Under these conditions, one mole of an ideal gas occupies 22.414 liters.
Temperature affects the kinetic energy of gas molecules. As temperature increases, the molecules move faster, leading to higher pressure if the volume is constant, or increased volume if the pressure is constant. Pressure, on the other hand, relates to how frequently gas molecules collide with each other and with the walls of their container. At higher pressures, molecules are more closely packed, which can potentially lead to deviations from ideal behavior.
When analyzing gas behavior using these conditions, it is critical to assume that all conditions are identical when comparing different gases, as this ensures that properties like volume, temperature, and pressure have a predictable influence on the number of molecules."}]}]}]}{}``` The
Temperature affects the kinetic energy of gas molecules. As temperature increases, the molecules move faster, leading to higher pressure if the volume is constant, or increased volume if the pressure is constant. Pressure, on the other hand, relates to how frequently gas molecules collide with each other and with the walls of their container. At higher pressures, molecules are more closely packed, which can potentially lead to deviations from ideal behavior.
When analyzing gas behavior using these conditions, it is critical to assume that all conditions are identical when comparing different gases, as this ensures that properties like volume, temperature, and pressure have a predictable influence on the number of molecules."}]}]}]}{}``` The
Temperature and Pressure Conditions
Temperature and pressure are critical factors that determine how a gas behaves. The standard conditions for temperature and pressure (often abbreviated as STP) are 0 degrees Celsius and 1 atm pressure. Under these conditions, one mole of an ideal gas occupies 22.414 liters.
Temperature affects the kinetic energy of gas molecules. As temperature increases, the molecules move faster, leading to higher pressure if the volume is constant, or increased volume if the pressure is constant. Pressure, on the other hand, relates to how frequently gas molecules collide with each other and with the walls of their container. At higher pressures, molecules are more closely packed, which can potentially lead to deviations from ideal behavior.
When analyzing gas behavior using these conditions, it is critical to assume that all conditions are identical when comparing different gases, as this ensures that properties like volume, temperature, and pressure have a predictable influence on the number of molecules."}
Temperature and Pressure Conditions
Temperature and pressure are critical factors that determine how gas behaves. The standard conditions for temperature and pressure (often abbreviated as STP) are 0 degrees Celsius and 1 atm pressure. Under these conditions, one mole of an ideal gas occupies 22.414 liters.
Temperature affects the kinetic energy of gas molecules. As temperature increases, the molecules move faster, leading to higher pressure if the volume is constant, or increased volume if the pressure is constant. Pressure, on the other hand, relates to how frequently gas molecules collide with each other and with the walls of their container. At higher pressures, molecules are more closely packed, which can potentially lead to deviations from ideal behavior.
When analyzing gas behavior using these conditions, it is critical to assume all conditions are identical when comparing different gases as this ensures that properties like volume, temperature, and pressure have a predictable influence on the number of molecules.
