Concept explainers
(a)
Interpretation:
True or false status of the following statement is to be verified - The total kinetic energy of two molecules in the gas phase is the same before and after they collide with each other.
Concept introduction:
Principally, the size and nature of gas molecules is stated by particulate level explanation of gases. Commonly, the presence of intermolecular forces and the rapid movement of gas molecules are to be explained by kinetic theory of gases. During the fast movement the molecules collide with the walls of the container, besides colliding among them. Thus, the gas molecules are termed to be in some pressure values.
Answer to Problem 56E
The total kinetic energy of two molecules in the gas phase is the same before and after they collide with each other – the statement is ‘true’.
Explanation of Solution
The presence of intermolecular forces and the rapid movement of gas molecules can be explained by kinetic theory of gases. During the fast movement the molecules collide with the walls of the container. The development of particulate theory extends the concept of gas molecules with their size, volume, attractive forces, average kinetic energy of gas molecules, and the interaction among the gas molecules. Notably, the total kinetic energy of two molecules in the gas is identical before and after the collision.
Thus, true or false status of the following statement is verified.
(b)
Interpretation:
True or false status of the following statement is to be verified - Gas molecules are strongly attracted to each other.
Concept introduction:
Commonly, the presence of intermolecular forces and the rapid movement of gas molecules can be explained by kinetic theory of gases. During the fast movement the molecules collide with the walls of the container. Thus, the gas molecules are termed to be in some pressure values.
Answer to Problem 56E
Gas molecules are strongly attracted to each other– the statement is ‘false’.
Explanation of Solution
The molecules of gas are in rapid movement and during the fast movement the molecules collide with the walls of the container. Notably, the attractive forces among the gas molecules are greater than the kinetic energy of gas molecules. Besides, the molecule occupies the position far apart from each other and this result in absence of attractive forces among the gas molecules.
Thus, true or false status of the following statement is verified.
(c)
Interpretation:
True or false status of the following statement is to be verified - Gauge pressure is always greater than absolute pressure, except in a vacuum.
Concept introduction:
The force subjected to a material in perpendicular direction in unit area of the surface is termed as pressure. The measurement of pressure in closed areas can be accomplished by open end manometer. The pressure related to open area is measured by electronic gauges and its working is based on the variation of pressure sensing object with variation of environment pressure.
Answer to Problem 56E
Gauge pressure is always greater than absolute pressure, except in a vacuum.
– the statement is ‘false’.
Explanation of Solution
The molecules of gas are in rapid movement and during the fast movement the molecules collide with the walls of the container. The acting force on gas molecules in unit area gives the pressure of molecules. When the pressure is observed in vacuum it is described as ‘Absolute pressure’. Its value is the sum of gauge pressure and atmospheric pressure values. The measurement of pressure of molecules with reference of air is termed as ‘Gauge pressure’. Its value is the difference between absolute and atmospheric pressure.
Thus, true or false status of the following statement is verified.
(d)
Interpretation:
True or false status of the following statement is to be verified - For a fixed amount of gas at constant temperature, if volume increases pressure decreases.
Concept introduction:
The relationship of temperature, pressure and volume of ideal gas is described by ‘Boyle’s law’. According to this law, when the temperature and number of moles of gas molecules remains constant, the variation of pressure is having inverse relationship with volume of the gas molecules.
Answer to Problem 56E
For a fixed amount of gas at constant temperature, if volume increases pressure decreases.
– the statement is ‘true’.
Explanation of Solution
Boyle’s law states that when the temperature and number of moles of gas molecules remains constant, the variation of pressure is having inverse relationship with volume of the gas molecules.
PV = constant
If the pressure of the system increases, its volume will decrease and vice versa. For the same gas at two different state, the relationship between pressure and volume is given as P1V1 = P2 V2.
Thus, true or false status of the following statement is verified.
(e)
Interpretation:
True or false status of the following statement is to be verified - For a fixed amount of gas at constant pressure, if temperature increases volume decreases.
Concept introduction:
The relationship of temperature, pressure and volume of ideal gas is described by ‘Charles’s law’. According to this law, when the pressure and number of moles of gas molecules remains constant, the variation of temperature is having direct relationship with volume of the gas molecules.
Answer to Problem 56E
For a fixed amount of gas at constant pressure, if temperature increases volume decreases.– the statement is ‘false’.
Explanation of Solution
Charles’s law states that when the pressure and number of moles of gas molecules remains constant, the variation of temperature is having direct relationship with volume of the gas molecules.
V / T = constant
If the volume of the system increases, its temperature will decrease and vice versa. For the same gas at two different state, the relationship between temperature and volume is given as V1T2 = V2T1.
Thus, true or false status of the following statement is verified.
(f)
Interpretation:
True or false status of the following statement is to be verified - For a fixed amount of gas at constant volume, if temperature increases pressure increases.
Concept introduction:
The relationship of temperature, pressure and volume of ideal gas is described by ‘Gay-Lussac’s law’. According to this law, when the volume and number of moles of gas molecules remains constant, the variation of pressure is having direct relationship with temperature of the gas molecules.
Answer to Problem 56E
For a fixed amount of gas at constant volume, if temperature increases pressure increases
– the statement is ‘true’.
Explanation of Solution
Gay-Lussac’s law states that when the volume and number of moles of gas molecules remains constant, the variation of pressure is having direct relationship with temperature of the gas molecules.
P / T = constant
If the pressure of the system increases, its temperature will increase and vice versa. For the same gas at two different state, the relationship between pressure and temperature is given as
P1T2 = P2T1.
Thus, true or false status of the following statement is verified.
(g)
Interpretation:
True or false status of the following statement is to be verified - At a given temperature, the number of degrees Celsius is larger than the number of kelvins.
Concept introduction:
The physical measurement of heat of a system is termed as temperature of the system. The various scales to measure the temperature of the system include Celsius, Fahrenheit, and Kelvin. Among the scales ‘Kelvin’ is of wide usage. The temperature in Kelvin is the absolute temperature in which the enthalpy and entropy factors of gas molecules entirely ceased.
Answer to Problem 56E
At a given temperature, the number of degrees Celsius is larger than the number of kelvins
– the statement is ‘false’.
Explanation of Solution
The relationship between Celsius and Kelvin temperature scales is given as 0 °C + 273 = 273 K. The boiling point of water in Celsius scale 100 °C. This value in Kelvin scale is 100 °C + 273 = 373 K. Thus, Celsius temperature scale is smaller than Kelvin scale.
Thus, true or false status of the following statement is verified.
(h)
Interpretation:
True or false status of the following statement is to be verified - Both temperature and pressure ratios are larger than 1 when calculating the final gas volume as conditions change from STP to 15 °C and 0.834 atm.
Concept introduction:
Generally, the measurement of heat of a system is termed as temperature of the system. The various scales to measure the temperature of the system include Celsius, Fahrenheit, and Kelvin. The temperature in Kelvin is the absolute temperature in which the movements of gas molecules are stopped completely. Similarly, the force acting on a unit of gas molecules is termed as ‘Pressure’. The various pressure scales are bar, atm, torr etc.
Answer to Problem 56E
Both temperature and pressure ratios are larger than 1 when calculating the final gas volume as conditions change from STP to 15 °C and 0.834 atm – the statement is ‘true’.
Explanation of Solution
When measuring temperature and pressure of a system at two different states, the common reference state is determined. Notably, the temperature and pressure value of gas molecules is described as 0 °C and 1 atm and this is called standard temperature and pressure (STP). If the state of a system is changed to another state such as 15 °C and 0.834 atm, the value of the temperature and pressure ratio will get greater value than one.
Thus, true or false status of the following statement is verified.
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Chapter 4 Solutions
Introductory Chemistry: An Active Learning Approach
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