Concept explainers
(a)
Interpretation:
Whether the statement “the molar volume of a gas at
Concept introduction:
The ideal gas equation is used to represent the relation between the volume, pressure, temperature and number of moles of an ideal gas. The ideal gas equation is represented as given below.
Answer to Problem 48E
The statement “the molar volume of a gas at
Explanation of Solution
It is given that pressure and temperature for the gas is
The conversion factor of temperature unit
Substitute the value of temperature in the above equation as shown below.
Ideal gas equation is given by the formula as shown below.
Where,
•
•
•
•
•
Rearrange the above equation in terms of molar volume as shown below.
Substitute the values of pressure and temperature of gas in the equation (2) to calculate molar volume as shown below.
The molar volume of a gas at
Therefore, the statement “the molar volume of a gas at
The statement “the molar volume of a gas at
(b)
Interpretation:
Whether the statement “the mass of
Concept introduction:
The ideal gas equation is used to represent the relation between the volume, pressure, temperature and number of moles of an ideal gas. The ideal gas equation is represented as given below.
Answer to Problem 48E
The statement “the mass of
Explanation of Solution
Ideal gas equation is given by the formula as shown below.
Where,
•
•
•
•
•
The number of moles is given by the formula as shown below.
Substitute the above equation in equation (1) as shown below.
Rearrange the above equation in terms of mass as shown below.
From the above equation, it is clear that the mass of a gas is directly proportion to its molar mass. This means the mass of
Therefore, the statement “the mass of
The statement “the mass of
(c)
Interpretation:
Whether the statement “at a given temperature and pressure, the densities of two gases are proportional to their molar masses” is true or false is to be stated.
Concept introduction:
The ideal gas equation is used to represent the relation between the volume, pressure, temperature and number of moles of an ideal gas. The ideal gas equation is represented as given below.
Answer to Problem 48E
The statement “at a given temperature and pressure, the densities of two gases are proportional to their molar masses” is true.
Explanation of Solution
Ideal gas equation is given by the formula as shown below.
Where,
•
•
•
•
•
The number of moles is given by the formula as shown below.
Substitute the above equation in equation (1) as shown below.
The density is given by the formula as shown below.
Rearrange equation (2) in terms of density using the above equation as shown below.
From the above equation, it is clear that the molar mass of a gas is directly proportion to its density.
Therefore, the statement “at a given temperature and pressure, the densities of two gases are proportional to their molar masses” is true.
The statement “at a given temperature and pressure, the densities of two gases are proportional to their molar masses” is true.
(d)
Interpretation:
Whether the statement “to change liters of a gas to moles, multiply by
Concept introduction:
The ideal gas equation is used to represent the relation between the volume, pressure, temperature and number of moles of an ideal gas. The ideal gas equation is represented as given below.
Answer to Problem 48E
The statement “to change liters of a gas to moles, multiply by
Explanation of Solution
Ideal gas equation is given by the formula as shown below.
Where,
•
•
•
•
•
Rearrange equation (1) in terms of number of moles as shown below.
From the above equation, it is clear that to calculate number of moles from liters of a gas, the volume is multiplied by
Therefore, the statement “to change liters of a gas to moles, multiply by
The statement “to change liters of a gas to moles, multiply by
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Chapter 14 Solutions
Introductory Chemistry: An Active Learning Approach
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