Concept explainers
What is the effect of the following on the volume of 1 mol of an ideal gas?
(a) The pressure is tripled (at constant T).
(b) The absolute temperature is increased by a factor of 3.0 (at constant P).
(c) Three more moles of the gas are added (at constant P and T).
(a)
Interpretation:
The effect on the volume of 1 mole of an ideal gas should be determined when the pressure is tripled at constant temperature.
Concept Introduction:
Boyle's Law gives the relationship between Pressure (P) and Volume (V).
According to Boyle's Law, the volume of gas changes inversely with the pressure of the gas if temperature and amount of a gas are constant.
PV = constant
The pressure of a gas decreases with increase in volume; volume of a gas decreases with increase in pressure.
Charles’s Law gives the relationship between Volume (V) and Temperature (T)
According to Charles’s Law, the volume of gas has direct relationship with temperature of the gas if pressure and amount of a gas are constant.
If the temperature or volume of a gas changes without any change in amount of a gas and pressure, then the final volume and temperature will give the same
Charles’s Law can be written as:
Where, T1 and V1 are the initial temperature and volume.
T2 and V2 are the final temperature and volume.
Avogadro's Law:
At same condition of pressure and temperature, equal volume of gases has same number of moles. In other words, at same temperature and pressure; one mole of a gas has the same volume.
According to Avogadro's Law, at STP, 1 mole of a gas consist of
The mathematical expression is given as:
Amonton's Law:
The pressure of a gas is directly related with the absolute temperature at constant number of moles and volume.
The mathematical expression is given as:
Or,
Answer to Problem 5.14P
At constant temperature, the volume of one mole of a gas is 1/3 of the initial volume when the pressure of a gas is tripled.
Explanation of Solution
Ideal gas law gives the relation between pressure, volume, number of moles and temperature.
The ideal gas law is:
Where,
P = Pressure
V = Volume
n = Number of moles
R = Universal gas constant (
T = Temperature
The new ideal expression is shown below, when the pressure is tripled.
Now, the new volume is calculated as:
Thus, new volume is:
Hence, at constant temperature, the volume of one mole of a gas is 1/3 of the initial volume when the pressure of a gas is tripled.
(b)
Interpretation:
The effect on the volume of 1 mole of an ideal gas should be determined when the absolute temperature is increased by factor of 3.0 at constant pressure.
Concept Introduction:
Boyle's Law gives the relationship between Pressure (P) and Volume (V).
According to Boyle's Law, the volume of gas changes inversely with the pressure of the gas if temperature and amount of a gas are constant.
PV = constant
The pressure of a gas decreases with increase in volume; volume of a gas decreases with increase in pressure.
Charles’s Law gives the relationship between Volume (V) and Temperature (T)
According to Charles’s Law, the volume of gas has direct relationship with temperature of the gas if pressure and amount of a gas are constant.
If the temperature or volume of a gas changes without any change in amount of a gas and pressure, then the final volume and temperature will give the same
Charles’s Law can be written as:
Where, T1 and V1 are the initial temperature and volume.
T2 and V2 are the final temperature and volume.
Avogadro's Law:
At same condition of pressure and temperature, equal volume of gases has same number of moles. In other words, at same temperature and pressure; one mole of a gas has the same volume.
According to Avogadro's Law, at STP, 1 mole of a gas consist of s
The mathematical expression is given as:
Amonton's Law:
The pressure of a gas is directly related with the absolute temperature at constant number of moles and volume.
The mathematical expression is given as:
Or,
Answer to Problem 5.14P
At constant pressure, the volume of one mole of a gas is triple of the initial volume when the absolute temperature of a gas is increased by factor 3.0.
Explanation of Solution
Ideal gas law gives the relation between pressure, volume, number of moles and temperature.
The ideal gas law is:
Where,
P = Pressure
V = Volume
n = Number of moles
R = Universal gas constant (
T = Temperature
The new ideal expression is shown below, when the temperature is increased by factor 3.0.
Now, the new volume is calculated as:
Thus, new volume is:
Hence, at constant pressure, the volume of one mole of a gas is triple of the initial volume when the absolute temperature of a gas is increased by factor 3.0.
(c)
Interpretation:
The effect on the volume of 1 mole of an ideal gas should be determined when three more number of moles of gas is added at constant pressure and temperature.
Concept Introduction:
Boyle's Law gives the relationship between Pressure (P) and Volume (V).
According to Boyle's Law, the volume of gas changes inversely with the pressure of the gas if temperature and amount of a gas are constant.
PV = constant
The pressure of a gas decreases with increase in volume; volume of a gas decreases with increase in pressure.
Charles’s Law gives the relationship between Volume (V) and Temperature (T)
According to Charles’s Law, the volume of gas has direct relationship with temperature of the gas if pressure and amount of a gas are constant.
If the temperature or volume of a gas changes without any change in amount of a gas and pressure, then the final volume and temperature will give the same
Charles’s Law can be written as:
Where, T1 and V1 are the initial temperature and volume.
T2 and V2 are the final temperature and volume.
Avogadro's Law:
At same condition of pressure and temperature, equal volume of gases has same number of moles. In other words, at same temperature and pressure; one mole of a gas has the same volume.
According to Avogadro's Law, at STP, 1 mole of a gas consist of
The mathematical expression is given as:
Amonton's Law:
The pressure of a gas is directly related with the absolute temperature at constant number of moles and volume.
The mathematical expression is given as:
Or,
Answer to Problem 5.14P
At constant pressure and temperature, the volume of one mole of a gas is increase by factor 4.0 when three more number of moles of a gas is added.
Explanation of Solution
Ideal gas law gives the relation between pressure, volume, number of moles and temperature.
The ideal gas law is:
Where,
P = Pressure
V = Volume
n = Number of moles
R = Universal gas constant (
T = Temperature
The new ideal expression is shown below, when three more number of moles of gas are added.
Now, the new volume is calculated as:
Thus, new volume is:
Hence, at constant pressure and temperature, the volume of one mole of a gas is increase by factor 4.0 when three more number of moles of a gas is added.
Want to see more full solutions like this?
Chapter 5 Solutions
Principles of General Chemistry
- perform stoichiometric ca1cu1uions for reactions involving gases as reactants or products.arrow_forwardExplain why the plot of PV for CO2 differs from that of an ideal gas.arrow_forward5-107 If 60.0 g of NH3 occupies 35.1 L under a pressure of 77.2 in. Hg, what is the temperature of the gas, in °C?arrow_forward
- Butane gas, C4H10, is sold to campers as bottled fuel. Its density at 25C and 1.00 atm is 2.38 g/L. What volume of butane gas at 25C and 1.00 atm is required to heat one gallon of water (d=1.00g/mL) from 25C to 98C ? The reaction for the combustion of butane (H f =125.6kJ/mol) is C4H10(g)+132 O2(g)4CO2(g)+5H2O(g)arrow_forwardWhat is the value of the ideal gas constant R if the volume is specified in milliliters rather than liters?arrow_forwardYou have a gas, one of the three known phosphorus-fluorine compounds (PF3, PF3, and P2F4). To find out which, you have decided to measure its molar mass. (a) First, yon determine that the density of the gas is 5.60 g/L at a pressure of 0.971 atm and a temperature of 18.2 C. Calculate the molar mass and identify the compound. (b) To check the results from part (a), you decide to measure the molar mass based on the relative rales of effusion of the unknown gas and CO2. You find that CO2 effuses at a rate of 0.050 mol/min, whereas the unknown phosphorus fluoride effuses at a rate of 0.028 mol/min. Calculate the molar mass of the unknown gas based on these results.arrow_forward
- Principles of Modern ChemistryChemistryISBN:9781305079113Author:David W. Oxtoby, H. Pat Gillis, Laurie J. ButlerPublisher:Cengage LearningChemistry: Matter and ChangeChemistryISBN:9780078746376Author:Dinah Zike, Laurel Dingrando, Nicholas Hainen, Cheryl WistromPublisher:Glencoe/McGraw-Hill School Pub CoGeneral, Organic, and Biological ChemistryChemistryISBN:9781285853918Author:H. Stephen StokerPublisher:Cengage Learning
- Introduction to General, Organic and BiochemistryChemistryISBN:9781285869759Author:Frederick A. Bettelheim, William H. Brown, Mary K. Campbell, Shawn O. Farrell, Omar TorresPublisher:Cengage LearningChemistry: Principles and ReactionsChemistryISBN:9781305079373Author:William L. Masterton, Cecile N. HurleyPublisher:Cengage LearningPhysical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,