The ideal gas law, expressed as \( PV = nRT \), serves as a foundational equation in understanding the relationships between pressure (P), volume (V), number of moles (n), and temperature (T) of an ideal gas. When faced with problems involving two sets of values for these variables, we can rearrange the ideal gas law to derive new equations that facilitate calculations.In scenarios where you have two pressures and two temperatures, or two volumes with two moles, the ideal gas law can be adapted to compare the initial and final states of a gas. This is particularly useful in applications such as gas expansion or compression, where you might need to find an unknown variable while knowing the others.For example, if you have an initial state represented as \( P_1, V_1, n_1, T_1 \) and a final state as \( P_2, V_2, n_2, T_2 \), you can set up the relationship as follows:\[\frac{P_1 V_1}{n_1 T_1} = \frac{P_2 V_2}{n_2 T_2}\]This equation allows you to solve for any unknown variable, provided you have the necessary information about the other variables. By understanding how to manipulate the ideal gas law in this way, you can effectively tackle a variety of problems involving gases under different conditions.
11 Gases
The Ideal Gas Law Derivations
11 Gases
The Ideal Gas Law Derivations: Videos & Practice Problems
Rearranging the ideal gas law allows for the derivation of equations related to pressure, volume, moles, and temperature, particularly when dealing with two sets of values. This is essential for solving problems involving variables such as pressure (P), volume (V), and temperature (T) in gas calculations. Understanding these relationships is crucial for applying the ideal gas law effectively in various scenarios, including calculations of moles and changes in conditions. Mastery of these concepts enhances problem-solving skills in chemistry, particularly in thermodynamics and gas behavior.
The Ideal Gas Law Derivations are a convenient way to solve gas calculations involving 2 sets of the same variables.
Ideal Gas Law Derivations
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concept
The Ideal Gas Law Derivations
Video duration:
47sThe Ideal Gas Law Derivations Video Summary
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example
The Ideal Gas Law Derivations Example 1
Video duration:
4m3
Problem
A sample of nitrogen dioxide gas at 130 ºC and 315 torr occupies a volume of 500 mL. What will the gas pressure be if the volume is reduced to 320 mL at 130 ºC?
A
0.65 atm
B
0.83 atm
C
0.92 atm
D
1.6 atm
E
2.7 atm
4
Problem
A cylinder with a movable piston contains 0.615 moles of gas and has a volume of 295 mL. What will its volume be if 0.103 moles of gas escaped?
A
0.176 L
B
0.217 L
C
0.246 L
D
0.361 L
E
1.28 L
5
Problem
On most spray cans it is advised to never expose them to fire. A spray can is used until all that remains is the propellant gas, which has a pressure of 1350 torr at 25 ºC. If the can is then thrown into a fire at 455 ºC, what will be the pressure (in torr) in the can?
a) 750 torr
b) 1800 torr
c) 2190 torr
d) 2850 torr
e) 3300 torr
A
750 torr
B
1800 torr
C
2190 torr
D
2850 torr
E
3300 torr
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Here’s what students ask on this topic:
What is the ideal gas law and how is it derived?
The ideal gas law is a fundamental equation in chemistry that relates the pressure (P), volume (V), temperature (T), and number of moles (n) of a gas. It is expressed as:
where R is the universal gas constant (8.314 J/(mol·K)). The law is derived from combining Boyle's Law (P∝1/V at constant T and n), Charles's Law (V∝T at constant P and n), and Avogadro's Law (V∝n at constant P and T). By combining these proportionalities, we get the ideal gas law.
How do you derive the combined gas law from the ideal gas law?
The combined gas law is derived from the ideal gas law to relate two sets of conditions for a gas. Starting with the ideal gas law:
For two sets of conditions (P1, V1, T1) and (P2, V2, T2), we can write:
This equation is the combined gas law, which allows us to calculate changes in pressure, volume, and temperature for a given amount of gas.
How do you use the ideal gas law to calculate the number of moles of a gas?
To calculate the number of moles (n) of a gas using the ideal gas law, you can rearrange the equation:
Solving for n, we get:
By substituting the known values of pressure (P), volume (V), temperature (T), and the gas constant (R), you can calculate the number of moles of the gas.
What are the common units used in the ideal gas law?
The common units used in the ideal gas law are:
- Pressure (P): atmospheres (atm), pascals (Pa), or torr
- Volume (V): liters (L) or cubic meters (m3)
- Temperature (T): Kelvin (K)
- Number of moles (n): moles (mol)
- Gas constant (R): 8.314 J/(mol·K) or 0.0821 L·atm/(mol·K)
It is crucial to ensure that all units are consistent when using the ideal gas law to avoid errors in calculations.
How do you derive the ideal gas law from the kinetic molecular theory?
The ideal gas law can be derived from the kinetic molecular theory, which describes the behavior of gas particles. According to this theory, the pressure exerted by a gas is due to collisions of gas particles with the walls of the container. The average kinetic energy of gas particles is proportional to the temperature (T). By combining these principles, we get:
This equation shows the relationship between pressure, volume, temperature, and the number of moles of a gas, consistent with the ideal gas law.
