Unit 5A (Gasses)
The ideal gas law is PV = nRT. Explain what each variable is in this equation and include a
common unit used to measure that variable
Variable P V n R T
Property Pressure
Unit Pa/bar/atmosphere
In a sealed bottle, the temperature is raised from 200 K to 400 K.
What happens to the remaining quantities
Pressure (P) (doubles / halves / stays constant )
Volume (V) (doubles / halves / stays constant )
Moles (n) (doubles / halves / stays constant )
Gas constant (R) (doubles / halves / stays constant )
Temperature (T) (doubles / halves / stays constant )
A life raft containing 200 g of air has another 200 g of air added.
What happens to the remaining quantities
Pressure (P) (doubles / halves / stays constant )
Volume (V) (doubles / halves / stays constant )
Moles (n) (doubles / halves / stays constant )
Gas constant (R) (doubles / halves / stays constant )
Temperature (T) (doubles / halves / stays constant )
Two quantities in the ideal gas equation that are directly proportional: _______ and ________
Two quantities in the ideal gas equation that are indirectly proportional: _______ and ________
Given that R= 0.0821(L⋅atm) / (mol⋅K) how many moles must be in a 2L container at
1.8 atmospheres with a temperature of 270K?
Ah, the ideal gas law! Let's clown around with it.
In the equation PV = nRT:
- P represents pressure, measured in pascals (Pa), bars, or atmospheres (atm).
- V stands for volume, which has units of liters (L).
- n represents the number of moles of gas, and it doesn't have a specific unit because it's just a count.
- R is the gas constant, which varies depending on the unit system used. In this case, it's given as 0.0821 (L⋅atm)/(mol⋅K), where K represents the temperature in Kelvin.
- T is temperature, measured in Kelvin (K).
Now, let the humorous explanations flow!
When the temperature in the sealed bottle rises from 200 K to 400 K:
- Pressure (P): It doubles! Just like how the chances of seeing a penguin in the Sahara Desert double.
- Volume (V): Stays the same! It's as constant as the feeling of regret after finishing a whole tub of ice cream.
- Moles (n): Remains constant! They're as unchanging as that person who always takes the last slice of pizza.
- Gas constant (R): Stays constant too! No need to change the clown costume; this one's a keeper.
- Temperature (T): Doubles, just like when someone tells you to calm down.
Now, for the life raft scenario:
When another 200 g of air is added to the life raft containing 200 g of air:
- Pressure (P): Doubles, just like the joy of finding Wi-Fi on a deserted island.
- Volume (V): Stays the same! Just like that person who never stops talking about their gluten-free diet.
- Moles (n): Doubles as well, as if another clown suddenly appeared at the circus. The more, the merrier, right?
- Gas constant (R): Constant! Don't need any more clowns causing mayhem in this equation.
- Temperature (T): Remains constant, like the calmness of a mime stuck in an invisible box.
And now, let's talk about direct and indirect relationships:
Directly proportional quantities: Volume (V) and moles (n). They go together like peanut butter and jelly or like clowns and confetti.
Indirectly proportional quantities: Pressure (P) and volume (V). They're like two clowns on a unicycle, always trying to balance things out.
Finally, let's calculate the number of moles in a 2L container at 1.8 atmospheres and 270K:
Using the formula, n = (PV) / (RT):
Plugging in the values, n = (1.8 atm * 2 L) / (0.0821 (L⋅atm)/(mol⋅K) * 270 K).
Just crunch those numbers, and you'll find the number of moles lurking in that container! It's like finding a hidden treasure, but instead of gold, you get moles.
In the ideal gas law equation PV = nRT:
- P represents pressure, measured in units such as Pascal (Pa), bar, or atmosphere (atm).
- V represents volume, typically measured in liters (L).
- n represents moles of the gas, which is a dimensionless quantity.
- R is the gas constant, which has a value of 0.0821 L⋅atm / (mol⋅K). It is a constant provided to relate the other variables.
- T represents temperature, typically measured in Kelvin (K).
Now, let's analyze what happens to the remaining quantities in the given scenarios:
1. When the temperature is raised from 200 K to 400 K in a sealed bottle:
- Pressure (P): Stays constant unless there are any other changes influencing it.
- Volume (V): Stays constant unless there are any other changes influencing it.
- Moles (n): Stays constant unless there are any other changes influencing it.
- Gas constant (R): Stays constant.
- Temperature (T): Doubles from 200 K to 400 K.
2. When 200 g of air is added to a life raft containing 200 g of air:
- Pressure (P): Stays constant unless there are any other changes influencing it.
- Volume (V): Stays constant unless there are any other changes influencing it.
- Moles (n): Doubles from the addition of the extra air.
- Gas constant (R): Stays constant.
- Temperature (T): Stays constant unless there are any other changes influencing it.
Two quantities in the ideal gas equation that are directly proportional are pressure (P) and temperature (T).
Two quantities in the ideal gas equation that are indirectly proportional are volume (V) and pressure (P).
To find the number of moles in a 2L container at 1.8 atmospheres and a temperature of 270K, we can rearrange the ideal gas law equation as n = PV / RT. Plugging in the given values:
n = (1.8 atm * 2 L) / (0.0821 L⋅atm / (mol⋅K) * 270K)
n ≈ 0.154 moles