An ideal gas is allowed to expand from 6.00 L to 45.0 L at constant temperature.
By what factor does the volume increase?
? Number
The pressure will
Increase by that factor or decrease by that factor?
If the initial pressure was 105 atm, what is the final pressure?
45.0/6.0 = ?
P will decrease by that factor.
105 atm/factor = ?
(Note: use P1V1 = P2V2 to check that.
To find the factor by which the volume increases, we need to divide the final volume by the initial volume.
Factor increase in volume = Final volume / Initial volume
Given:
Initial volume (Vi) = 6.00 L
Final volume (Vf) = 45.0 L
Factor increase in volume = 45.0 L / 6.00 L
Now, let's calculate the factor increase in volume:
Factor increase in volume = 7.5
So, the volume increases by a factor of 7.5.
Next, since the temperature is constant and the gas is ideal, we can use Boyle's Law to determine the change in pressure.
Boyle's Law states that at constant temperature, the pressure and volume of an ideal gas are inversely proportional.
Mathematically, Boyle's Law can be written as:
Pi * Vi = Pf * Vf
Where:
Pi = Initial pressure
Vi = Initial volume
Pf = Final pressure
Vf = Final volume
We are given:
Pi = 105 atm
Vi = 6.00 L
Vf = 45.0 L
Using the equation, we can solve for Pf:
Pi * Vi = Pf * Vf
105 atm * 6.00 L = Pf * 45.0 L
Dividing both sides by 45.0 L:
105 atm * 6.00 L / 45.0 L = Pf
Simplifying:
14 atm = Pf
Therefore, the final pressure (Pf) is 14 atm.
In summary:
- The volume of the ideal gas increases by a factor of 7.5.
- The pressure decreases because the volume increases.
- The final pressure is 14 atm.