A sample of oxygen is in a 570 L balloon at 118.8 kPa. What is the volume of the balloon, in litres (to 1 decimal place, input value only) if the pressure is changed to 1.359 atm? Assume that the temperature remains constant.
To find the new volume of the balloon when the pressure is changed, we can use Boyle's Law equation:
P1 * V1 = P2 * V2
where:
P1 = initial pressure of the oxygen in the balloon = 118.8 kPa
V1 = initial volume of the balloon = 570 L
P2 = final pressure of the oxygen in the balloon = 1.359 atm (converted from kPa to atm)
V2 = volume of the balloon after the pressure is changed (unknown)
First, we need to convert the initial pressure from kPa to atm.
1 atm = 101.325 kPa
So, the initial pressure in atm is calculated as:
118.8 kPa / 101.325 kPa = 1.1723 atm (rounded to 4 decimal places)
Now, we can substitute the values into the Boyle's Law equation:
1.1723 atm * 570 L = 1.359 atm * V2
To find V2, divide both sides of the equation by 1.359 atm:
(1.1723 atm * 570 L) / 1.359 atm = V2
V2 ≈ 492.8 L (rounded to 1 decimal place)
Therefore, the volume of the balloon, when the pressure is changed to 1.359 atm, is approximately 492.8 L (to 1 decimal place).
To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature.
Boyle's Law formula: P1 * V1 = P2 * V2
Where:
P1 = Initial pressure (in kPa)
V1 = Initial volume (in liters)
P2 = Final pressure (in atm)
V2 = Final volume (to be found)
Given:
P1 = 118.8 kPa
V1 = 570 L
P2 = 1.359 atm
To find V2, we'll rearrange Boyle's Law formula to isolate V2:
V2 = (P1 * V1) / P2
Now, let's substitute the given values into the formula:
V2 = (118.8 kPa * 570 L) / 1.359 atm
To convert kPa to atm, we need to divide by 101.325 (1 atm = 101.325 kPa):
V2 = (118.8 kPa * 570 L) / (1.359 atm * 101.325 kPa/atm)
Simplifying this expression:
V2 = (67836 kPa*L) / (137.889735 atm*kPa)
Now, we can cancel out the units:
V2 = 492.8 L
Therefore, the volume of the balloon when the pressure is changed to 1.359 atm is approximately 492.8 liters.
When temperature remains constant, use Boyle's law:
PV = constant, or P1V1=P2V2
Also, for conversion, use
1 atm = 101.325 kPa