a flexible container, like a balloon, with an initial volume of 1.0L is occupied by a gas at a pressure 1.5atm at 25 Celsius.
what is the new volume if the pressure of the gas increases to 6.0atm and the temperature is raised to 100 degree Celsius?
the Si unit for pressure is KPa. do u convert the pressure in the question to KPa or u solve the way it is?
Gases are measured using three variables: temperature (T), pressure (P), and volume (V).
When more than one variable is changing you use the universal gas law which combines Boyle's Law and Charles's Law into one general equation.
That equation is:
(P1 x V1)/T1 = (P2 x V2)/T2
where P1, V1 & T1 are initial conditions and P2,V2,T2 are final conditions.
There are three important things you need to watch when solving these problems:
1: make sure the temperature is converted to degrees Kelvin using the formula: K = 273.15 + degrees C
2. make sure the units for pressure are the same for the initial state and final state. You do not have to change them to kPa unless that is the units you are asked to use in the final answer.
3. make sure the units for volume are the same for the initial and final states.
Once you have done this, put your known values into the equation above and solv e for the unknown.
In this problem:
P1 = 1.5 atm
V1 = 1 liter
T1 = 25 degrees C = 298.15 K
P2 = 6 atm
V2 = ?
T2 = 100 degrees C = 373.15 K
(1.5 x 1)/298.15 = (6V2)/373.15
first multiply both sides by 373.15 and you get
(373.15 x 1.5 x1)/298.15 = 6V2
now divide both sides by 6 to find V2
(373.15 x 1.5 x1)/(298.15 x 6) = V2
solving you get V2 = .313 liters or 313 mL
Notice that in this case the increased pressure had a greater effect on the final volume than the increased temperature.
As per Universal gas law for a given mass of gas:
PV/T = constant
P = Pressure
V = Volume
T = Temperature in Kelvin
Thus if the initial pressure, volume and temperature of the gas in the balloon are represented by P1, V1 an T1 respectively, and the final pressure, volume and temperature of the gas in the balloon are represented by P2, V2 an T2 respectively.
P1V1/T1 = P2V2/T2
The given Values of these variables are:
P1 =1.5 atm
V1 = 1.0 l
T1 = 25 degrees C = 25 + 273.15 = 298.15 degrees Kelvin
P2 = 6.0 atm
V2 = To be determined
T2 = 100 degrees C = 100 + 273.15 = 373.15 degrees Kelvin
Substituting these values in the above equation:
(1.5*1.0)/298.15 = (6.0*V2)/373.15
==> V2 = (1.5*1.0)(373.15/6.0)/298.15
==> V2 = 1.0*(1.5/6.0)(373.15/298.15)
==> V2 = 0.3129 l
New volume = 0.3129 l
Please note that in solving this question we can use any units for pressure and volume, as long as these are same for initial and final conditions. However the temperature must be measured only in terms of absolute temperature. This is the reason why we have converted the temperature from Celsius to Kelvin.