DETERMINE THE TEMPERATURE REQUIRED FOR 0.0354MOL OF GAS TO FILL A BALLOON TO 2.5L UNDER 0.998K PA PRESSURE
PV = nRT.
Change kPa to atmospheres and use R = 0.08206 L*atm/mol*K.
To determine the temperature required, we can use the ideal gas law equation: PV = nRT.
First, let's convert the pressure from kPa to atmospheres.
Given:
Pressure (P) = 0.998 kPa
1 atmosphere (atm) = 101.325 kPa
So, the pressure in atmospheres is:
0.998 kPa / 101.325 kPa = 0.00985 atm
Now, we can rearrange the ideal gas law equation to solve for T (temperature):
PV = nRT
Rearranging the equation:
T = PV / (nR)
Given:
Pressure (P) = 0.00985 atm
Volume (V) = 2.5 L
Moles (n) = 0.0354 mol
Gas constant (R) = 0.08206 L*atm/mol*K
Plugging in the values:
T = (0.00985 atm * 2.5 L) / (0.0354 mol * 0.08206 L*atm/mol*K)
Now, let's calculate:
T = (0.024625 atm L) / (0.028875876 mol L*atm^-1 K^-1)
T ≈ 0.852 K
Therefore, the temperature required for 0.0354 mol of gas to fill a balloon to 2.5 L under 0.998 kPa pressure is approximately 0.852 K.