a 500.0 mL gas sample at STP is compressed to a volume of 300.0 ml and the temperature is increased to 35.0 C. What is the new pressure of the gas in pascals?
Working the Problem Out:
P1(V1) P2(V2) CrossMulti. 1atm(500.0mL) P2(300.0)
______ = ______ ------> _____________ = __________
T1 T2 273K 308K
Answer: 1.88atm
(P1V1)/T1 = (P2V2)/T2
Remember T is in Kelvin.
I would use 1 atm for P1 so P2 will be in atm. Then convert to Pa.
456.0 pa
1.28
P1(V1)
---------- = ----------
T1
P1(V1) P2(V2) CrossMulti. 1atm(500.0mL) P2(300.0)
______ = ______ ------> _____________ = __________
T1 T2 273K
To find the new pressure of the gas sample, we can use the combined gas law formula. The formula is:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = Initial pressure
V1 = Initial volume
T1 = Initial temperature
P2 = Final pressure (what we want to find)
V2 = Final volume
T2 = Final temperature
Given values:
P1 = Pressure at STP = 1 atmosphere or 101.3 kPa
V1 = Initial volume = 500.0 mL = 0.5 L
T1 = Initial temperature at STP = 0 degrees Celsius = 273.15 Kelvin
V2 = Final volume = 300.0 mL = 0.3 L
T2 = Final temperature = 35.0 degrees Celsius = 308.15 Kelvin
Now we can plug in these values into the formula and solve for P2:
(101.3 kPa * 0.5 L) / (273.15 K) = (P2 * 0.3 L) / (308.15 K)
To simplify the equation, convert all units to the same system, such as pascals and kelvin:
(101300 Pa * 0.5 L) / (273.15 K) = (P2 * 0.3 L) / (308.15 K)
Now, solve for P2:
P2 = (101300 Pa * 0.3 L) / (273.15 K) * (308.15 K) / (0.5 L)
P2 = 111226.47 Pa
Therefore, the new pressure of the gas in pascals is approximately 111226.47 Pa.