Answer:
Step-by-step explanation:
To solve the given gas law problems, we can use the ideal gas law equation:
PV = nRT
where:
P = pressure (in atmospheres or Torr)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K) or 62.36 L·Torr/(mol·K))
T = temperature (in Kelvin)
Given information:
Initial volume (V1) = 22.4 L
Initial pressure (P1) = 1 atm (at STP)
Final temperature (T2) = 765 K (part a)
Final volume (V2) = 250 mL = 0.25 L (part b)
Final pressure (P2) = Unknown (part b)
Final volume (V2) = 16.2 L (part c)
Final pressure (P2) = 200 Torr (part c)
a) Calculate the volume when the temperature increases to 765 K at constant pressure:
Using the equation PV = nRT, we can write:
P1V1/T1 = P2V2/T2
Plugging in the known values, we get:
(1 atm) * (22.4 L) / (273 K) = P2 * V2 / (765 K)
Solving for V2, we find:
V2 = (1 atm) * (22.4 L) * (765 K) / (273 K)
V2 ≈ 63.38 L
Therefore, the volume when the temperature increases to 765 K at constant pressure is approximately 63.38 L.
b) Calculate the pressure if the volume is compressed to 250 mL at constant temperature:
Using the equation PV = nRT, we can write:
P1V1/T1 = P2V2/T2
Plugging in the known values, we get:
(1 atm) * (22.4 L) / (273 K) = P2 * (0.25 L) / (273 K)
Solving for P2, we find:
P2 = (1 atm) * (0.25 L) / (22.4 L)
P2 ≈ 0.0112 atm
Therefore, the pressure when the volume is compressed to 250 mL at constant temperature is approximately 0.0112 atm.
c) Calculate the temperature if the volume drops to 16.2 L and the pressure is reduced to 200 Torr:
Using the equation PV = nRT, we can write:
P1V1/T1 = P2V2/T2
Plugging in the known values, we get:
(1 atm) * (22.4 L) / (273 K) = (200 Torr) * (16.2 L) / T2
Solving for T2, we find:
T2 = (200 Torr) * (16.2 L) * (273 K) / (1 atm) * (22.4 L)
T2 ≈ 263.03 K
Therefore, the temperature when the volume drops to 16.2 L and the pressure is reduced to 200 Torr is approximately 263.03 K.