a gas has a volume of 2 liters at 323 K and 3 atms. what will the new volume be if the temperature is lowered to 273 K and the pressure is lowered to 1 atm?
To find the new volume of the gas when the temperature is lowered to 273 K and the pressure is lowered to 1 atm, we can use the combined gas law. The combined gas law relates the initial and final conditions of pressure, volume, and temperature for a given amount of gas.
The combined gas law equation is:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure
V2 = final volume
T2 = final temperature
Let's substitute the given values into the equation:
P1 = 3 atm
V1 = 2 liters
T1 = 323 K
P2 = 1 atm
T2 = 273 K
Now we can solve for V2. Rearranging the equation, we get:
V2 = (P1 * V1 * T2) / (P2 * T1)
Plugging in the values, we have:
V2 = (3 atm * 2 liters * 273 K) / (1 atm * 323 K)
Simplifying further:
V2 = (6 atm * 273 liters) / (323 atm)
Finally, calculating V2:
V2 = 5.09 liters
Therefore, the new volume of the gas will be approximately 5.09 liters when the temperature is lowered to 273 K and the pressure is lowered to 1 atm.