A 12.8 L sample of Ne gas initially has a temperature of 32.7oC at a pressure of 2.57 atm. What is the new pressure, in atm, if the volume is changed to 10.6 L and the temperature is decreased to 13.9oC?
(P1V1/T1) = (P2V2/T2)
T must be in kelvin.
To solve this problem, we can use the combined gas law formula, which relates the initial and final conditions of pressure, volume, and temperature.
The formula for the combined gas law 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 = 2.57 atm
V1 = 12.8 L
T1 = 32.7°C = (32.7 + 273.15) K
V2 = 10.6 L
T2 = 13.9°C = (13.9 + 273.15) K
Plugging in the values into the formula, we get:
(2.57 atm * 12.8 L) / (32.7 + 273.15) K = (P2 * 10.6 L) / (13.9 + 273.15) K
Now we can solve for P2:
(2.57 atm * 12.8 L * (13.9 + 273.15) K) = (P2 * 10.6 L * (32.7 + 273.15) K)
To get P2, we can rearrange the equation:
P2 = (2.57 atm * 12.8 L * (13.9 + 273.15) K) / (10.6 L * (32.7 + 273.15) K)
Calculating this equation will give us the value of P2 in atm.
To solve this problem, we can use the combined gas law equation, which relates the pressure, volume, and temperature of a gas.
The formula for the combined gas law is:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure of the gas
V1 = initial volume of the gas
T1 = initial temperature of the gas
P2 = final pressure of the gas (what we're solving for)
V2 = final volume of the gas
T2 = final temperature of the gas
Now let's plug in the given values:
P1 = 2.57 atm
V1 = 12.8 L
T1 = 32.7°C = 273.85K (converted to Kelvin using the formula T(K) = T(°C) + 273.15)
V2 = 10.6 L
T2 = 13.9°C = 287.05K
Now we can solve for P2 by rearranging the formula:
P2 = (P1 * V1 * T2) / (V2 * T1)
Plugging in the values:
P2 = (2.57 atm * 12.8 L * 287.05K) / (10.6 L * 273.85K)
Calculating this expression will give us the final pressure, in atm.