Consider 4.00L of a gas at 365mmHg and 20*C. If the container is compressed to 2.80L and the temperature is increased to 35*C, what is the new pressure,P2 , inside the container? Assume no
change in the amount of gas inside the cylinder
(P1V1/T1) = (P2V2/T2)
T must be in kelvin.
To find the new pressure, P2, inside the container, we can use the ideal gas law equation, which states:
PV = nRT
Where:
P is the pressure
V is the volume
n is the number of moles of gas
R is the ideal gas constant
T is the temperature in Kelvin
First, we need to convert the given temperature and pressure values into Kelvin and atmosphere, respectively.
Given data:
Initial volume, V1 = 4.00 L
Initial pressure, P1 = 365 mmHg
Initial temperature, T1 = 20°C
Final volume, V2 = 2.80 L
Final temperature, T2 = 35°C
To convert temperature from Celsius to Kelvin, we use the formula:
T(K) = T(°C) + 273.15
Converting the temperatures:
T1 = 20°C + 273.15 = 293.15 K
T2 = 35°C + 273.15 = 308.15 K
Next, we need to convert the initial pressure from mmHg to atm, using the conversion factor:
1 atm = 760 mmHg
Converting the pressure:
P1 = 365 mmHg / 760 mmHg/atm = 0.4803 atm
Now, we have all the necessary values to calculate the new pressure using the ideal gas law equation:
P1V1 / T1 = P2V2 / T2
Plugging in the values:
(0.4803 atm) * (4.00 L) / (293.15 K) = P2 * (2.80 L) / (308.15 K)
Simplifying the equation, we get:
P2 = (0.4803 atm) * (4.00 L) * (308.15 K) / (2.80 L) * (293.15 K)
Calculating, we find:
P2 ≈ 0.837 atm
Therefore, the new pressure inside the container, P2, after compressing the volume and increasing the temperature, is approximately 0.837 atm.