One mole of an ideal gas is sealed in a 22.4-L container at a pressure of 1 and a temperature of 273 K . The temperature is then increased to 305 K , but the container does not expand. What will the new pressure be?
To solve this problem, we can use the ideal gas law equation, which is:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the ideal gas constant
T is the temperature of the gas in Kelvin
We are given:
Initial pressure, P1 = 1 atm
Initial temperature, T1 = 273 K
Final temperature, T2 = 305 K
Volume, V = 22.4 L (constant)
Since the container is sealed and does not expand, the volume remains constant. So we can ignore the V term in the equation.
To find the new pressure, P2, we can rearrange the equation as follows:
P1/T1 = P2/T2
Now we can substitute the given values into the equation:
1 atm / 273 K = P2 / 305 K
Next, cross-multiply and solve for P2:
P2 = (1 atm * 305 K) / 273 K
P2 = 305 atm / 273
P2 ≈ 1.12 atm
Therefore, the new pressure, P2, will be approximately 1.12 atm.