Determine the final pressure of a gas that has initial pressure of 1.00 atm and is heated from 20.0 C to 30.0 C in a container with a fixed volume.
1.06 atm
(P1/T1) = (P2/T2)
T must be in kelvin.
To determine the final pressure of the gas, we can use the ideal gas law:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
In this case, we are given the initial pressure (P1 = 1.00 atm), the initial temperature (T1 = 20.0 °C), and the final temperature (T2 = 30.0 °C). The volume is fixed, which means it remains constant (V1 = V2).
To solve for the final pressure (P2), we need to use the ratio of the temperatures (in Kelvin) and apply it to the ideal gas law formula.
Step 1: Convert temperatures to Kelvin
T1 = 20.0 °C + 273.15 = 293.15 K
T2 = 30.0 °C + 273.15 = 303.15 K
Step 2: Set up the equation using the ideal gas law
P1 * V1 = n * R * T1
P2 * V2 = n * R * T2
Since the volume (V1 = V2), we can rewrite the equation as:
P1 = (n * R * T1) / V
P2 = (n * R * T2) / V
Step 3: Calculate the final pressure
P2 = (P1 * T2) / T1
Substituting the given values:
P2 = (1.00 atm * 303.15 K) / 293.15 K
P2 ≈ 1.03 atm
Therefore, the final pressure of the gas when heated to 30.0 °C is approximately 1.03 atm.