Answer: To find the final pressure of the gas after the reaction goes to completion and the temperature rises, we can use the combined gas law. The combined gas law relates the initial and final states of a gas when the amount of gas and the number of moles are constant.
The combined gas law equation is given by:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
where:
P1 = Initial pressure of the gas (before the reaction, in Pa)
V1 = Initial volume of the gas (before the reaction, in mL)
T1 = Initial temperature of the gas (before the reaction, in Kelvin)
P2 = Final pressure of the gas (after the reaction, in Pa)
V2 = Final volume of the gas (after the reaction, in mL, which is the same as V1 as the container is closed)
T2 = Final temperature of the gas (after the reaction, in Kelvin)
Now, let's begin the calculations step by step:
Step 1: Convert the initial temperature from Celsius to Kelvin:
T1 = 52.5 °C + 273.15 = 325.65 K
Step 2: Convert the final temperature from Celsius to Kelvin:
T2 = 112.0 °C + 273.15 = 385.15 K
Step 3: Convert the initial volume to liters (V1):
V1 = 3.00 × 10^3 mL = 3.00 L
Step 4: Convert the final volume to liters (V2):
V2 = 3.00 L (since the container is closed, the volume remains the same)
Step 5: Convert the initial pressure to Pascals (P1):
P1 = 8.47 × 10^5 Pa
Step 6: Calculate the final pressure (P2) using the combined gas law:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
P2 = (P1 * V1 * T2) / (V2 * T1)
Now, plug in the values and calculate:
P2 = (8.47 × 10^5 Pa * 3.00 L * 385.15 K) / (3.00 L * 325.65 K)
P2 ≈ 111102.81 Pa
Step 7: Convert the final pressure from Pascals to bars:
1 bar = 100,000 Pa
Final pressure (P2) = 111102.81 Pa ÷ 100,000 Pa/bar ≈ 1.11 bar
So, the final pressure of the gas after the reaction goes to completion and the temperature rises to 112.0 ℃ is approximately 1.11 bar.