Answer:
The final pressure inside the scuba tank after it cools to 25.0°C is 3.787 atm.
Explanation:
We can use the ideal gas law to solve this problem:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.
First, we need to convert the initial temperature from Celsius to Kelvin:
T1 = 1.00 × 10³ + 273.15 = 1273.15 K
The final temperature is 25.0°C + 273.15 = 298.15 K.
Next, we can use the ideal gas law to find the initial number of moles of gas:
n1 = PV1 / RT1
where P is the initial pressure and V is the volume of the scuba tank. We don't know the volume, but we can assume that it remains constant during the cooling process. The gas constant R is 0.08206 L·atm/(mol·K).
n1 = (130.0 atm) V / (0.08206 L·atm/(mol·K) × 1273.15 K)
n1 = 13.944 V
Now we can use the ideal gas law again to find the final pressure:
P2 = n2RT2 / V
where n2 is the final number of moles of gas. We can assume that the number of moles of gas remains constant during the cooling process (since the tank is sealed), so n2 = n1.
P2 = (n1 × R × T2) / V
P2 = (13.944 V × 0.08206 L·atm/(mol·K) × 298.15 K) / V
P2 = 3.787 atm
Therefore, the final pressure inside the scuba tank after it cools to 25.0°C is 3.787 atm.