17 liters of a gas is at an initial temperature of 67 degrees C and a pressure of 88.89 atm, what will be the pressure of the gas if the tempetature of the gas is raised to 94 degrees C and the volume of the gas is decreased to 12 liters?
177 atm
36.3 atm
108 atm
136 atm
219 atm
(P1V1/T1) = (P2V2/T2)
T must be in kelvin
To solve this problem, we can apply the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of the gas
R = ideal gas constant
T = temperature of the gas in Kelvin
First, let's convert the temperatures to Kelvin:
Initial temperature = 67 degrees C = 67 + 273 = 340 K
Final temperature = 94 degrees C = 94 + 273 = 367 K
Now let's substitute the given values into the equation:
Initial pressure, P1 = 88.89 atm
Initial volume, V1 = 17 L
Initial temperature, T1 = 340 K
Final volume, V2 = 12 L
Final temperature, T2 = 367 K
Now, rearrange the ideal gas law equation to solve for the final pressure, P2:
P2 = (P1 * V1 * T2) / (V2 * T1)
Substitute the values we have:
P2 = (88.89 atm * 17 L * 367 K) / (12 L * 340 K)
P2 = 219 atm
Therefore, the pressure of the gas when the temperature is raised to 94 degrees C and the volume is decreased to 12 liters is approximately 219 atm.
To solve this problem, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of the gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature of the gas in Kelvin (K)
First, let's convert the initial temperature from Celsius to Kelvin:
T1 = 67°C + 273.15 = 340.15 K
We are given:
V1 = 17 liters
P1 = 88.89 atm
T1 = 340.15 K
Now, let's convert the final temperature from Celsius to Kelvin:
T2 = 94°C + 273.15 = 367.15 K
We are given:
V2 = 12 liters
We can rearrange the ideal gas law equation to find the final pressure, P2:
P2 = (P1 * V1 * T2) / (V2 * T1)
Let's plug in the values:
P2 = (88.89 atm * 17 L * 367.15 K) / (12 L * 340.15 K)
P2 ≈ 136 atm
Therefore, the pressure of the gas, when the temperature is raised to 94 degrees C and the volume is decreased to 12 liters, is approximately 136 atm.