3 moles of an ideal gas initially at a pressure of 1 atm and a temprature of 100°C are expanded to twice the initial volume and then heated to 200°C at the new volume.What is the final pressure in atm?
(P1V1/T1) = (P2V2/T2)
You don't need to use moles of gas if you use this formula. Notice that you have no initial volume and no actual final volume (just twice the initial). I would pick a convenient number (any number) for V1 and multiply that by 2 for V2.
To find the final pressure of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, let's convert the initial temperature from Celsius to Kelvin:
T1 = 100°C + 273.15 = 373.15 K
Next, let's calculate the initial volume using the given conditions. Since the gas is expanded to twice the initial volume, we can find V2 as follows:
V2 = 2 * V1
Let's substitute the values into the ideal gas law equation for the initial state:
(1 atm) * V1 = (3 moles) * (0.0821 L·atm/(mol·K)) * (373.15 K)
Simplifying the equation:
V1 = (3 moles) * (0.0821 L·atm/(mol·K)) * (373.15 K) / (1 atm)
V1 ≈ 91.85 L
Now, let's calculate the final volume at the new temperature, which is given as T2 = 200°C:
T2 = 200°C + 273.15 = 473.15 K
Since the volume is doubled, we can find the final volume V2:
V2 = 2 * V1 ≈ 2 * 91.85 L ≈ 183.7 L
Finally, let's solve for the final pressure P2 using the ideal gas law equation with the final volume and temperature:
P2 * V2 = (3 moles) * (0.0821 L·atm/(mol·K)) * (473.15 K)
P2 ≈ [(3 moles) * (0.0821 L·atm/(mol·K)) * (473.15 K)] / (183.7 L)
Calculating the final pressure:
P2 ≈ 3.16 atm
Therefore, the final pressure of the gas is approximately 3.16 atm.