If 2.4 m3 of a gas initially at STP is compressed to 1.6 m3 and its temperature raised to 30oC, what is the final pressure?
(P1V1)/T1 = (P2V2)/T2
Don't forget to convert T to Kelvin.
168689.42
To find the final pressure of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
Since we have the initial and final volume, as well as the initial and final temperature, we can calculate the final pressure.
First, let's calculate the initial pressure using the values for the initial volume and temperature at STP (Standard Temperature and Pressure). At STP, the temperature is 0°C or 273.15 K, and the pressure is 1 atmosphere or 101.3 kPa.
Considering the values at STP, we can express them as follows:
P initial * V initial = n * R * T initial
Now, let's calculate the final pressure using the final volume and temperature:
P final * V final = n * R * T final
Since the initial and final number of moles and the ideal gas constant (R) are the same, we can set up the following equation:
P initial * V initial / T initial = P final * V final / T final
Now we can rearrange the equation to solve for the final pressure:
P final = (P initial * V initial * T final) / (V final * T initial)
Substituting the values:
P final = (1 atm * 2.4 m^3 * (30 + 273.15) K) / (1.6 m^3 * 273.15 K)
Simplifying the equation:
P final = 4.1 atm
Therefore, the final pressure of the gas is 4.1 atm.