A cylinder with a moveable piston holds 2.40 mol of argon at a constant temperature of 295 K. As the gas is compressed isothermally, its pressure increases from 101 kPa to 141 kPa. What is the final volume of the gas? I don't know where to begin. I tried using Pv=nRT: [(2.4)(8.31)(295)]/ 40 = 147.087. This is wrong. I wasn't sure if I use the difference in pressure and if I have to convert from kPa to Pa. Can anyone help?
You have to work this in Pascals, Volume will be in m3
I'm having the same problem
To solve this problem, you can use the ideal gas law, which is represented by the equation PV = nRT, where P is the pressure of the gas, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
Here's the step-by-step process to find the final volume of the gas:
1. Convert the initial and final pressures from kilopascals (kPa) to pascals (Pa). Since 1 kPa = 1000 Pa, the initial pressure is 101 kPa * 1000 = 101,000 Pa, and the final pressure is 141 kPa * 1000 = 141,000 Pa.
2. Convert the number of moles from mol to SI units. Since 1 mol = 6.022 x 10^23 particles, the number of moles of argon is 2.40 mol.
3. Convert the temperature from Celsius to Kelvin. You are given that the temperature is 295 K, so no conversion is needed.
4. Substitute the known values into the ideal gas law equation: P1 * V1 = n * R * T, where P1 is the initial pressure, V1 is the initial volume (which is what you need to find), n is the number of moles, R is the ideal gas constant (8.31 J/mol·K), and T is the temperature.
5. Rearrange the equation to solve for V1: V1 = (n * R * T) / P1.
6. Plug in the values: V1 = (2.40 mol * 8.31 J/mol·K * 295 K) / 101,000 Pa.
7. Calculate the result: V1 = 0.0561 m^3.
Therefore, the final volume of the gas is approximately 0.0561 cubic meters.