one mole of an ideal gas is allowed to expand isothermally at 29.3 degree celsius from a volume of 4.0 litres and pressure of 5.0 atm to a volume of 10.0l and pressure of 2.0atm
To solve this problem, we can use the ideal gas law equation:
PV = nRT
Where:
P = Pressure
V = Volume
n = moles of gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin
The first step is to convert the given temperature from Celsius to Kelvin. To do that, we add 273.15 to the Celsius temperature:
T = 29.3°C + 273.15 = 302.45 K
Next, we need to calculate the number of moles of gas (n) using the ideal gas law:
n = PV / RT
For the initial conditions:
P1 = 5.0 atm
V1 = 4.0 L
R = 0.0821 L·atm/(mol·K)
T = 302.45 K
Plugging in these values, we get:
n1 = (5.0 atm * 4.0 L) / (0.0821 L·atm/(mol·K) * 302.45 K) ≈ 0.827 moles
Now, let's find the final number of moles (n2). Since the process is isothermal, the number of moles remains constant.
n2 = n1 = 0.827 moles
Finally, we can calculate the final volume (V2) using the ideal gas law:
V2 = n2RT / P2
For the final conditions:
P2 = 2.0 atm
R = 0.0821 L·atm/(mol·K)
T = 302.45 K
Plugging in these values, we get:
V2 = (0.827 moles * 0.0821 L·atm/(mol·K) * 302.45 K) / 2.0 atm ≈ 10.63 L
Therefore, the final volume (V2) is approximately 10.63 L.
To solve this problem, we can use the ideal gas law equation, which states:
PV = nRT
Where:
- P is the pressure of the gas,
- V is the volume of the gas,
- n is the number of moles of gas,
- R is the ideal gas constant (0.0821 L·atm/(mol·K)), and
- T is the temperature in Kelvin.
We are given the pressure, volume, and temperature of the gas. Let's solve for n, the number of moles of gas:
n = PV / RT
1. Convert the given temperature from Celsius to Kelvin:
T = 29.3 °C + 273.15 = 302.45 K
2. Substitute the given values into the equation:
n = (5.0 atm * 4.0 L) / (0.0821 L·atm/(mol·K) * 302.45 K)
n ≈ 0.52 moles
Therefore, we have 0.52 moles of gas.
Now, let's use the ideal gas law again to find the new volume:
V = (nRT) / P
1. Substitute the given values into the equation:
V = (0.52 moles * 0.0821 L·atm/(mol·K) * 302.45 K) / 2.0 atm
V ≈ 6.74 L
Therefore, the final volume of the gas after expansion is approximately 6.74 L.