four moles of gas are contained in 2 litre vessel at the temperature of 200c at a pressure of 10atm.the gas is allowed to expand to anew volume of a 4litres ,but at the same time maintening the original temperature.what is the new pressure?
To find the new pressure of the gas when it expands to a volume of 4 liters while maintaining the original temperature, you can use the Ideal Gas Law equation:
PV = nRT
Where:
P = pressure
V = volume
n = moles of gas
R = ideal gas constant
T = temperature (in Kelvin)
First, we need to convert the temperature from Celsius to Kelvin. The Kelvin temperature scale starts from absolute zero, and 0°C is equal to 273.15K.
Given:
n = 4 moles
V1 = 2 liters (initial volume)
T1 = 200°C = 200 + 273.15 = 473.15K
V2 = 4 liters (final volume)
T2 = T1 (as the temperature is maintained)
Now, we can substitute the values into the formula:
P1V1/T1 = P2V2/T2
P1 = 10 atm (initial pressure)
V1 = 2 liters
T1 = 473.15K
V2 = 4 liters
T2 = 473.15K
10 * 2 / 473.15 = P2 * 4 / 473.15
Simplifying the equation:
20 / 473.15 = P2 / 118.29
Now, cross-multiply and solve for P2:
P2 = (20 / 473.15) * 118.29
P2 ≈ 4.997 atm
Therefore, the new pressure of the gas when it expands to a volume of 4 liters while maintaining the original temperature is approximately 4.997 atm.