if the volume of a gas is 500cm3 at 127degree centigrade and 380mm of mercury, calculate the volume of this gas at s.t.p
To calculate the volume of a gas at Standard Temperature and Pressure (STP), we need to use the ideal gas law, which states:
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)
Given:
Volume of the gas (V1) = 500 cm^3
Temperature (T1) = 127 degrees Celsius = 127 + 273 = 400 Kelvin
Pressure (P1) = 380 mm of mercury
First, we need to convert the volume from cm^3 to liters:
V1 (in liters) = V1 (in cm^3) / 1000
V1 (in liters) = 500 / 1000
V1 (in liters) = 0.5 liters
Next, we need to convert the pressure from mmHg to atm:
P1 (in atm) = P1 (in mmHg) / 760
P1 (in atm) = 380 / 760
P1 (in atm) = 0.5 atm
Now we can use the ideal gas law to calculate the number of moles of gas (n):
n = (P1 * V1) / (R * T1)
n = (0.5 * 0.5) / (0.0821 * 400)
n = 0.006104 moles (rounded to four decimal places)
Finally, we can calculate the volume of the gas at STP (V2) using the molar volume of gas at STP, which is 22.4 liters/mole:
V2 = (n * V2) / n
V2 = (0.006104 * 22.4) / 0.006104
V2 = 22.4 liters
Therefore, the volume of the gas at STP is 22.4 liters.