In a tank volume of 50 liters of gas contained oxygen at a temperature of 57º C and a pressure of 75 atm . What is the mass of the gas ?
PV = nRT and solvle for n, then n = grams/molar mass = ?
To find the mass of a gas, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, let's convert the temperature from Celsius to Kelvin:
T(K) = T(C) + 273.15
T(K) = 57 + 273.15
T(K) = 330.15 K
Next, convert the pressure from atm to pascals (Pa):
1 atm = 101325 Pa
P(Pa) = P(atm) * 101325
P(Pa) = 75 * 101325
P(Pa) = 7599375 Pa
Now, let's rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
Rearranging further, we get:
n = (P * V) / (R * T)
We'll need to know the molar mass of oxygen (O2) to calculate the mass. The molar mass of oxygen is approximately 32 g/mol.
Finally, we can calculate the mass of the gas:
mass = n * molar mass
Let's substitute the values into the equation:
mass = ((P * V) / (R * T)) * molar mass
mass = ((7599375 * 50) / (8.314 * 330.15)) * 32
Calculating the expression will give us the mass of the gas in grams. Simply plug in the values into a calculator or spreadsheet to determine the answer.