Two liters of a perfect gas are at 0 degree C and 1 atm.If the gas is nitrogen, N2.
Determine the number of moles?
Determine the mass of the gas?
Perfect gas? Nitrogen? You have to be kidding.
PV=nRT
1atm*2liters=n*R*273 solve for n, thenumbe of moles. Watch what units of R you use atm, liters...
mass of the gas=n*molemassN2
To determine the number of moles of nitrogen gas (N2) and the mass of the gas, we can use the ideal gas equation and the molar mass of nitrogen.
Step 1: Determine the molar mass of nitrogen (N2)
The molar mass of nitrogen (N2) is calculated by summing the atomic masses of its constituent elements: nitrogen (N).
The atomic mass of nitrogen (N) is approximately 14.01 g/mol.
Since nitrogen gas (N2) consists of two nitrogen atoms, we multiply the atomic mass by 2:
Molar mass of N2 = (2 * 14.01 g/mol) = 28.02 g/mol
Step 2: Convert the volume to moles using the ideal gas equation
The ideal gas equation is given by:
PV = nRT
Where:
P = pressure in atm
V = volume in liters
n = number of moles
R = ideal gas constant (0.0821 atm⋅L/mol⋅K)
T = temperature in Kelvin (K)
Given that the volume is 2 liters, the pressure is 1 atm, and the temperature is 0 degrees Celsius, let's convert the temperature to Kelvin:
T(K) = T(°C) + 273.15
= 0 + 273.15
= 273.15 K
Now we can rearrange the ideal gas equation to solve for the number of moles:
n = PV / (RT)
Substituting the values:
n = (1 atm * 2 L) / [(0.0821 atm⋅L/mol⋅K) * 273.15 K]
n = 0.0733 mol (rounded to four decimal places)
Therefore, the number of moles of nitrogen (N2) gas is approximately 0.0733 mol.
Step 3: Calculate the mass of the gas
To calculate the mass of the gas, we can multiply the number of moles by the molar mass of nitrogen (N2):
Mass = number of moles * molar mass
Mass = 0.0733 mol * 28.02 g/mol
Mass = 2.048 g (rounded to three decimal places)
Therefore, the mass of the nitrogen gas (N2) is approximately 2.048 grams.
To determine the number of moles of gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (1 atm in this case)
V = volume (2 liters)
n = number of moles (what we are trying to find)
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin (0 degree Celsius = 273.15 Kelvin)
Rearranging the equation to solve for moles:
n = PV / RT
Substituting the given values:
n = (1 atm * 2 L) / (0.0821 L·atm/(mol·K) * 273.15 K)
n ≈ 0.091 moles
Therefore, there are approximately 0.091 moles of nitrogen gas.
To determine the mass of the gas, we can use the molar mass of nitrogen. The molar mass of N2 is approximately 28 g/mol.
Using the equation:
Mass = moles * molar mass
Mass = 0.091 moles * 28 g/mol
Mass ≈ 2.548 grams
Therefore, the mass of the nitrogen gas is approximately 2.548 grams.