What volume would 10.5 g of nitrogen gas, N2 occupy at 200.K and 2.02 atm.
To determine the volume of nitrogen gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = Pressure (in atm)
V = Volume (in liters)
n = Number of moles
R = Ideal gas constant (0.0821 L·atm/mol·K)
T = Temperature (in Kelvin)
First, let's convert the temperature from degrees Celsius to Kelvin by adding 273.15:
T = 200 K
Now, we need to convert the mass of nitrogen gas to moles using its molar mass. The molar mass of N2 is:
Molar mass of N2 = (2 x Atomic mass of Nitrogen) = (2 x 14.01 g/mol) = 28.02 g/mol
Number of moles (n) = Mass (m) / Molar mass (M)
n = 10.5 g / 28.02 g/mol
After performing the calculation, we find that the number of moles of nitrogen gas is approximately 0.374 mol.
Now, we can rearrange the ideal gas law equation to solve for volume (V):
V = (nRT) / P
Substituting the given values:
V = (0.374 mol) x (0.0821 L·atm/mol·K) x (200 K) / (2.02 atm)
After calculating this expression, we find that the volume of 10.5 g of nitrogen gas at 200 K and 2.02 atm is approximately 7.19 L.