What is the density of CO2 gas at -25.2 degrees celsius and 98.0kPa?
PV=nRT
density =mass/volume =mass/V
n=mass/M where M = molar mass
PV=mass R T /M
rearrange
PM/RT=mass/V=density
Oh and with questions like this it is worth making sure that the question makes sense.
In this case -25.2 degrees celsius and 98.0kPa is located below and to the right of the triple point for CO2 see
http://stevengoddard.files.wordpress.com/2010/09/co2_phase_diagram.gif?w=500&h=380
and so is definitely a gas.
To find the density of CO2 gas at -25.2 degrees Celsius and 98.0 kPa, we can use the ideal gas law and the equation for density.
The ideal gas law is given by:
PV = nRT
Where:
P = pressure (in pascals)
V = volume (in cubic meters)
n = number of moles
R = ideal gas constant (8.31 J/(mol·K))
T = temperature (in Kelvin)
First, we need to convert the temperature from Celsius to Kelvin by adding 273.15:
T = -25.2 + 273.15 = 247.95 K
Now, we rearrange the ideal gas law equation to solve for n/V (number of moles per unit volume):
n/V = (P / RT)
Next, we need to find the molar mass of CO2, which is the sum of the atomic masses of one carbon atom and two oxygen atoms:
Molar mass (CO2) = (12.01 g/mol) + 2 * (16.00 g/mol) = 12.01 g/mol + 32.00 g/mol = 44.01 g/mol
Now, we can calculate the density using the equation:
Density = (n / V) * (molar mass)
Density = ((P / RT) * (molar mass)
Substituting the given values:
Density = ((98.0 kPa) / (8.31 J/(mol·K) * 247.95 K) * (44.01 g/mol)
Note: We convert the pressure from kPa to pascals (Pa) for consistent units.
Thus, the density of CO2 gas at -25.2 degrees Celsius and 98.0 kPa is given by the calculations above.