Find the density and specific gravity of the following
(a) SO2 at 700F and 1 atm
(b) Mixture of 10 mole% CH4 and 90 mole% argon at 5400C and 28.9 inch Hg
(c) Air containing 0.045 lbm H2O per pound mass of dry air at 2000F and 29.7 in Hg absolute pressure
To find the density and specific gravity of the given substances, we need to use the ideal gas law and the properties of the gases involved. Here's how you can calculate them:
(a) SO2 at 700°F and 1 atm:
To find the density, we need to use the ideal gas law, which is given by:
PV = nRT
Where:
P = pressure (1 atm)
V = volume (can be assumed to be 1 mole)
n = number of moles of gas
R = ideal gas constant (0.0821 atm·L/mol·K)
T = temperature (700°F converted to Kelvin)
Rearranging the equation, we get:
n/V = P/(RT)
The molar mass of sulfur dioxide (SO2) is approximately 64 g/mol.
Using the n/V ratio, we can calculate the density of SO2:
Density = (n/V) * molar mass
(b) Mixture of 10 mole% CH4 and 90 mole% argon at 540°C and 28.9 inches Hg:
Similar to part (a), we can use the ideal gas law to calculate the density of this mixture. However, since it is a mixture of gases, we need to consider the molar fractions of each gas in the mixture.
The molar fraction of CH4 is 10% (0.10), and the molar fraction of argon is 90% (0.90).
We can use the following equation to calculate the density of the mixture:
Density_mixture = Sum(density of each gas * molar fraction of each gas)
To find the specific gravity, we need to compare the density of the mixture to the density of a reference substance at the same conditions. Typically, air at the given temperature and pressure is used as the reference substance. The specific gravity is calculated by:
Specific gravity = Density_mixture / Density_air
(c) Air containing 0.045 lbm H2O per pound of dry air at 200°F and 29.7 in Hg absolute pressure:
To find the density of this air-water mixture, we first need to find the molar mass of the dry air and the molar mass of water vapor. Then, we can use the ideal gas law to calculate the density.
The molar mass of dry air is approximately 28.97 g/mol, and the molar mass of water vapor is approximately 18.02 g/mol.
Using the known molar mass values, we can find the number of moles of dry air, n_dryair, and the number of moles of water vapor, n_water:
n_dryair = (mass of dry air) / (molar mass of dry air)
n_water = (mass of water vapor) / (molar mass of water vapor)
Then, the total number of moles of gas, n_total, can be determined by adding n_water to n_dryair.
Finally, we can use the ideal gas law to calculate the density of the air-water mixture using the following equation:
Density = (n_total * (RT))/(mass of dry air + mass of water vapor)
To calculate the specific gravity, we can compare the density of the mixture to the density of a reference substance, which is typically dry air at the given temperature and pressure, using the same equation as mentioned in part (b).