what is the density of carbon dioxide at 26.5 degrees C and 755 mm Hg?
Use the modified general gas equation.
P*molar mass = density*RT
if i'm using PV=nRT, and manipulate that formula to V=nRT/P to find the volume, do i use 44.01g as my molar mass of CO2 and convert that to moles to find 'n'? i'm really confused how to do this b/c it's not at STP.
the answer i came up w/ is 1.76g/L. is this correct?
...but i did it a different way. i looked at an example in the textbook, but still don't really understand what i did.
for P, i calculated 0.993 atm
for n, i calculated 0.040 mol CO2
for T, i calculated 299.5 K
then, i calculated 0.040 mol CO2 x 44.01g/1 mol CO2 = 1.76 g CO2 (stoichiometry)
density = 1.76 g/L (but i don't understand how or why i went from 1.76 g CO2 to 1.76 g/L)
i'm very lost!! :(
To find the density of carbon dioxide at a given temperature and pressure, we need to use the ideal gas law and the formula for density.
The ideal gas law equation is:
PV = nRT
Where:
P = pressure (in pascals)
V = volume (in cubic meters)
n = number of moles
R = ideal gas constant (8.314 J/(mol·K))
T = temperature (in Kelvin)
To convert the given temperature of 26.5 degrees Celsius to Kelvin, we add 273.15:
T = 26.5 + 273.15 = 299.65 K
Since we are given the pressure in millimeters of mercury (mmHg), we need to convert it to pascals. The conversion factor is 1 atm = 101325 pascals and 1 atm = 760 mmHg:
P = (755 mmHg / 760 mmHg) * 101325 pascals = 100586.197 pascals
Now we need to find the molar mass of carbon dioxide (CO2), which is the sum of the atomic masses of carbon (C) and oxygen (O), taking into account the number of atoms present. The atomic masses are approximately 12.01 g/mol for carbon and 16.00 g/mol for oxygen:
molar mass of CO2 = (12.01 g/mol) + (16.00 g/mol x 2) = 44.01 g/mol
Next, we need to find the number of moles of CO2. To do this, we divide the given pressure by the ideal gas constant and the temperature:
n = PV / RT
Plugging in the values:
n = (100586.197 pascals) / (8.314 J/(mol·K) * 299.65 K) = 40.27 moles
Finally, we can calculate the density using the formula:
density = mass / volume
Since the molar mass of CO2 is 44.01 g/mol and 1 mole of any gas occupies 22.4 liters at standard temperature and pressure (273.15 K and 1 atm), we can calculate the volume of 40.27 moles of CO2:
volume = 40.27 mol * 22.4 L/mol = 902.15 L
Now we can calculate the density:
density = (molar mass * n) / volume
density = (44.01 g/mol * 40.27 mol) / 902.15 L = 1.96 g/L
Therefore, the density of carbon dioxide at 26.5 degrees C and 755 mm Hg is approximately 1.96 g/L.