Density of Gases with Examples
Density of gases is too small with respect to solid and gas phases. We can find density with following formula;
if we substitute it into the ideal gas law;
P.V=n.R.T where n=mass/molar mass
As you can see from the formula; density of gases is directly proportional to pressure and molar mass and inversely proportional to temperature.
Example: Find density of C4H8 at 273 0C and under 2 atm pressure. (H=1, C=12)
Solution: we make unit conventions first;
Using formula given above;
Example: If we add some CH4 to container given below under constant temperature; which ones of the following statements are true related to gases in this container? (He=4, C=12, H=1)
I. Density of mixture increases
II. Volume increases
III. Pressure increases
Molar mass of CH4=12+4.1=16
Since piston of container is dynamic, when we add CH4, volume of mixture increases. Molar mass of CH4 is greater than He, thus density of mixture also increases.
Increasing in the volume of gas balance pressure and it stays constant.
Example: Which ones of the graphs are true for ideal gas.
I. Using ideal gas law;
Since R, n and V are constant, P is directly proportional to temperature. Graph I is true.
II. Molar volume is V/n. Using ideal gas law;
Since R, P and T are constant V/n must be constant. Thus second graph is false, line showing relation between V and n must be parallel to n.
III. We write ideal gas law for density;
Mm, R and P are constant , thus d is inversely proportional to T. III. graph is true.
Example: Graph given below shows density vs. volume relation of X(gas) at 00C. If the pressure of X(gas) at point A is 1 atm, which ones of the following statement are true for this gas.
II. Pressure at point B is 0,5 atm
III. Molar mass of gas is 56 g
I. Ideal gas law at point A;
T=0 0C or 273 K
I is false.
II. n and T are constant, thus we can write;
PB=0,5 atm, II is true
III. density at point A is;
1 mol gas contains 56 g, so III is true.
Example: Which ones of the following statements are true for He and O2 gases under same temperature. (He=4, O=16)
III. Average kinetic energies of He and O2 are equal.
We find pressures of gases using manometers.
To find relation between number of moles of gases we use ideal gas law.
Ratio of nHe and nO2
nHe/nO2=4/1 Thus, I is true.
We find density of gases again using ideal gas law.
Molar mass of He=4 and Molar mass of O2=2.16=32
Ratio of densities;
dHe/d/O2=1/4 so, II is false.
III. Since temperature of gases same, their average kinetic energies are also same. III is true.
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