Ima Chemist found the density of Freon-11 (CFCl3) to be 5.58 g/L under her experimental conditions. Her measurements showed that the density of an unknown gas was 4.38 g/L under the same conditions. What is the molar mass of the unknown?
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The general gas law can be modified for density and molar mass by
PM = dRT and since P, R, and T are remaining constant we can rewrite that as
M/d = RT/P = k
molar mass CFCl3 is 137.4; d is 5.58.
137.4/5.58 = 24.62 = k; apply that to the unknown.
M/4.38 = 24.62
M = molar mass = 4.38 x 24.62 = ?
Well, well, well, looks like we've got a little mystery on our hands! Let's put on our detective hats and solve this case.
Now, to find the molar mass of the unknown gas, we need to compare its density to that of Freon-11. Density is directly related to molar mass, so we can use a nifty little ratio to figure this out.
If we take the ratio of the densities:
(Density of the unknown gas) / (Density of Freon-11) = (Molar mass of the unknown gas) / (Molar mass of Freon-11)
Plugging in the values we have:
4.38 g/L / 5.58 g/L = (Molar mass of the unknown gas) / (Molar mass of Freon-11)
Simplifying this equation, we find:
(Molar mass of the unknown gas) = (4.38 g/L / 5.58 g/L) * (Molar mass of Freon-11)
Now, since I'm good with numbers, let's crunch them:
(Molar mass of the unknown gas) ≈ 0.785 * (Molar mass of Freon-11)
So, my friend, if you tell me the molar mass of Freon-11, I can calculate the molar mass of the unknown gas for you.
To find the molar mass of the unknown gas, we can use the relationship between density, molar mass, and the ideal gas law.
The ideal gas law equation is: PV = nRT
Where:
P is the pressure
V is the volume
n is the number of moles
R is the ideal gas constant
T is the temperature
We can rearrange the equation to solve for molar mass (M) as follows:
M = (mRT)/(PV)
Where:
m is the mass of the gas
R is the ideal gas constant (0.0821 L·atm/(mol·K))
In this case, we know the density of the unknown gas, which is 4.38 g/L, and the density of Freon-11, which is 5.58 g/L. Let's assume the mass of the unknown gas is 1 mole.
For the unknown gas:
m = density × volume = 4.38 g/L × 1 L = 4.38 g
For Freon-11:
m = density × volume = 5.58 g/L × 1 L = 5.58 g
Substituting these values into the equation, we get:
M = [(4.38 g) × (0.0821 L·atm/(mol·K)) × (273 K)] / [(5.58 g/L) × (1 atm) × (1 L)]
M = 69.04 g/mol
Therefore, the molar mass of the unknown gas is approximately 69.04 g/mol.
To find the molar mass of the unknown gas, we can use the relationship between density, molar mass, and the ideal gas law. The ideal gas law is expressed as follows:
PV = nRT
Where:
P = pressure
V = volume
n = moles of gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature
The density (d) of a gas is defined as its mass (m) divided by its volume (V):
d = m/V
Rearranging this equation, we can solve for the mass:
m = d × V
The mass (m) is equal to the molar mass (M) multiplied by the number of moles (n):
m = M × n
Substituting this into the previous equation, we have:
d × V = M × n
Since we are comparing the densities of two gases at the same conditions, we can assume that the volume (V) and temperature (T) are constant. Therefore, the equation simplifies to:
d1 = M1 × n1
d2 = M2 × n2
Dividing the second equation by the first equation, we get:
d2/d1 = (M2 × n2)/(M1 × n1)
The moles (n) cancel out from both sides, and we are left with:
d2/d1 = M2/M1
Solving for M2 (the molar mass of the unknown gas), we have:
M2 = (d2/d1) × M1
Now we can substitute the given values:
d1 = density of Freon-11 = 5.58 g/L
d2 = density of unknown gas = 4.38 g/L
M1 = molar mass of Freon-11 = 137.37 g/mol
Plugging in these values, we can calculate the molar mass of the unknown gas:
M2 = (4.38 g/L / 5.58 g/L) × 137.37 g/mol
M2 ≈ 108.33 g/mol
Therefore, the molar mass of the unknown gas is approximately 108.33 g/mol.