In an effusion 15 ml of HBr effused in 1.0 min. In the same apparatus under the same conditions, 20.3 ml of an unknown gas diffused in 1.0 min. If the unknown contains only carbon and hydrogen. determine the molecular formula of the unknown gas,
To determine the molecular formula of the unknown gas, we need to compare the effusion rates of the two gases and use the molar masses of carbon and hydrogen to calculate the possible molecular formulas.
First, let's compare the effusion rates of the two gases. We have the following information:
Effusion rate of HBr (HBr): 15 ml/1 min
Effusion rate of unknown gas (UNK): 20.3 ml/1 min
To compare the effusion rates, we can use Graham's Law of Effusion. According to Graham's law, the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
Mathematically, the ratio of effusion rates is given by:
(r1/r2) = √(M2/M1)
Where r1 and r2 are the rates of effusion of gases 1 and 2, and M1 and M2 are the molar masses of gases 1 and 2, respectively.
Let's plug in the values we have:
(r1/r2) = (√M2/√M1) = (15/20.3)
Squaring both sides of the equation, we get:
(M2/M1) = (15/20.3)^2
Now, let's calculate the ratio of molar masses:
M2/M1 = (15/20.3)^2
M2/M1 ≈ 0.678
To determine the molecular formula of the unknown gas, we need to consider the possible combinations of carbon and hydrogen that could have a molar mass ratio close to 0.678.
The molar masses of carbon and hydrogen are approximately 12.01 g/mol and 1.01 g/mol, respectively. Let's calculate the molar mass ratio for possible molecular formulas:
- C1H1 (methane): M2/M1 = (12.01/1.01) ≈ 11.90
- C2H2 (ethyne): M2/M1 = (24.02/2.02) ≈ 11.88
- C3H3: M2/M1 = (36.03/3.03) ≈ 11.88
- C4H4: M2/M1 = (48.04/4.04) ≈ 11.88
- C5H5: M2/M1 = (60.05/5.05) ≈ 11.88
As you can see, none of these molecular formulas match the calculated molar mass ratio of 0.678.
Therefore, based on the information provided, it is not possible to determine the molecular formula of the unknown gas containing only carbon and hydrogen. Additional information or experimental data would be required to determine the molecular formula accurately.