A gas of unknown identity diffuses at a rate of 83.3 mL/s in a diffusion apparatus in which carbon dioxide diffuses at the rate of 102 mL/s. Calculate the molecular mass of the unknown gas. Give your answers in units of g/mol to three significant figures.
Grahams Law: Rate of diffusionis inversely prop to sqrt of mass
102/83.3 = sqrt (M/44) (molmass CO2 is 44amu)
Mass= (102/83.3)^2 *44
To determine the molecular mass of the unknown gas, we can use Graham's law of diffusion, which states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.
According to Graham's law, the ratio of the diffusion rates can be expressed as:
Rate of unknown gas / Rate of CO2 = sqrt(molar mass of CO2 / molar mass of unknown gas)
Let's substitute the given values into this equation:
83.3 mL/s / 102 mL/s = sqrt(Molar mass of CO2 / Molar mass of unknown gas)
Simplifying the left side:
0.816 = sqrt(Molar mass of CO2 / Molar mass of unknown gas)
To isolate the molar mass of the unknown gas, we can square both sides of the equation:
0.816^2 = (Molar mass of CO2 / Molar mass of unknown gas)
0.667456 = Molar mass of CO2 / Molar mass of unknown gas
Now, rearrange the equation to solve for the molar mass of the unknown gas:
Molar mass of unknown gas = Molar mass of CO2 / 0.667456
The molecular mass of carbon dioxide (CO2) is approximately 44.01 g/mol.
Let's substitute this value into the equation:
Molar mass of unknown gas = 44.01 g/mol / 0.667456
Calculating the right side:
Molar mass of unknown gas ≈ 65.98 g/mol
Therefore, the molecular mass of the unknown gas is approximately 65.98 g/mol.
To calculate the molecular mass of the unknown gas, we can use Graham's law of diffusion. According to Graham's law, the rate of diffusion is inversely proportional to the square root of the molecular masses of the gases.
The formula for Graham's law is:
Rate1 / Rate2 = sqrt(Molar Mass2 / Molar Mass1)
Let's plug in the given values:
83.3 mL/s (rate of the unknown gas) / 102 mL/s (rate of CO2) = sqrt(Molar Mass CO2 / Molar Mass Unknown gas)
Simplifying the formula, we get:
sqrt(Molar Mass Unknown gas) = (83.3 / 102) * sqrt(Molar Mass CO2)
Now we can solve for the molar mass of the unknown gas:
(Molar Mass Unknown gas) = ((83.3 / 102) * sqrt(Molar Mass CO2))^2
Using the known molar mass of carbon dioxide (CO2) as 44.01 g/mol, we can substitute this value into the formula:
(Molar Mass Unknown gas) = ((83.3 / 102) * sqrt(44.01))^2
Calculating this expression, we find:
(Molar Mass Unknown gas) ≈ 28.29 g/mol
Therefore, the molecular mass of the unknown gas is approximately 28.29 g/mol.