"The analyzer said that at 20degreesC the unknown gas was 82.8% carbon by weight and 17.2% hydrogen. The analyzer also diffused the gas through a special apparatus and measured the rate of its diffusion compared to how fast oxygen gas diffused under the same conditions. The rates of diffusion were 5.0cm(cubed)/sec for oxygen gas and 3.7cm(cubed)/for unknown gas. With this information figure out the molecular formula for the unknown gas
See your post above.
To determine the molecular formula of the unknown gas, we need to analyze the relative masses of carbon and hydrogen present in the gas and use the information about the rates of diffusion compared to oxygen gas.
First, let's calculate the mass percent of carbon and hydrogen in the unknown gas:
Mass percent of carbon = (mass of carbon / total mass of gas) * 100
Mass percent of hydrogen = (mass of hydrogen / total mass of gas) * 100
Given that the unknown gas is 82.8% carbon by weight and 17.2% hydrogen, we can assume a total mass of 100 grams to simplify the calculations:
Mass of carbon = 82.8 grams (82.8% of 100 grams)
Mass of hydrogen = 17.2 grams (17.2% of 100 grams)
Next, we need to calculate the molar masses of carbon and hydrogen:
Molar mass of carbon = 12.01 g/mol
Molar mass of hydrogen = 1.008 g/mol
Now, we will determine the number of moles of carbon and hydrogen in the gas by dividing the masses by their respective molar masses:
Number of moles of carbon = Mass of carbon / Molar mass of carbon
Number of moles of hydrogen = Mass of hydrogen / Molar mass of hydrogen
Now, let's calculate the ratio of moles of carbon to moles of hydrogen:
Ratio of moles of carbon to moles of hydrogen = Number of moles of carbon / Number of moles of hydrogen
Finally, we need to relate the rates of diffusion with the molar masses of the gases. The rate of diffusion is inversely proportional to the molar mass of the gas according to Graham's Law of Diffusion:
Rate of diffusion of unknown gas / Rate of diffusion of oxygen gas = Square root of (Molar mass of oxygen gas / Molar mass of unknown gas)
We know the rates of diffusion are 5.0 cm³/s for oxygen gas and 3.7 cm³/s for the unknown gas, so we can substitute these values into the equation above.
Now, we have two equations:
Ratio of moles of carbon to moles of hydrogen = Number of moles of carbon / Number of moles of hydrogen
Rate of diffusion of unknown gas / Rate of diffusion of oxygen gas = Square root of (Molar mass of oxygen gas / Molar mass of unknown gas)
By solving these equations simultaneously, we can determine the molecular formula of the unknown gas.