Understanding Methanol Vapor Density Using Ideal Gas Law

Determining the vapor density of methanol (CH3OH) at standard temperature and pressure (STP) can be approached using the ideal gas law and its fundamental definitions. We will walk through the steps to calculate the vapor density of 64 grams of CH3OH when it occupies a volume of 44.8 liters.

Step 1: Determine the Molar Mass of Methanol

To find the number of moles of methanol (CH3OH), we start by calculating its molar mass. Methanol consists of one carbon (C), four hydrogen (H) atoms, and one oxygen (O) atom.

Carbon (C): 12.01 g/mol Hydrogen (H): 1.008 g/mol × 4 4.032 g/mol Oxygen (O): 16.00 g/mol

The molar mass of CH3OH can be calculated as follows:

Total Molar Mass of CH3OH:

32.042 g/mol

Now, we can find the number of moles in 64 grams of CH3OH:

Number of Moles:

Number of Moles frac{64 text{ g}}{32.042 text{ g/mol}} approx 1.997 text{ mol}

Step 2: Calculate the Vapor Density

Vapor density is defined as the mass of the gas divided by the volume it occupies at a given temperature and pressure. The formula for vapor density (d) is:

d frac{text{mass}}{text{volume}}end{code>

Given that the mass of CH3OH is 64 grams and it occupies 44.8 liters at STP, we can substitute these values into the formula:

Vapor Density:

d frac{64 text{ g}}{44.8 text{ L}} approx 1.43 text{ g/L}end{code>

Conclusion

The vapor density of methanol (CH3OH) when 64 grams occupies 44.8 liters at STP is approximately 1.43 g/L.

Note:

The provided information regarding the molar mass and the volume occupied by 64 grams of CH3OH at STP assumes ideal behavior. In reality, at STP, the vapor pressure of methanol is around 30 mm or 0.04 atm, which means that 64 grams of methanol would not occupy 44.8 liters but would instead be mixed with air, significantly reducing the concentration of CH3OH in the vapor phase. This real-world scenario introduces variables that make the problem entirely theoretical for the purpose of applying the ideal gas law but cannot be accurately solved with the provided data.

Keywords: vapor density, methanol, STP