An empty flask weighs 123.591 g. After vaporization of a sample of volatile liquid at a temperature of 99.9 °C, the flask was sealed, cooled to room temperature, and found to have a mass of 123.907 g. The atmospheric pressure was 760.2 mm Hg. The flask was rinsed and completely filled with water at 18.5 °C. The mass of the water-filled flask was determined to be 375.639 g.

What is the mass of the gas that fills the flask in grams?

The mass of the gas that fills the flask is 0.316 grams. To find the mass of the gas, we need to consider the changes in mass and volume of the flask before and after vaporization.

Firstly, we calculate the change in mass of the flask after vaporization, which is 123.907 g - 123.591 g = 0.316 g. This change in mass represents the mass of the vaporized liquid.

Next, we need to determine the volume of the flask. Since the flask was completely filled with water at 18.5 °C, we can assume that the volume of the flask is equal to the volume of water it can hold. We can use the density of water, which is approximately 1 g/cm³, to convert the mass of the water-filled flask (375.639 g) to volume.

Volume = Mass / Density = 375.639 g / 1 g/cm³ = 375.639 cm³

Now we need to consider the ideal gas law to relate the volume and mass of the gas at room temperature and pressure. 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, and T is the temperature in Kelvin.

Since we know the temperature and pressure, we can rearrange the ideal gas law equation to solve for the number of moles (n):

n = PV / RT

Converting the pressure from mm Hg to atm (atmospheres) and the temperature from Celsius to Kelvin:

P = 760.2 mm Hg / 760 mm Hg/atm = 1 atm

T = 18.5 °C + 273.15 = 291.65 K

Substituting the values into the equation, we get:

[tex]n = (1 atm) \times (375.639 cm^3) / [(0.0821 L\,atm/mol\,K) \times (291.65 K)]=0.0123 mol[/tex]

Finally, we convert the moles of gas to grams using the molar mass of the gas. Since the identity of the gas is not provided, we cannot determine its molar mass precisely. However, assuming the gas is a volatile organic compound, we can estimate its molar mass to be around 26 g/mol. Therefore, the mass of the gas is:

[tex]Mass = moles \times molar mass = (0.0123 mol) \times (26 g/mol) = 0.316 g[/tex]

Hence, the mass of the gas that fills the flask is approximately 0.316 grams.

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