An empty flask weighs 128.632g. After vaporization of a sample of volatile liquid, at a measured temperature of 99.8 C. The flask is sealed, cooled to room temperature, and weighed. The mass is now 129.225g. The measured P atm is 757.7 torr. The flask is rinsed and filled completely with water at 21.8 C. The mass of the flask is now 381.676g.
1. Calculate the volume of the flask from the mass of the water contained in the flask and the density.
2. Calculate the molar mass of the volatile liquid.
Have you worked through this for an answer and want us to check it? If so, what have you done? Give us an indication of the procedure you have used.
To solve these problems, we will need to use the following formulas and concepts:
1. Density (d) is defined as mass (m) divided by volume (V):
d = m/V
2. The ideal gas law equation relates the pressure (P), volume (V), number of moles (n), and temperature (T) of a gas:
PV = nRT
3. Molar mass (M) is the mass of one mole of a substance. It can be calculated using the formula:
M = m/n
Now let's solve the problems step by step:
1. Calculate the volume of the flask from the mass of the water contained in the flask and the density:
First, we need to find the mass of the water in the flask.
Mass of water = Mass of flask + Water - Mass of flask
= 381.676g - 128.632g
= 253.044g
Next, we need the density of water. At room temperature, the density of water is around 1 g/cm³ or 1000 kg/m³.
To convert this density to g/mL, divide by 1000:
Density of water = 1 g/cm³ = 1 g/mL
Using the density formula, we can find the volume of the flask:
Volume = Mass/Density
= 253.044g/1 g/mL
= 253.044 mL
Therefore, the volume of the flask is 253.044 mL.
2. Calculate the molar mass of the volatile liquid:
Firstly, we need to convert the pressure from torr to atm. Since 1 atm = 760 torr, we have:
Pressure (P) = 757.7 torr/760 torr/atm
= 0.996 atm
We also need to convert the temperature from Celsius (C) to Kelvin (K). The conversion formula is:
Temperature (T) = Celsius + 273.15
= 99.8 C + 273.15
= 373.95 K
Now we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV/RT
where:
P = pressure in atm = 0.996 atm
V = volume in liters (converted from mL) = 253.044 mL/1000 = 0.253044 L
R = ideal gas constant = 0.0821 L·atm/mol·K
T = temperature in Kelvin = 373.95 K
Plugging the values into the equation:
n = (0.996 atm * 0.253044 L) / (0.0821 L·atm/mol·K * 373.95 K)
The units of liters cancel out, leaving us with moles:
n ≈ 0.0082 moles
Finally, we can calculate the molar mass (M) using the given mass of the volatile liquid:
M = mass/n
= (129.225g - 128.632g) / 0.0082 moles
= 73.9 g/mol
Therefore, the molar mass of the volatile liquid is approximately 73.9 g/mol.